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Research Article Real Time Cardan Shaft State Estimation of High-Speed Train Based on Ensemble Empirical Mode Decomposition Cai Yi, 1 Jianhui Lin, 1 Tengda Ruan, 1 and Yanping Li 2 1 State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China 2 College of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China Correspondence should be addressed to Cai Yi; [email protected] Received 25 February 2015; Revised 21 May 2015; Accepted 31 May 2015 Academic Editor: Changjun Zheng Copyright © 2015 Cai Yi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Due to the special location and structure of transmission system on high-speed train named CRH5, dynamic unbalance state of the cardan shaſt will pose a threat to the train servicing safety, so effective methods that test the cardan shaſt operating information and estimate the performance state in real time are needed. In this study a useful estimation method based on ensemble empirical mode decomposition (EEMD) is presented. By using this method, time-frequency characteristic of cardan shaſt can be extracted effectively by separating the gearbox vibration acceleration data. Preliminary analysis suggests that the pinions rotating vibration separated from gearbox vibration by EEMD can be used as important assessment basis to estimate cardan shaſt state. With two sets gearbox vibration signals collected from the in-service train at different running speed, the comparative analysis verifies that the proposed method has high effectiveness for cardan-shaſt state estimate. Of course, it needs further research to quantify the performance state of cardan shaſt based on this method. 1. Introduction In order to achieve the dynamic performance of the train running at high speed, the transmission system structure of high-speed train is always used with body hanging or frame hanging method, both of which all need to use a coupling to adapt to the free movement of the wheel [1]. For the high-speed train centralized power, Blue Arrow EMU (Electric Multiple Units) used the six hollow shaſt couplings, and French TGV adopted universal shaſt couplings. For the high-speed distributed power, such as CRH1 (China Railway High-speed 1), CRH2 (China Railway High-speed 2), and CRH3 (China Railway High-speed 3), all used the drum gear coupling [2]. While the transmission system of CRH5 (China Railway High-speed 5) adopted the retractable cross cardan shaſt and the traction motor suspended from the train body to reduce the bogie mass, both of the special structures help to improve vehicle dynamics performance but also improve the reliability and maintainability of the motor. So being different from other high-speed trains, the transmission system of CRH5 consists of the gearbox, cardan shaſt, traction motor, other rotating parts, and supporting component parts, as shown in Figure 1. Motor is the drive device, which is installed at the bottom of the train equipment cabin to lighten the unsprung mass and promote the vehicle dynamic performance. Cardan shaſt disposed longitudinally is connected to the motor and gearbox by cross gimbal at both ends, and its main function is to transfer the drive torque from motor to gearbox [3]. ere is a set of conical gear pair in gearbox, and the pinion is connected with cardan shaſt, so it has the synchronous rotating speed with the cardan shaſt. e big gear is connected with axle bearing, which also have the same rotating speed. e transmission ratio of this transmission system is 2.22. e end of the cardan shaſt is supported by rigid bear- ing and bearing seat; obviously, it is a typical rigid rotor mechanical system. Unbalance of the rotor system is the main inducement in rotating machinery fault [4]. e defect of design structure, the unreasonable and uneven of the materials, assembling error, and the strain of the long-term use all would lead to the unbalance of the rotor system. When the rotor system is in a working state of imbalance, Hindawi Publishing Corporation Shock and Vibration Volume 2015, Article ID 912483, 12 pages http://dx.doi.org/10.1155/2015/912483
13

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Page 1: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Research ArticleReal Time Cardan Shaft State Estimation of High-Speed TrainBased on Ensemble Empirical Mode Decomposition

Cai Yi1 Jianhui Lin1 Tengda Ruan1 and Yanping Li2

1State Key Laboratory of Traction Power Southwest Jiaotong University Chengdu 610031 China2College of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Cai Yi justinyi163com

Received 25 February 2015 Revised 21 May 2015 Accepted 31 May 2015

Academic Editor Changjun Zheng

Copyright copy 2015 Cai Yi et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Due to the special location and structure of transmission system on high-speed train named CRH5 dynamic unbalance state ofthe cardan shaft will pose a threat to the train servicing safety so effective methods that test the cardan shaft operating informationand estimate the performance state in real time are needed In this study a useful estimation method based on ensemble empiricalmode decomposition (EEMD) is presented By using this method time-frequency characteristic of cardan shaft can be extractedeffectively by separating the gearbox vibration acceleration data Preliminary analysis suggests that the pinions rotating vibrationseparated from gearbox vibration by EEMD can be used as important assessment basis to estimate cardan shaft state With twosets gearbox vibration signals collected from the in-service train at different running speed the comparative analysis verifies thatthe proposed method has high effectiveness for cardan-shaft state estimate Of course it needs further research to quantify theperformance state of cardan shaft based on this method

1 Introduction

In order to achieve the dynamic performance of the trainrunning at high speed the transmission system structureof high-speed train is always used with body hanging orframe hanging method both of which all need to use acoupling to adapt to the free movement of the wheel [1] Forthe high-speed train centralized power Blue Arrow EMU(Electric Multiple Units) used the six hollow shaft couplingsand French TGV adopted universal shaft couplings For thehigh-speed distributed power such as CRH1 (China RailwayHigh-speed 1) CRH2 (China Railway High-speed 2) andCRH3 (China Railway High-speed 3) all used the drumgear coupling [2] While the transmission system of CRH5(China Railway High-speed 5) adopted the retractable crosscardan shaft and the traction motor suspended from thetrain body to reduce the bogie mass both of the specialstructures help to improve vehicle dynamics performancebut also improve the reliability and maintainability of themotor So being different from other high-speed trains thetransmission system of CRH5 consists of the gearbox cardan

shaft traction motor other rotating parts and supportingcomponent parts as shown in Figure 1 Motor is the drivedevice which is installed at the bottomof the train equipmentcabin to lighten the unsprung mass and promote the vehicledynamic performance Cardan shaft disposed longitudinallyis connected to themotor and gearbox by cross gimbal at bothends and its main function is to transfer the drive torquefrom motor to gearbox [3] There is a set of conical gear pairin gearbox and the pinion is connected with cardan shaftso it has the synchronous rotating speed with the cardanshaftThe big gear is connected with axle bearing which alsohave the same rotating speed The transmission ratio of thistransmission system is 222

The end of the cardan shaft is supported by rigid bear-ing and bearing seat obviously it is a typical rigid rotormechanical system Unbalance of the rotor system is themain inducement in rotating machinery fault [4] The defectof design structure the unreasonable and uneven of thematerials assembling error and the strain of the long-termuse all would lead to the unbalance of the rotor systemWhen the rotor system is in a working state of imbalance

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 912483 12 pageshttpdxdoiorg1011552015912483

2 Shock and Vibration

Gearbox Cardan shaft Traction motor

Figure 1 CRH5 transmission system

its mass centre will offset from the rotation centre axiswhich will lead to the bend of shaft the internal pressureboosted the abrasion of bearing parts accelerated and evenhorrific accident [5] So the unbalance state estimation in realtime of cardan shaft is an important measure to ensure theoperational safety for CRH5

By considering practical engineering application wefocus on the indirect assessment method based on the gear-box vibration acceleration as there is no effective monitoringto directly access the signal of the cardan shaft state Theends of cardan shaft are connected to the traction motor andgearbox and maybe we could gain the state information ofcardan shaft by one end or two so we must explore andcompare the vibration contribution of cardan shaft to twosides separately

According to the structure of the traction motor there isa spiral spring below the motor to achieve elastic suspensionwhich buffer and weaken most of the vibrational energyof the motor [6 7] The vibration contribution of dynamicimbalance of cardan shaft to the motor is relatively small soit is negligible for the preliminary estimation of the cardanshaft state However it is quite necessary to monitor thevibration of the motor when we want to detect and identifythe fault source of the transmission system accurately On theother hand the vibration contribution of dynamic imbalanceof cardan shaft to the gearbox is quite significant and thegearbox vibration contains more state information of thetransmission system To prove the effect relationship betweengearbox vibration and cardan shaft state we implemented thebench test which is shown in Figure 2

There are three cardan shafts for the bench test and thestate of these shafts respectively is new (represented by thered line) special repairing (represented by the purple line)and close to the use limit (represented by the black line)the bench test result is shown in Figure 2 It can be seenclearly that the higher the speed is the severer the dynamicimbalance state of the cardan shaft becomes and the larger thevibration of gearbox generated by cardan shaft is Obviouslythe gearbox vibration character to some extent reflects thedynamic imbalance state of cardan shaft

For exploring the mapping relationship between thegearbox vibration and the cardan shaft state in practicalapplication we conducted an in-service train monitoringexperiment and picked up the real-time detecting data whilethe train was running at the different speed To avoid chang-ing the structure of the transmission system and bringing

additional risks to the train the sensor was seated on theauxiliary hole where it is in upper of the gearbox to monitorthe vibration acceleration of the gearbox and as shownin Figure 3 it can be seen that an advantage of gearboxacceleration measurement device is their simple structureswhich make it easier to carry out maintenance However thegearbox acceleration waveform contains too much vibrationinformation and the amplitude is affected greatly by the trainrunning speed

In this paper we presented a method to measure cardanshaft on servicing high-speed train named CRH5 using gear-box vibration acceleration signal Frequency family separa-tion mechanism based on ensemble empirical mode decom-position (EEMD) is applied and the target frequency banddetermination based on average instantaneous frequency andthe dominant frequency of Fourier spectrum is proposedwhich can be used as assessment basis for state estimation ofcardan shaftThe novelty of this work is that the data analysisis based on real-world and the signal processing techniqueshould be suitable for on-line application which have morepractical significance

