A