The rest of this paper is organized as follows In Section 2the EMD algorithm is described briefly then EEMD andits superiority of decomposition are explained Section 3presents the method for state estimation The verificationof the proposed method with in-service train monitoringexperiment is shown and discussed in Section 4 Section 5summarizes the conclusion

2 Ensemble Empirical Mode Decomposition

The review and principles of the EMDmethod are conductedbased on [8 9] Thanks to the definition of the interpolatingsplines the extraction of a mean function 119898(119905) is possibleand it can be removed from the initial signal 119909(119905) in orderto obtain

1199091 (119905) = 119909 (119905) minus119898 (119905) (1)The obtained signal1199091(119905) is now examinedwith the aimof

evaluating if it respects the intrinsic mode functions (IMFs)definition Each mode should be independent of the othersIn this way it can smooth uneven signals and each signalcould be decomposed into a number of IMFs [10ndash12] AnIMF represents a simple oscillatory mode compared with thesimple harmonic function If the two previous conditions arenot satisfied the resulting signal 1199091(119905) is not an IMF and thenthe previous stems are repeatedThe sifting process runs untilthe extracted signal respects the two IMF conditions then thefunction obtained represents the first intrinsicmode function1198881(119905) and it is subtracted from the initial signal

1199031 (119905) = 119909 (119905) minus 1198881 (119905) (2)where 1199031(119905) is the residual signal This signal represents theinput for the second IMF calculation by means of the siftingprocess From the above and with the definition any signal119909(119905) can be decomposed as

119909 (119905) =

119899

sum

119894=1119888119894+ 119903119899(119905) (3)

Shock and Vibration 3

1000 1500 2000 2500 30000

05

1

15

2

25

3Gearbox vertical vibration effective value

Cardan shaft rotating speed (rpm)

RMS

(g)

Higher

Worse

Larger

Close to the use limit

Special repairing

New

Gearbox-sensor

Cardan shaft state

Figure 2 Cardan shaft beach test and test result

Sensor position

In-service train

Gearbox vibration time domain variation (5 s)

5

6

4

3

2

1

00 2000 4000 6000 8000 10000

RMS

(g)

Figure 3 In-service train monitoring experiment

The original signal can be expressed as the sum of all theIMFs and the residue The IMFs include different frequencybands ranging from high to low

Empirical mode decomposition is an adaptive time-frequency signal processing method and has been success-fully applied to rotating machinery fault diagnosis and struc-ture health monitoring such as structural damage detection[13] misalignment diagnosis [14] rolling bearing defect

diagnosis [15 16] and rotor fault diagnosis [17 18] Howeverit cannot extract fault features accurately because of theproblem of mode mixing [19] To alleviate mode mixing WuandHuang develop ensemble empiricalmode decomposition(EEMD) to improve EMD [20] By adding noise to theoriginal signal and calculating the means of IMFs repeatedlycompared with EMD EEMD is more accurate and effectivefor rotating machinery fault diagnosis [21ndash23]

4 Shock and Vibration

EEMDrsquos Procedures Are as Follows

(1) Add a random white noise signal 119899119895(119905) to 119909(119905)

119909119895(119905) = 119909 (119905) + 119899

119895(119905) (4)

where 119909119895(119905) is the noise-added signal 119895 = 1 2 3

119872 and119872 is the number of trial(2) Decompose 119909

119895(119905) into a series of intrinsic mode

functions 119888119894119895utilizing EMD as follows

119909119895(119905) =

119873119895

sum

119894=1119888119894119895+ 119903119873119869 (5)

where 119888119894119895denotes the 119894th IMF of the 119895th trial 119903

119873119869

denotes the residue of 119895th trial and 119873119895is the IMFs

number of the 119895th trial(3) If 119895 lt 119872 then repeat steps (1) and (2) and add

different random white noise signals each time(4) Obtain 119868 = min(1198731 1198732 119873119872) and calculate the

ensemble means of corresponding IMFs of the decom-positions as the final result

119888119894=

(sum119872

119895=1 119888119894119895)

119872

(6)

where 119894 = 1 2 3 119868 and 119888119894(119894 = 1 2 3 119868) is the

ensemble mean of corresponding IMF of the decom-positions

For each IMF 119888119894(119905) we can always have its Hilbert trans-

form and 119891(119905) can be expressed by convolution of 119891(119905) and1120587119909 as

119888119894(119905) = 119888

119894(119905) lowast

1120587119905

= int

+infin

minusinfin

119888119894(1199051015840

)

1120587 (119905 minus 119905

1015840)

119889119905

= int

+infin

minusinfin

119888119894(119905 minus 1199051015840

)

11205871199051015840119889119905

(7)

Then the analytical signal of the original signal is obtainedby

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

(8)

119886119894(119905) = radic119888

119894(119905)

2+ 119888119894(119905)

2 (9)

120579119894(119905) = arctan(

119888119894(119905)

119888119894(119905)

) (10)

Instantaneous amplitude and instantaneous phase areexpressed by (9) and (10) In (10) we can have the instanta-neous frequency as

120596119894(119905) =

119889120579119894(119905)

119889 (119905)

(11)

Then

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

= 119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905 (12)

After performing the Hilbert transform to each IMFcomponent the original signal can be expressed as the realpart (Re) in the following form

119909 (119905) =

119899

sum

119894=1119888119894(119905) = Re

119899

sum

119894=1119911119894(119905) = Re

119899

sum

119894=1119886119894(119905) 119890119895120579119894(119905)

= Re119899

sum

119894=1119886119894(119905) 119890119895 int

119879

0 120579119894(119905)119889119905

(13)

Meanwhile for the same signal 119909(119905) the Fourier expan-sion can be expressed as

119909 (119905) =

infin

sum

119894=1119886119894119890119895120579119894119905 (14)

From (13) and (14) it is shown that the Fourier transformis a special form of the HT Amplitude variation and instanta-neous frequency not only improve the effectiveness of decom-position significantly but also make HT based on EEMDsuitable for nonstationary signals The transformations ofamplitude and frequency can be clearly separated by usingeach IMF componentrsquos expansion which mitigates Fouriertransformrsquos limitation in terms of invariable amplitude andfrequency The time-frequency amplitude distribution isdesignated as the signalrsquos Hilbert spectrum 119867(120596 119905) whichcan accurately describe amplitude changes with time andfrequency and further reflect the signalrsquos inherent time-varying characteristics With the Hilbert spectrum definedthe Hilbert marginal spectrum can be shown as

ℎ (120596) = int

+infin

minusinfin

119867(120596 119905) 119889119905

= int

+infin

minusinfin

Re119899

sum

119894=0119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905119889119905

(15)

Obviously the Hilbert spectrum offers a measure ofamplitude distribution from each frequency and time whilethe marginal spectrum gives a measure of the total amplitudedistribution from each frequency

3 The Method for State Estimation

According to the motion transmission principles and struc-ture of the transmission system there are some characteristicfrequencies which have high relativity with cardan shaftworking condition being shaft rotation frequency pinionsrotating frequency big gear rotating frequency and gearmesh frequency All of these characteristic frequencies arecalculated with the real-time train speed V wheel diameter119889 and transmission ratio 119894 According to the structure of thecardan shaft and gearbox the cardan shaft rotation frequencyis approximately equal as pinions rotating frequency andthe big gear rotating frequency approximately equal as train-wheel rotation frequency When the train is running at thespeed 248 kmh all the related parameters and characteristicfrequencies are shown as Table 1

Shock and Vibration 5

Table 1 Related parameter and characteristic frequencies

Index ValueTrain speed (V) 248 kmhTransmission ratio (119894) 222Wheel diameter (119889) 088mNumber of teeth (119899) 27Pinions rotating frequency (119891

119908) 5535Hz

Gear mesh frequency (119891119899) 149435Hz

Big gear rotating frequency (119891119888) 2493Hz

Due to the sensor position locating on the upper ofgearbox where is not effected by the damping device of thebogie the signal collected from gearbox contains a number ofwheel-rail coupling vibration noise In addition the vibrationof the wheel-shaft dynamic imbalance cardan shaft dynamicimbalance and the gear meshing would also be collected bythemeasuring pointWhen the cardan shaftwith the dynamicimbalance or the gears with fatigue crack are meshingboth the amplitude and phase of vibration signal would bemodulated Leaving out the effect of transport function thegearbox vibration signal picked up by sensor can be expressedas follows [24]

119910119894(119905)

=

119872

sum

119898=1119883119898[1+119889

119898] cos [2120587119898119911119891

119908+120601119898+ 119887119898(119905)]

(16)

where 119883119898is the amplitude of the 119898 component 120601

119898is the

phase and 119891119908is the main frequency It is clear that it is

an amplitude modulation and frequency modulation signalEquation (14) can be also expressed as

119910 (119905) =

119872

sum

119898=1119901119898(119905) cos 120579

119898(119905) (17)

In addition according to (7)ndash(10) each IMF whichresulted from EEMD of the gearbox vibration signal can beexpressed as

119888119894(119905) = 119886

119894(119905) cos120601

119894(119905) (18)

As the envelope amplitude function 119886119894(119905) obtained by (9)

is a slowly changing signal compared with the phase function120601119894(119905) obtained by (10) each IMF 119888

119894(119905) which resulted from

EEMD can be the signal which contains the frequency andphase informationTherefore omitting the residual 119903

119899 (3) can

be expressed as

119909 (119905) =

119899

sum

119894=1119886119894(119905) cos120601

119894(119905) (19)

By comparing (17) and (19) we know that gearboxvibration signal consists of a number of frequency familycomponents each of which is an amplitude modulationsignal On the other hand the gearbox vibration signalconsists of a number of IMFs each of which is also exactly

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 4 The IMF1sim6 of one set gearbox vibration acceleration atspeed 248 kmh

a modulation signal The representation forms in (17) and(19) are different However the representative frequencycomponents are consistent Therefore it is viable to applyEEMD method to decompose the gearbox vibration signalinto a number of IMF components in which it contains theinformation of the cardan shaft dynamic unbalance state andother faults in the transmission system

Freely choose one set of gearbox vibration accelerationsignal to analysis by EEMD which is collected from in-service train with a new cardan shaft at 248 kmh runningspeed In this case the noise added has amplitude (standarddeviation) of 030 and the ensemble number of EEMD is 100The total number of IMFs is specified as log 2(119873)minus1 in someoccasions the components may be excessively extracted andin these cases the sum of the latest columns may alreadysatisfy the definition of a trend in this paper the number ofthe IMFs is fixed as 20 by experience Figures 4 and 5 givethe IMFs of this set data and the residue It appears that thefirst IMFs describe high frequency phenomena while the lastone is related to the low frequency components of the signalsthat could have no physical meaning and could be due to thestop criteria set in the sifting process So the IMF1ndashIMF19are the effective frequency components and the IMF20 is theresidual frequency component that the whole signal deductsIMF1ndash19 represented by a trend

Then how to make sure the target family frequency orcorresponding IMFs component which is representative thecharacteristic frequency for example gear mesh frequencyThere are two calculation methods to survey the frequencycharacteristic of every IMF one is the average instantaneousfrequency called AIF by us and the other is the dominantfrequency of Fourier spectrum called DFF by us the calcu-lation results are shown as Figure 6 Due to the complexityand uncertainty of actual monitoring data in real-world two

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

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Page 2: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

2 Shock and Vibration

Gearbox Cardan shaft Traction motor

Figure 1 CRH5 transmission system

its mass centre will offset from the rotation centre axiswhich will lead to the bend of shaft the internal pressureboosted the abrasion of bearing parts accelerated and evenhorrific accident [5] So the unbalance state estimation in realtime of cardan shaft is an important measure to ensure theoperational safety for CRH5

By considering practical engineering application wefocus on the indirect assessment method based on the gear-box vibration acceleration as there is no effective monitoringto directly access the signal of the cardan shaft state Theends of cardan shaft are connected to the traction motor andgearbox and maybe we could gain the state information ofcardan shaft by one end or two so we must explore andcompare the vibration contribution of cardan shaft to twosides separately

According to the structure of the traction motor there isa spiral spring below the motor to achieve elastic suspensionwhich buffer and weaken most of the vibrational energyof the motor [6 7] The vibration contribution of dynamicimbalance of cardan shaft to the motor is relatively small soit is negligible for the preliminary estimation of the cardanshaft state However it is quite necessary to monitor thevibration of the motor when we want to detect and identifythe fault source of the transmission system accurately On theother hand the vibration contribution of dynamic imbalanceof cardan shaft to the gearbox is quite significant and thegearbox vibration contains more state information of thetransmission system To prove the effect relationship betweengearbox vibration and cardan shaft state we implemented thebench test which is shown in Figure 2

There are three cardan shafts for the bench test and thestate of these shafts respectively is new (represented by thered line) special repairing (represented by the purple line)and close to the use limit (represented by the black line)the bench test result is shown in Figure 2 It can be seenclearly that the higher the speed is the severer the dynamicimbalance state of the cardan shaft becomes and the larger thevibration of gearbox generated by cardan shaft is Obviouslythe gearbox vibration character to some extent reflects thedynamic imbalance state of cardan shaft

For exploring the mapping relationship between thegearbox vibration and the cardan shaft state in practicalapplication we conducted an in-service train monitoringexperiment and picked up the real-time detecting data whilethe train was running at the different speed To avoid chang-ing the structure of the transmission system and bringing

additional risks to the train the sensor was seated on theauxiliary hole where it is in upper of the gearbox to monitorthe vibration acceleration of the gearbox and as shownin Figure 3 it can be seen that an advantage of gearboxacceleration measurement device is their simple structureswhich make it easier to carry out maintenance However thegearbox acceleration waveform contains too much vibrationinformation and the amplitude is affected greatly by the trainrunning speed

In this paper we presented a method to measure cardanshaft on servicing high-speed train named CRH5 using gear-box vibration acceleration signal Frequency family separa-tion mechanism based on ensemble empirical mode decom-position (EEMD) is applied and the target frequency banddetermination based on average instantaneous frequency andthe dominant frequency of Fourier spectrum is proposedwhich can be used as assessment basis for state estimation ofcardan shaftThe novelty of this work is that the data analysisis based on real-world and the signal processing techniqueshould be suitable for on-line application which have morepractical significance

The rest of this paper is organized as follows In Section 2the EMD algorithm is described briefly then EEMD andits superiority of decomposition are explained Section 3presents the method for state estimation The verificationof the proposed method with in-service train monitoringexperiment is shown and discussed in Section 4 Section 5summarizes the conclusion

2 Ensemble Empirical Mode Decomposition

The review and principles of the EMDmethod are conductedbased on [8 9] Thanks to the definition of the interpolatingsplines the extraction of a mean function 119898(119905) is possibleand it can be removed from the initial signal 119909(119905) in orderto obtain

1199091 (119905) = 119909 (119905) minus119898 (119905) (1)The obtained signal1199091(119905) is now examinedwith the aimof

evaluating if it respects the intrinsic mode functions (IMFs)definition Each mode should be independent of the othersIn this way it can smooth uneven signals and each signalcould be decomposed into a number of IMFs [10ndash12] AnIMF represents a simple oscillatory mode compared with thesimple harmonic function If the two previous conditions arenot satisfied the resulting signal 1199091(119905) is not an IMF and thenthe previous stems are repeatedThe sifting process runs untilthe extracted signal respects the two IMF conditions then thefunction obtained represents the first intrinsicmode function1198881(119905) and it is subtracted from the initial signal

1199031 (119905) = 119909 (119905) minus 1198881 (119905) (2)where 1199031(119905) is the residual signal This signal represents theinput for the second IMF calculation by means of the siftingprocess From the above and with the definition any signal119909(119905) can be decomposed as

119909 (119905) =

119899

sum

119894=1119888119894+ 119903119899(119905) (3)

Shock and Vibration 3

1000 1500 2000 2500 30000

05

1

15

2

25

3Gearbox vertical vibration effective value

Cardan shaft rotating speed (rpm)

RMS

(g)

Higher

Worse

Larger

Close to the use limit

Special repairing

New

Gearbox-sensor

Cardan shaft state

Figure 2 Cardan shaft beach test and test result

Sensor position

In-service train

Gearbox vibration time domain variation (5 s)

5

6

4

3

2

1

00 2000 4000 6000 8000 10000

RMS

(g)

Figure 3 In-service train monitoring experiment

The original signal can be expressed as the sum of all theIMFs and the residue The IMFs include different frequencybands ranging from high to low

Empirical mode decomposition is an adaptive time-frequency signal processing method and has been success-fully applied to rotating machinery fault diagnosis and struc-ture health monitoring such as structural damage detection[13] misalignment diagnosis [14] rolling bearing defect

diagnosis [15 16] and rotor fault diagnosis [17 18] Howeverit cannot extract fault features accurately because of theproblem of mode mixing [19] To alleviate mode mixing WuandHuang develop ensemble empiricalmode decomposition(EEMD) to improve EMD [20] By adding noise to theoriginal signal and calculating the means of IMFs repeatedlycompared with EMD EEMD is more accurate and effectivefor rotating machinery fault diagnosis [21ndash23]

4 Shock and Vibration

EEMDrsquos Procedures Are as Follows

(1) Add a random white noise signal 119899119895(119905) to 119909(119905)

119909119895(119905) = 119909 (119905) + 119899

119895(119905) (4)

where 119909119895(119905) is the noise-added signal 119895 = 1 2 3

119872 and119872 is the number of trial(2) Decompose 119909

119895(119905) into a series of intrinsic mode

functions 119888119894119895utilizing EMD as follows

119909119895(119905) =

119873119895

sum

119894=1119888119894119895+ 119903119873119869 (5)

where 119888119894119895denotes the 119894th IMF of the 119895th trial 119903

119873119869

denotes the residue of 119895th trial and 119873119895is the IMFs

number of the 119895th trial(3) If 119895 lt 119872 then repeat steps (1) and (2) and add

different random white noise signals each time(4) Obtain 119868 = min(1198731 1198732 119873119872) and calculate the

ensemble means of corresponding IMFs of the decom-positions as the final result

119888119894=

(sum119872

119895=1 119888119894119895)

119872

(6)

where 119894 = 1 2 3 119868 and 119888119894(119894 = 1 2 3 119868) is the

ensemble mean of corresponding IMF of the decom-positions

For each IMF 119888119894(119905) we can always have its Hilbert trans-

form and 119891(119905) can be expressed by convolution of 119891(119905) and1120587119909 as

119888119894(119905) = 119888

119894(119905) lowast

1120587119905

= int

+infin

minusinfin

119888119894(1199051015840

)

1120587 (119905 minus 119905

1015840)

119889119905

= int

+infin

minusinfin

119888119894(119905 minus 1199051015840

)

11205871199051015840119889119905

(7)

Then the analytical signal of the original signal is obtainedby

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

(8)

119886119894(119905) = radic119888

119894(119905)

2+ 119888119894(119905)

2 (9)

120579119894(119905) = arctan(

119888119894(119905)

119888119894(119905)

) (10)

Instantaneous amplitude and instantaneous phase areexpressed by (9) and (10) In (10) we can have the instanta-neous frequency as

120596119894(119905) =

119889120579119894(119905)

119889 (119905)

(11)

Then

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

= 119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905 (12)

After performing the Hilbert transform to each IMFcomponent the original signal can be expressed as the realpart (Re) in the following form

119909 (119905) =

119899

sum

119894=1119888119894(119905) = Re

119899

sum

119894=1119911119894(119905) = Re

119899

sum

119894=1119886119894(119905) 119890119895120579119894(119905)

= Re119899

sum

119894=1119886119894(119905) 119890119895 int

119879

0 120579119894(119905)119889119905

(13)

Meanwhile for the same signal 119909(119905) the Fourier expan-sion can be expressed as

119909 (119905) =

infin

sum

119894=1119886119894119890119895120579119894119905 (14)

From (13) and (14) it is shown that the Fourier transformis a special form of the HT Amplitude variation and instanta-neous frequency not only improve the effectiveness of decom-position significantly but also make HT based on EEMDsuitable for nonstationary signals The transformations ofamplitude and frequency can be clearly separated by usingeach IMF componentrsquos expansion which mitigates Fouriertransformrsquos limitation in terms of invariable amplitude andfrequency The time-frequency amplitude distribution isdesignated as the signalrsquos Hilbert spectrum 119867(120596 119905) whichcan accurately describe amplitude changes with time andfrequency and further reflect the signalrsquos inherent time-varying characteristics With the Hilbert spectrum definedthe Hilbert marginal spectrum can be shown as

ℎ (120596) = int

+infin

minusinfin

119867(120596 119905) 119889119905

= int

+infin

minusinfin

Re119899

sum

119894=0119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905119889119905

(15)

Obviously the Hilbert spectrum offers a measure ofamplitude distribution from each frequency and time whilethe marginal spectrum gives a measure of the total amplitudedistribution from each frequency

3 The Method for State Estimation

According to the motion transmission principles and struc-ture of the transmission system there are some characteristicfrequencies which have high relativity with cardan shaftworking condition being shaft rotation frequency pinionsrotating frequency big gear rotating frequency and gearmesh frequency All of these characteristic frequencies arecalculated with the real-time train speed V wheel diameter119889 and transmission ratio 119894 According to the structure of thecardan shaft and gearbox the cardan shaft rotation frequencyis approximately equal as pinions rotating frequency andthe big gear rotating frequency approximately equal as train-wheel rotation frequency When the train is running at thespeed 248 kmh all the related parameters and characteristicfrequencies are shown as Table 1

Shock and Vibration 5

Table 1 Related parameter and characteristic frequencies

Index ValueTrain speed (V) 248 kmhTransmission ratio (119894) 222Wheel diameter (119889) 088mNumber of teeth (119899) 27Pinions rotating frequency (119891

119908) 5535Hz

Gear mesh frequency (119891119899) 149435Hz

Big gear rotating frequency (119891119888) 2493Hz

Due to the sensor position locating on the upper ofgearbox where is not effected by the damping device of thebogie the signal collected from gearbox contains a number ofwheel-rail coupling vibration noise In addition the vibrationof the wheel-shaft dynamic imbalance cardan shaft dynamicimbalance and the gear meshing would also be collected bythemeasuring pointWhen the cardan shaftwith the dynamicimbalance or the gears with fatigue crack are meshingboth the amplitude and phase of vibration signal would bemodulated Leaving out the effect of transport function thegearbox vibration signal picked up by sensor can be expressedas follows [24]

119910119894(119905)

=

119872

sum

119898=1119883119898[1+119889

119898] cos [2120587119898119911119891

119908+120601119898+ 119887119898(119905)]

(16)

where 119883119898is the amplitude of the 119898 component 120601

119898is the

phase and 119891119908is the main frequency It is clear that it is

an amplitude modulation and frequency modulation signalEquation (14) can be also expressed as

119910 (119905) =

119872

sum

119898=1119901119898(119905) cos 120579

119898(119905) (17)

In addition according to (7)ndash(10) each IMF whichresulted from EEMD of the gearbox vibration signal can beexpressed as

119888119894(119905) = 119886

119894(119905) cos120601

119894(119905) (18)

As the envelope amplitude function 119886119894(119905) obtained by (9)

is a slowly changing signal compared with the phase function120601119894(119905) obtained by (10) each IMF 119888

119894(119905) which resulted from

EEMD can be the signal which contains the frequency andphase informationTherefore omitting the residual 119903

119899 (3) can

be expressed as

119909 (119905) =

119899

sum

119894=1119886119894(119905) cos120601

119894(119905) (19)

By comparing (17) and (19) we know that gearboxvibration signal consists of a number of frequency familycomponents each of which is an amplitude modulationsignal On the other hand the gearbox vibration signalconsists of a number of IMFs each of which is also exactly

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 4 The IMF1sim6 of one set gearbox vibration acceleration atspeed 248 kmh

a modulation signal The representation forms in (17) and(19) are different However the representative frequencycomponents are consistent Therefore it is viable to applyEEMD method to decompose the gearbox vibration signalinto a number of IMF components in which it contains theinformation of the cardan shaft dynamic unbalance state andother faults in the transmission system

Freely choose one set of gearbox vibration accelerationsignal to analysis by EEMD which is collected from in-service train with a new cardan shaft at 248 kmh runningspeed In this case the noise added has amplitude (standarddeviation) of 030 and the ensemble number of EEMD is 100The total number of IMFs is specified as log 2(119873)minus1 in someoccasions the components may be excessively extracted andin these cases the sum of the latest columns may alreadysatisfy the definition of a trend in this paper the number ofthe IMFs is fixed as 20 by experience Figures 4 and 5 givethe IMFs of this set data and the residue It appears that thefirst IMFs describe high frequency phenomena while the lastone is related to the low frequency components of the signalsthat could have no physical meaning and could be due to thestop criteria set in the sifting process So the IMF1ndashIMF19are the effective frequency components and the IMF20 is theresidual frequency component that the whole signal deductsIMF1ndash19 represented by a trend

Then how to make sure the target family frequency orcorresponding IMFs component which is representative thecharacteristic frequency for example gear mesh frequencyThere are two calculation methods to survey the frequencycharacteristic of every IMF one is the average instantaneousfrequency called AIF by us and the other is the dominantfrequency of Fourier spectrum called DFF by us the calcu-lation results are shown as Figure 6 Due to the complexityand uncertainty of actual monitoring data in real-world two

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

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Page 3: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Shock and Vibration 3

1000 1500 2000 2500 30000

05

1

15

2

25

3Gearbox vertical vibration effective value

Cardan shaft rotating speed (rpm)

RMS

(g)

Higher

Worse

Larger

Close to the use limit

Special repairing

New

Gearbox-sensor

Cardan shaft state

Figure 2 Cardan shaft beach test and test result

Sensor position

In-service train

Gearbox vibration time domain variation (5 s)

5

6

4

3

2

1

00 2000 4000 6000 8000 10000

RMS

(g)

Figure 3 In-service train monitoring experiment

The original signal can be expressed as the sum of all theIMFs and the residue The IMFs include different frequencybands ranging from high to low

Empirical mode decomposition is an adaptive time-frequency signal processing method and has been success-fully applied to rotating machinery fault diagnosis and struc-ture health monitoring such as structural damage detection[13] misalignment diagnosis [14] rolling bearing defect

diagnosis [15 16] and rotor fault diagnosis [17 18] Howeverit cannot extract fault features accurately because of theproblem of mode mixing [19] To alleviate mode mixing WuandHuang develop ensemble empiricalmode decomposition(EEMD) to improve EMD [20] By adding noise to theoriginal signal and calculating the means of IMFs repeatedlycompared with EMD EEMD is more accurate and effectivefor rotating machinery fault diagnosis [21ndash23]

4 Shock and Vibration

EEMDrsquos Procedures Are as Follows

(1) Add a random white noise signal 119899119895(119905) to 119909(119905)

119909119895(119905) = 119909 (119905) + 119899

119895(119905) (4)

where 119909119895(119905) is the noise-added signal 119895 = 1 2 3

119872 and119872 is the number of trial(2) Decompose 119909

119895(119905) into a series of intrinsic mode

functions 119888119894119895utilizing EMD as follows

119909119895(119905) =

119873119895

sum

119894=1119888119894119895+ 119903119873119869 (5)

where 119888119894119895denotes the 119894th IMF of the 119895th trial 119903

119873119869

denotes the residue of 119895th trial and 119873119895is the IMFs

number of the 119895th trial(3) If 119895 lt 119872 then repeat steps (1) and (2) and add

different random white noise signals each time(4) Obtain 119868 = min(1198731 1198732 119873119872) and calculate the

ensemble means of corresponding IMFs of the decom-positions as the final result

119888119894=

(sum119872

119895=1 119888119894119895)

119872

(6)

where 119894 = 1 2 3 119868 and 119888119894(119894 = 1 2 3 119868) is the

ensemble mean of corresponding IMF of the decom-positions

For each IMF 119888119894(119905) we can always have its Hilbert trans-

form and 119891(119905) can be expressed by convolution of 119891(119905) and1120587119909 as

119888119894(119905) = 119888

119894(119905) lowast

1120587119905

= int

+infin

minusinfin

119888119894(1199051015840

)

1120587 (119905 minus 119905

1015840)

119889119905

= int

+infin

minusinfin

119888119894(119905 minus 1199051015840

)

11205871199051015840119889119905

(7)

Then the analytical signal of the original signal is obtainedby

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

(8)

119886119894(119905) = radic119888

119894(119905)

2+ 119888119894(119905)

2 (9)

120579119894(119905) = arctan(

119888119894(119905)

119888119894(119905)

) (10)

Instantaneous amplitude and instantaneous phase areexpressed by (9) and (10) In (10) we can have the instanta-neous frequency as

120596119894(119905) =

119889120579119894(119905)

119889 (119905)

(11)

Then

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

= 119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905 (12)

After performing the Hilbert transform to each IMFcomponent the original signal can be expressed as the realpart (Re) in the following form

119909 (119905) =

119899

sum

119894=1119888119894(119905) = Re

119899

sum

119894=1119911119894(119905) = Re

119899

sum

119894=1119886119894(119905) 119890119895120579119894(119905)

= Re119899

sum

119894=1119886119894(119905) 119890119895 int

119879

0 120579119894(119905)119889119905

(13)

Meanwhile for the same signal 119909(119905) the Fourier expan-sion can be expressed as

119909 (119905) =

infin

sum

119894=1119886119894119890119895120579119894119905 (14)

From (13) and (14) it is shown that the Fourier transformis a special form of the HT Amplitude variation and instanta-neous frequency not only improve the effectiveness of decom-position significantly but also make HT based on EEMDsuitable for nonstationary signals The transformations ofamplitude and frequency can be clearly separated by usingeach IMF componentrsquos expansion which mitigates Fouriertransformrsquos limitation in terms of invariable amplitude andfrequency The time-frequency amplitude distribution isdesignated as the signalrsquos Hilbert spectrum 119867(120596 119905) whichcan accurately describe amplitude changes with time andfrequency and further reflect the signalrsquos inherent time-varying characteristics With the Hilbert spectrum definedthe Hilbert marginal spectrum can be shown as

ℎ (120596) = int

+infin

minusinfin

119867(120596 119905) 119889119905

= int

+infin

minusinfin

Re119899

sum

119894=0119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905119889119905

(15)

Obviously the Hilbert spectrum offers a measure ofamplitude distribution from each frequency and time whilethe marginal spectrum gives a measure of the total amplitudedistribution from each frequency

3 The Method for State Estimation

According to the motion transmission principles and struc-ture of the transmission system there are some characteristicfrequencies which have high relativity with cardan shaftworking condition being shaft rotation frequency pinionsrotating frequency big gear rotating frequency and gearmesh frequency All of these characteristic frequencies arecalculated with the real-time train speed V wheel diameter119889 and transmission ratio 119894 According to the structure of thecardan shaft and gearbox the cardan shaft rotation frequencyis approximately equal as pinions rotating frequency andthe big gear rotating frequency approximately equal as train-wheel rotation frequency When the train is running at thespeed 248 kmh all the related parameters and characteristicfrequencies are shown as Table 1

Shock and Vibration 5

Table 1 Related parameter and characteristic frequencies

Index ValueTrain speed (V) 248 kmhTransmission ratio (119894) 222Wheel diameter (119889) 088mNumber of teeth (119899) 27Pinions rotating frequency (119891

119908) 5535Hz

Gear mesh frequency (119891119899) 149435Hz

Big gear rotating frequency (119891119888) 2493Hz

Due to the sensor position locating on the upper ofgearbox where is not effected by the damping device of thebogie the signal collected from gearbox contains a number ofwheel-rail coupling vibration noise In addition the vibrationof the wheel-shaft dynamic imbalance cardan shaft dynamicimbalance and the gear meshing would also be collected bythemeasuring pointWhen the cardan shaftwith the dynamicimbalance or the gears with fatigue crack are meshingboth the amplitude and phase of vibration signal would bemodulated Leaving out the effect of transport function thegearbox vibration signal picked up by sensor can be expressedas follows [24]

119910119894(119905)

=

119872

sum

119898=1119883119898[1+119889

119898] cos [2120587119898119911119891

119908+120601119898+ 119887119898(119905)]

(16)

where 119883119898is the amplitude of the 119898 component 120601

119898is the

phase and 119891119908is the main frequency It is clear that it is

an amplitude modulation and frequency modulation signalEquation (14) can be also expressed as

119910 (119905) =

119872

sum

119898=1119901119898(119905) cos 120579

119898(119905) (17)

In addition according to (7)ndash(10) each IMF whichresulted from EEMD of the gearbox vibration signal can beexpressed as

119888119894(119905) = 119886

119894(119905) cos120601

119894(119905) (18)

As the envelope amplitude function 119886119894(119905) obtained by (9)

is a slowly changing signal compared with the phase function120601119894(119905) obtained by (10) each IMF 119888

119894(119905) which resulted from

EEMD can be the signal which contains the frequency andphase informationTherefore omitting the residual 119903

119899 (3) can

be expressed as

119909 (119905) =

119899

sum

119894=1119886119894(119905) cos120601

119894(119905) (19)

By comparing (17) and (19) we know that gearboxvibration signal consists of a number of frequency familycomponents each of which is an amplitude modulationsignal On the other hand the gearbox vibration signalconsists of a number of IMFs each of which is also exactly

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 4 The IMF1sim6 of one set gearbox vibration acceleration atspeed 248 kmh

a modulation signal The representation forms in (17) and(19) are different However the representative frequencycomponents are consistent Therefore it is viable to applyEEMD method to decompose the gearbox vibration signalinto a number of IMF components in which it contains theinformation of the cardan shaft dynamic unbalance state andother faults in the transmission system

Freely choose one set of gearbox vibration accelerationsignal to analysis by EEMD which is collected from in-service train with a new cardan shaft at 248 kmh runningspeed In this case the noise added has amplitude (standarddeviation) of 030 and the ensemble number of EEMD is 100The total number of IMFs is specified as log 2(119873)minus1 in someoccasions the components may be excessively extracted andin these cases the sum of the latest columns may alreadysatisfy the definition of a trend in this paper the number ofthe IMFs is fixed as 20 by experience Figures 4 and 5 givethe IMFs of this set data and the residue It appears that thefirst IMFs describe high frequency phenomena while the lastone is related to the low frequency components of the signalsthat could have no physical meaning and could be due to thestop criteria set in the sifting process So the IMF1ndashIMF19are the effective frequency components and the IMF20 is theresidual frequency component that the whole signal deductsIMF1ndash19 represented by a trend

Then how to make sure the target family frequency orcorresponding IMFs component which is representative thecharacteristic frequency for example gear mesh frequencyThere are two calculation methods to survey the frequencycharacteristic of every IMF one is the average instantaneousfrequency called AIF by us and the other is the dominantfrequency of Fourier spectrum called DFF by us the calcu-lation results are shown as Figure 6 Due to the complexityand uncertainty of actual monitoring data in real-world two

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

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Page 4: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

4 Shock and Vibration

EEMDrsquos Procedures Are as Follows

(1) Add a random white noise signal 119899119895(119905) to 119909(119905)

119909119895(119905) = 119909 (119905) + 119899

119895(119905) (4)

where 119909119895(119905) is the noise-added signal 119895 = 1 2 3

119872 and119872 is the number of trial(2) Decompose 119909

119895(119905) into a series of intrinsic mode

functions 119888119894119895utilizing EMD as follows

119909119895(119905) =

119873119895

sum

119894=1119888119894119895+ 119903119873119869 (5)

where 119888119894119895denotes the 119894th IMF of the 119895th trial 119903

119873119869

denotes the residue of 119895th trial and 119873119895is the IMFs

number of the 119895th trial(3) If 119895 lt 119872 then repeat steps (1) and (2) and add

different random white noise signals each time(4) Obtain 119868 = min(1198731 1198732 119873119872) and calculate the

ensemble means of corresponding IMFs of the decom-positions as the final result

119888119894=

(sum119872

119895=1 119888119894119895)

119872

(6)

where 119894 = 1 2 3 119868 and 119888119894(119894 = 1 2 3 119868) is the

ensemble mean of corresponding IMF of the decom-positions

For each IMF 119888119894(119905) we can always have its Hilbert trans-

form and 119891(119905) can be expressed by convolution of 119891(119905) and1120587119909 as

119888119894(119905) = 119888

119894(119905) lowast

1120587119905

= int

+infin

minusinfin

119888119894(1199051015840

)

1120587 (119905 minus 119905

1015840)

119889119905

= int

+infin

minusinfin

119888119894(119905 minus 1199051015840

)

11205871199051015840119889119905

(7)

Then the analytical signal of the original signal is obtainedby

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

(8)

119886119894(119905) = radic119888

119894(119905)

2+ 119888119894(119905)

2 (9)

120579119894(119905) = arctan(

119888119894(119905)

119888119894(119905)

) (10)

Instantaneous amplitude and instantaneous phase areexpressed by (9) and (10) In (10) we can have the instanta-neous frequency as

120596119894(119905) =

119889120579119894(119905)

119889 (119905)

(11)

Then

119911119894(119905) = 119888

119894(119905) + 119894119888

119894(119905) = 119886

119894(119905) 119890119895120579119894(119905)

= 119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905 (12)

After performing the Hilbert transform to each IMFcomponent the original signal can be expressed as the realpart (Re) in the following form

119909 (119905) =

119899

sum

119894=1119888119894(119905) = Re

119899

sum

119894=1119911119894(119905) = Re

119899

sum

119894=1119886119894(119905) 119890119895120579119894(119905)

= Re119899

sum

119894=1119886119894(119905) 119890119895 int

119879

0 120579119894(119905)119889119905

(13)

Meanwhile for the same signal 119909(119905) the Fourier expan-sion can be expressed as

119909 (119905) =

infin

sum

119894=1119886119894119890119895120579119894119905 (14)

From (13) and (14) it is shown that the Fourier transformis a special form of the HT Amplitude variation and instanta-neous frequency not only improve the effectiveness of decom-position significantly but also make HT based on EEMDsuitable for nonstationary signals The transformations ofamplitude and frequency can be clearly separated by usingeach IMF componentrsquos expansion which mitigates Fouriertransformrsquos limitation in terms of invariable amplitude andfrequency The time-frequency amplitude distribution isdesignated as the signalrsquos Hilbert spectrum 119867(120596 119905) whichcan accurately describe amplitude changes with time andfrequency and further reflect the signalrsquos inherent time-varying characteristics With the Hilbert spectrum definedthe Hilbert marginal spectrum can be shown as

ℎ (120596) = int

+infin

minusinfin

119867(120596 119905) 119889119905

= int

+infin

minusinfin

Re119899

sum

119894=0119886119894(119905) 119890119895 int

119879

0 120596119894(119905)119889119905119889119905

(15)

Obviously the Hilbert spectrum offers a measure ofamplitude distribution from each frequency and time whilethe marginal spectrum gives a measure of the total amplitudedistribution from each frequency

3 The Method for State Estimation

According to the motion transmission principles and struc-ture of the transmission system there are some characteristicfrequencies which have high relativity with cardan shaftworking condition being shaft rotation frequency pinionsrotating frequency big gear rotating frequency and gearmesh frequency All of these characteristic frequencies arecalculated with the real-time train speed V wheel diameter119889 and transmission ratio 119894 According to the structure of thecardan shaft and gearbox the cardan shaft rotation frequencyis approximately equal as pinions rotating frequency andthe big gear rotating frequency approximately equal as train-wheel rotation frequency When the train is running at thespeed 248 kmh all the related parameters and characteristicfrequencies are shown as Table 1

Shock and Vibration 5

Table 1 Related parameter and characteristic frequencies

Index ValueTrain speed (V) 248 kmhTransmission ratio (119894) 222Wheel diameter (119889) 088mNumber of teeth (119899) 27Pinions rotating frequency (119891

119908) 5535Hz

Gear mesh frequency (119891119899) 149435Hz

Big gear rotating frequency (119891119888) 2493Hz

Due to the sensor position locating on the upper ofgearbox where is not effected by the damping device of thebogie the signal collected from gearbox contains a number ofwheel-rail coupling vibration noise In addition the vibrationof the wheel-shaft dynamic imbalance cardan shaft dynamicimbalance and the gear meshing would also be collected bythemeasuring pointWhen the cardan shaftwith the dynamicimbalance or the gears with fatigue crack are meshingboth the amplitude and phase of vibration signal would bemodulated Leaving out the effect of transport function thegearbox vibration signal picked up by sensor can be expressedas follows [24]

119910119894(119905)

=

119872

sum

119898=1119883119898[1+119889

119898] cos [2120587119898119911119891

119908+120601119898+ 119887119898(119905)]

(16)

where 119883119898is the amplitude of the 119898 component 120601

119898is the

phase and 119891119908is the main frequency It is clear that it is

an amplitude modulation and frequency modulation signalEquation (14) can be also expressed as

119910 (119905) =

119872

sum

119898=1119901119898(119905) cos 120579

119898(119905) (17)

In addition according to (7)ndash(10) each IMF whichresulted from EEMD of the gearbox vibration signal can beexpressed as

119888119894(119905) = 119886

119894(119905) cos120601

119894(119905) (18)

As the envelope amplitude function 119886119894(119905) obtained by (9)

is a slowly changing signal compared with the phase function120601119894(119905) obtained by (10) each IMF 119888

119894(119905) which resulted from

EEMD can be the signal which contains the frequency andphase informationTherefore omitting the residual 119903

119899 (3) can

be expressed as

119909 (119905) =

119899

sum

119894=1119886119894(119905) cos120601

119894(119905) (19)

By comparing (17) and (19) we know that gearboxvibration signal consists of a number of frequency familycomponents each of which is an amplitude modulationsignal On the other hand the gearbox vibration signalconsists of a number of IMFs each of which is also exactly

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 4 The IMF1sim6 of one set gearbox vibration acceleration atspeed 248 kmh

a modulation signal The representation forms in (17) and(19) are different However the representative frequencycomponents are consistent Therefore it is viable to applyEEMD method to decompose the gearbox vibration signalinto a number of IMF components in which it contains theinformation of the cardan shaft dynamic unbalance state andother faults in the transmission system

Freely choose one set of gearbox vibration accelerationsignal to analysis by EEMD which is collected from in-service train with a new cardan shaft at 248 kmh runningspeed In this case the noise added has amplitude (standarddeviation) of 030 and the ensemble number of EEMD is 100The total number of IMFs is specified as log 2(119873)minus1 in someoccasions the components may be excessively extracted andin these cases the sum of the latest columns may alreadysatisfy the definition of a trend in this paper the number ofthe IMFs is fixed as 20 by experience Figures 4 and 5 givethe IMFs of this set data and the residue It appears that thefirst IMFs describe high frequency phenomena while the lastone is related to the low frequency components of the signalsthat could have no physical meaning and could be due to thestop criteria set in the sifting process So the IMF1ndashIMF19are the effective frequency components and the IMF20 is theresidual frequency component that the whole signal deductsIMF1ndash19 represented by a trend

Then how to make sure the target family frequency orcorresponding IMFs component which is representative thecharacteristic frequency for example gear mesh frequencyThere are two calculation methods to survey the frequencycharacteristic of every IMF one is the average instantaneousfrequency called AIF by us and the other is the dominantfrequency of Fourier spectrum called DFF by us the calcu-lation results are shown as Figure 6 Due to the complexityand uncertainty of actual monitoring data in real-world two

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

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Page 5: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Shock and Vibration 5

Table 1 Related parameter and characteristic frequencies

Index ValueTrain speed (V) 248 kmhTransmission ratio (119894) 222Wheel diameter (119889) 088mNumber of teeth (119899) 27Pinions rotating frequency (119891

119908) 5535Hz

Gear mesh frequency (119891119899) 149435Hz

Big gear rotating frequency (119891119888) 2493Hz

Due to the sensor position locating on the upper ofgearbox where is not effected by the damping device of thebogie the signal collected from gearbox contains a number ofwheel-rail coupling vibration noise In addition the vibrationof the wheel-shaft dynamic imbalance cardan shaft dynamicimbalance and the gear meshing would also be collected bythemeasuring pointWhen the cardan shaftwith the dynamicimbalance or the gears with fatigue crack are meshingboth the amplitude and phase of vibration signal would bemodulated Leaving out the effect of transport function thegearbox vibration signal picked up by sensor can be expressedas follows [24]

119910119894(119905)

=

119872

sum

119898=1119883119898[1+119889

119898] cos [2120587119898119911119891

119908+120601119898+ 119887119898(119905)]

(16)

where 119883119898is the amplitude of the 119898 component 120601

119898is the

phase and 119891119908is the main frequency It is clear that it is

an amplitude modulation and frequency modulation signalEquation (14) can be also expressed as

119910 (119905) =

119872

sum

119898=1119901119898(119905) cos 120579

119898(119905) (17)

In addition according to (7)ndash(10) each IMF whichresulted from EEMD of the gearbox vibration signal can beexpressed as

119888119894(119905) = 119886

119894(119905) cos120601

119894(119905) (18)

As the envelope amplitude function 119886119894(119905) obtained by (9)

is a slowly changing signal compared with the phase function120601119894(119905) obtained by (10) each IMF 119888

119894(119905) which resulted from

EEMD can be the signal which contains the frequency andphase informationTherefore omitting the residual 119903

119899 (3) can

be expressed as

119909 (119905) =

119899

sum

119894=1119886119894(119905) cos120601

119894(119905) (19)

By comparing (17) and (19) we know that gearboxvibration signal consists of a number of frequency familycomponents each of which is an amplitude modulationsignal On the other hand the gearbox vibration signalconsists of a number of IMFs each of which is also exactly

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 4 The IMF1sim6 of one set gearbox vibration acceleration atspeed 248 kmh

a modulation signal The representation forms in (17) and(19) are different However the representative frequencycomponents are consistent Therefore it is viable to applyEEMD method to decompose the gearbox vibration signalinto a number of IMF components in which it contains theinformation of the cardan shaft dynamic unbalance state andother faults in the transmission system

Freely choose one set of gearbox vibration accelerationsignal to analysis by EEMD which is collected from in-service train with a new cardan shaft at 248 kmh runningspeed In this case the noise added has amplitude (standarddeviation) of 030 and the ensemble number of EEMD is 100The total number of IMFs is specified as log 2(119873)minus1 in someoccasions the components may be excessively extracted andin these cases the sum of the latest columns may alreadysatisfy the definition of a trend in this paper the number ofthe IMFs is fixed as 20 by experience Figures 4 and 5 givethe IMFs of this set data and the residue It appears that thefirst IMFs describe high frequency phenomena while the lastone is related to the low frequency components of the signalsthat could have no physical meaning and could be due to thestop criteria set in the sifting process So the IMF1ndashIMF19are the effective frequency components and the IMF20 is theresidual frequency component that the whole signal deductsIMF1ndash19 represented by a trend

Then how to make sure the target family frequency orcorresponding IMFs component which is representative thecharacteristic frequency for example gear mesh frequencyThere are two calculation methods to survey the frequencycharacteristic of every IMF one is the average instantaneousfrequency called AIF by us and the other is the dominantfrequency of Fourier spectrum called DFF by us the calcu-lation results are shown as Figure 6 Due to the complexityand uncertainty of actual monitoring data in real-world two

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

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Page 6: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

6 Shock and Vibration

Table 2 The frequency characteristic of the IMFs shown in Figures 10 and 11

IMF 1 2 3 4 5 6 7 8 9 10 11 12AIFHz 4845 3222 1549 877 5599 3963 2093 571 423 268 153 72DFFHz 4662 2998 1499 8607 5996 4247 1664 533 396 273 149 6

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 5 The IMF7sim12 of one set gearbox vibration acceleration atspeed 248 kmh

calculation methods all are used to ensure the credibility andreliability of the vibration signals and method

From Figure 6 we see that the average instantaneousfrequencies of the IMFs are basically consistent with thedominant frequencies of Fourier spectrum of every IMFexcept IMF1 Moreover when the train running speed is248 kmh the meshing frequency of the transmission systemis 149435Hz the pinions rotating frequency is 5535Hz andthe big gear rotating frequency is 2493Hz therefore IMF3 isidentified as the corresponding intrinsicmode function of thegear mesh vibration IMF8 as the corresponding one of thepinions rotating vibration and IMF10 as the correspondingone of the big gear rotating vibrationThe details of the time-frequencies characteristic of the original signal IMF3 IMF8and IMF10 are shown as Figures 7 and 8 which verifies thatalthough there always is great amount noise in the collecteddata of the gearbox vibration in high-speed train from real-world it is very efficient to separate the vibration frequencyfamily of the signal by using EEMD there is a high fit degreebetween the original signal and gear mesh vibration andpinions rotating vibration curve is the centre line of theirchanging curve the big gear rotating vibration value is almostconstant when the train running speed remains stable whichchanges over the speed of the train So for the contributionamount of the measuring point vibration the gear meshvibration and the pinions rotating vibration are bigger thanthe big gear rotating vibration on the other hand based onthis measuring point seated on the auxiliary hole in upper of

the gearbox the gear mesh vibration and the pinions rotatingvibration are more likely to be used to assess the work state ofcardan shaft

IMF3 and IMF8 are exerted toHilbert transform to get theHilbert instantaneous frequency spectrum and the spectrumfeatures can be surveyed from Figure 9 By comparing thefrequency characteristic of the gear meshing vibration andthe pinions rotation the energy of the pinions rotatingvibration is more stable and constant when the high-speedtrain keeps a certain speed and the stability of the charac-teristic value is the key property for evaluating benchmarkaccording to the structure of the transmission system thecardan shaft rotation frequency is approximately equal aspinions rotating frequency so the vibration contributionof cardan shaft rotation to the measuring point is passedthrough the pinions rotation From what has been discussedabove we fully believe that the frequency characteristic of thepinions rotating vibration separated by EEMD can be usedas important assessment basis to estimate the work state ofcardan shaft in operating high-speed train

4 Verification with In-Service TrainMonitoring Experiment

There is another set of gearbox vibration signals collectedfrom the same in-service high-speed train at the samepathway and of course they are also at the same speed248 kmh however in this transmission system the cardanshaft is close to the use limit whose unbalance value is3552 gcm (the unbalance value of the criterion old cardanshaft is 384 gcm) and the new cardan shaft was used totake the place of this old one Figures 10 and 11 describethe EEMD calculated result of the gearbox vibration whosecardan shaft is close to the use limit To catch the target familyfrequency we calculate the AIF and DFF of IMF1ndash12 shownin Table 2 Obviously IMF3 is identified as the correspondingintrinsic mode function of the gear mesh vibration IMF8as the pinions rotating vibration and IMF10 as the big gearrotating vibration which are coincident with the new cardanshaft

Comparing the IMF3 IMF8 and IMF10 of gearboxvibration whose cardan shaft is close to the use limit withthe new cardan shaft respectively is to demonstrate theeffectiveness of the conclusion in Section 3 and the resultsare shown in Figures 12ndash14 The gear mesh vibrations of theold cardan shaft and new one are basically identical describedby Figure 11 and there is no regularity for the big gearrotating vibrations shown in Figure 13 it follows that whenthe work state of cardan shaft is worse there is almost noobvious change for gear mesh vibration and big gear rotatingvibration However to the cardan shaft close to use limit andthe new one the pinions rotating vibration shows apparently

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Shock and Vibration 7

1 2 3 4 5 6 7 8 9 10 11 120

1000

2000

3000

4000

5000

6000

IMFs

AIF average instantaneous frequencyDFF dominant frequency of Fourier spectrum

0 500 1000 1500 2000 2500 30000

01020304

0 05 1 15 2 25 3 35 4

05 IMF3

0 05 1 15 2 25 3 35 405

10

Time (s)

Freq

uenc

y (H

z)

Instantaneous frequency

minus5

f (Hz)

X 1484Y 02764IM

F3

ampl

itude

IMFAIFDFF

1 2 3 4 5 6 7 8 9 10 11 12

5321

5938

3105

2969

1521

1485

880

870

594

594

412

396

195

168

58

55

338

40

278

28

137

11

73

6

Freq

uenc

y(H

z)

times103

Figure 6 The frequency characteristic of the IMFs shown in Figures 4 and 5

0 1000 2000 3000 4000 5000 6000

02468

10

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

minus10

Figure 7 The time domain characteristic of the original signalIMF3 IMF8 and IMF10

sensitive characteristics in a measure apparently the pinionsrotating vibration amplitude of the cardan shaft close tothe use limit is much larger than the new one described inFigure 12

All of above seems that the method and analysis conclu-sion are effective and correct described in Section 3 whenthe two kinds of work state of cardan shaft are servicing inthe train running speed at 248 kmh if the cardan shaft isin another different kind of operating mode would we getthe same conclusion There are two sets gearbox vibrationsignals collected from the same in-service high-speed train

4400 4450 4500 4550 4600 4650 4700 4750 4800 4850 4900

0

2

4

6

8

Original signalIMF3 (gear mesh vibration)IMF8 (pinions rotating vibration)IMF10 (big gear rotating vibration)

minus2

minus4

minus6

minus8

Figure 8 The detailed drawing of Figure 7

and the same two state cardan shafts but at different pathwaywith the above signals however one set data is collectedat the train running speed 199 kmh when the old cardanshaft which is close to the use limit has not been replacedby the new one and the other set is collected at the trainrunning speed 201 kmh which has the new cardan shaftAll the related parameters and characteristic frequencies ofthe two sets signals are shown as Table 3 and the IMFs aredescribed by Figures 15ndash18

In general when the train is running at a lower speedthe vibration response amplitude of the measuring point issmaller where 1198791 = 1198792 the time period of periodic shockwaves presented in IMF7 respectively in Figures 16 and 18

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

8 Shock and Vibration

0 05 1 15 2 25 3 35 40

200

400

600

800

1000

1200

1400

1600

1800

1495

554

Figure 9 The instantaneous frequency spectrum of IMF3 andIMF8

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

02

IMF6

minus2

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

Figure 10 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

is consistent which may be caused by the wheel-rail impacthowever its further verification needs to take into accountthe rail state and line information Calculating the AIF andDFF of IMF 1ndash12 is shown in Table 4 and comparing withTable 3 obviously IMF4 is identified as the correspondingintrinsic mode function of the gear mesh vibration and IMF9as the pinions rotating vibration which are different from thesituation when the train running speed is 248 kmh

Figure 19 is the comparison of gear mesh and pinionsrotating vibration at two kinds of cardan shaft states one isclose to the use limit at train running speed 199 kmh andthe other is a new one at train running speed 201 kmhThis figure shows that the time domain amplitude of gearmesh vibration is almost overlapping although the state ofone cardan shaft has been close to the use limit when theyare servicing at the same speed however there is significant

0 05 1 15 2 25 3 35 4 45

02

IMF7

0 05 1 15 2 25 3 35 4 45

02

IMF8

IMF9

IMF1

0IM

F11

002

IMF1

2

minus02

minus2

minus2

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

005

minus05

0 05 1 15 2 25 3 35 4 45

Figure 11 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

2

4

6

8

10

IMF3

Gear mesh vibration whose cardan shaft is close

Gear mesh vibration whose cardan shaft is new

minus2

minus4

minus6

minus8

minus10

to the use limit

Figure 12 The compare of gear mesh vibration of two states ofcardan shaft at speed 248 kmh

Table 3 Related parameter and characteristic frequencies

Index Value (the oldshaft)

Value (the newshaft)

Train speed V 199 kmh 201 kmhPinions rotatingfrequency 119891

119908

444Hz 448Hz

Gear mesh frequency 119891119899

11988Hz 12107HzBig gear rotatingfrequency 119891

119888

200Hz 202Hz

difference between the pinions rotating vibration of the newcardan shaft and the old one As a result the method and

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Shock and Vibration 9

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF8

Pinions rotating vibration whose cardan shaft is close

Pinions rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 13 The compare of pinions rotating vibration of two statesof cardan shaft at speed 248 kmh

0 05 1 15 2 25 3 35 4 45

0

05

1

15

IMF1

0

Big gear rotating vibration whose cardan shaft is close

Big gear rotating vibration whose cardan shaft is new

minus05

minus1

minus15

to the use limit

Figure 14 The compare of big gear rotating vibration of two statesof cardan shaft at speed 248 kmh

analysis conclusion are also effective and correct described inSection 3 when the train is running at another speed level

Figure 20 is another comparison of gearmesh andpinionsrotating vibration at two kinds of cardan shaft state onewhich is close to the use limit is at train running speed199 kmh but the new one is at train running speed 250 kmhBecause the running speed of the new cardan shaft is higherthe time domain amplitude of the gear mesh vibration isalso bigger than the old one which has been verified in theprevious section however although the speed rating of thenew cardan shaft is higher than the old one the pinionsrotating vibration amplitude of the new one is smaller thanthe old one on the contrary So this is more persuasiveto verify that the pinions rotating vibration characteristics

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

05

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus5

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

05

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 15 The IMF1sim6 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

X 1858Y 04088

T1

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

005

IMF1

2

minus05

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

Figure 16 The IMF7sim12 of gearbox vibration whose cardan shaftclose to use limit at speed 199 kmh

separated by EEMD can be used as important assessmentbasis to estimate the work state of cardan shaft in operatinghigh-speed train

5 Conclusion

In this paper a state estimation method and technique basedon EEMD are proposed to identify the work state of cardanshaft in case of in in-service high-speed train The vibrationsignals of running transmission system with the cardan shaft

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

10 Shock and Vibration

0 05 1 15 2 25 3 35 4 45

05

IMF1

0 05 1 15 2 25 3 35 4 45

02

IMF2

IMF3

IMF4

IMF5

01

IMF6

minus1

minus2

minus5

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

02

minus2

0 05 1 15 2 25 3 35 4 45

Figure 17 The IMF1sim6 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

0 05 1 15 2 25 3 35 4 45

01

IMF7

0 05 1 15 2 25 3 35 4 45

01

IMF8

IMF9

IMF1

0IM

F11

01

IMF1

2

minus1

minus1

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

01

minus1

0 05 1 15 2 25 3 35 4 45

X 1858

T2

Y minus0007847

Figure 18 The IMF7sim12 of gearbox vibration whose cardan shaft isnew at speed 201 kmh

at the bad work state including unbalance and damageare decomposed by EEMD method and the target familyfrequency of the associated IMF is determined by usingAIF and DFF calculation method The calculation resultshows that the frequency characteristic of the pinions rotationcan be used as important assessment basis to estimate thework state of cardan shaft in operating high-speed trainand the effectiveness and usefulness of the proposed methodare verified by two sets gearbox vibration signals collected

Table 4The frequency characteristic of the IMFs shown in Figures15ndash18

IMF Old shaft New shaftAIFHz DFFHz AIFHz DFFHz

1 4694 52524 5235 536022 2340 23779 3524 311133 1664 14013 2416 230224 1170 11971 1208 123295 5987 6019 6242 75556 2222 2969 5236 52357 1722 176 2013 23028 896 682 9311 10559 431 422 4489 45310 192 188 3356 36811 87 99 2144 23712 42 55 911 93

05 1 15 2 25 3 35 4

0

1

2

IMF4

05 1 15 2 25 3 35 4

0

05

1

IMF9

Gear mesh vibration

Pinions rotating vibration

minus05

minus1

minus1

minus2

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 201 kmh

Figure 19The compare of gear mesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus201 kmh

from the in-service train at different speed According to theresearch work in this paper it also can be concluded that

(1) EEMD can decompose the signal into a numberof IMF each IMF contains the sampling frequencyand also changes with the signal itself So EEMDmethod has shown great recognition performances inanalyzing the nonlinear and nonstationary signals inpractical application of real-world

(2) considering that there is no effective monitoring todirectly access the signal of the cardan shaft state itis feasible to estimate the work state of cardan shaftfrom gearbox vibration by EEMDmethod where thesensor is seated on the auxiliary hole in upper of thegearbox

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 11: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

Shock and Vibration 11

0 05 1 15 2 25 3 35 4 45

0

5

IMF4

and

3

0 05 1 15 2 25 3 35 4 45

0

05

1

IMF

9 an

d 8

Pinions rotating vibration

Gear mesh vibration

minus05

minus5

minus1

Vibration whose cardan shaft is close to use limitat speed 199kmhVibration whose cardan shaft is new at speed 250 kmh

Figure 20The compare of gearmesh vibration and pinions rotatingvibration under two states of cardan shaft at speed 199 kmh versus250 kmh

(3) of course there still is toomuch further researchworkto do to format the quantitative estimation methodfor quantifying the work state of cardan shaft in in-service high-speed train on line

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research work described in this paper is supported byTraction Power State Key Laboratory and Changzhou South-west Jiaotong University Rail Transit Institute China underthe Project nos 2013J008-A BY201003 and CE20110062

References

[1] Y Luo and D C Jin ldquoResearch on the rules of suspensionparameters to driving equipment suspended in bogie framesrdquoChina Railway Science vol 28 no 4 pp 36ndash42 2007

[2] W S Zhong S N Xiao and H Y Liu ldquoDevelopment andexperimental research of light frame used in high speed powerbogierdquo Journal of the China Railway Society vol 20 no 2 pp32ndash37 1998

[3] Y M Su and Z Y Wang ldquoResearch on rotating machineryfault mechanismrdquo Journal of Yangtze University (Natural ScienceEdition) vol 4 no 4 pp 55ndash59 2009

[4] G A Yang Rotor Balancing Practical Techniques China Petro-chemical Press Beijing China 2012

[5] S Leva A P Morando and P Colombaioni ldquoDynamic analysisof a high-speed trainrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 1 pp 107ndash119 2008

[6] Y Liu X J Zhang YM Zhang and Y GMeng ldquoExperimentalresearch on reasonable lubricant quantity for transmission gearsused in high-speed trainrdquo Science China Technological Sciencesvol 55 no 12 pp 3455ndash3461 2012

[7] H J Zhang Y Yao Y Luo and Q-Z Li ldquoAnalysis on technicalcharacteristics of CRH5 cardan drive systemrdquo Journal of theChina Railway Society vol 31 no 2 pp 115ndash119 2009

[8] N E Huang Z Shen and S R Long ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 pp 903ndash995 1998

[9] R Ricci P Pennacchi M Lombardi and C Mirabile ldquoFailurediagnostics of a spiral bevel gearbox using EMD and HHTrdquoin Proceedings of the ISMA2010 Including USD pp 2965ndash29792010

[10] N E Huang and S S P Shen Hilbert-Huang Transform and ItsApplication vol 4 World Scientific Singapore 2005

[11] N E Huang Z Shen S R Long and N E Huang ldquoTheempirical mode decomposition and the Hilbert spectrum fornonlinear and non-stationary time series analysisrdquo Proceedingsof the Royal Society of London Series A vol 454 pp 903ndash9951998

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A vol 454 no 1971 pp 903ndash995 1998

[13] H Li X Deng and H Dai ldquoStructural damage detectionusing the combination method of EMD and wavelet analysisrdquoMechanical Systems and Signal Processing vol 21 no 1 pp 298ndash306 2007

[14] T Y Wu and Y L Chung ldquoMisalignment diagnosis of rotatingmachinery through vibration analysis via the hybrid EEMDandEMD approachrdquo Smart Materials and Structures vol 18 ArticleID 095004 pp 1ndash13 2009

[15] Q Du and S Yang ldquoImprovement of the EMD method andapplications in defect diagnosis of ball bearingsrdquo MeasurementScience and Technology vol 17 no 8 pp 2355ndash2361 2006

[16] Z K Peng P W Tse and F L Chu ldquoA comparison studyof improved Hilbert-Huang transform and wavelet transformapplication to fault diagnosis for rolling bearingrdquo MechanicalSystems and Signal Processing vol 19 no 5 pp 974ndash988 2005

[17] Q Gao C Duan H Fan and QMeng ldquoRotatingmachine faultdiagnosis using empirical mode decompositionrdquo MechanicalSystems and Signal Processing vol 22 no 5 pp 1072ndash1081 2008

[18] X Zhao T H Patel and M J Zuo ldquoMultivariate EMD and fullspectrum based condition monitoring for rotating machineryrdquoMechanical Systems and Signal Processing vol 27 no 1 pp 712ndash728 2012

[19] H Li L Yang and D Huang ldquoThe study of the intermittencytest filtering character of Hilbert-HUAng transformrdquo Mathe-matics and Computers in Simulation vol 70 no 1 pp 22ndash322005

[20] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[21] YG Lei Z JHe andYY Zi ldquoApplication of the EEMDmethodto rotor fault diagnosis of rotating machineryrdquo MechanicalSystems and Signal Processing vol 23 no 4 pp 1327ndash1338 2009

[22] Y G Lei and M J Zuo ldquoFault diagnosis of rotating machineryusing an improved HHT based on EEMD and sensitive IMFsrdquoMeasurement Science and Technology vol 20 no 12 Article ID125701 2009

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 12: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

12 Shock and Vibration

[23] J Zhang R Yan R XGao andZ Feng ldquoPerformance enhance-ment of ensemble empirical mode decompositionrdquoMechanicalSystems and Signal Processing vol 24 no 7 pp 2104ndash2123 2010

[24] J S Cheng D J Yu J S Tang and Y Yang ldquoApplication offrequency family separation method based upon EMD andlocal Hilbert energy spectrum method to gear fault diagnosisrdquoMechanism and Machine Theory vol 43 no 6 pp 712ndash7232008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 13: Research Article Real Time Cardan Shaft State Estimation of …downloads.hindawi.com/journals/sv/2015/912483.pdf ·  · 2015-11-23Based on Ensemble Empirical Mode Decomposition ...

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of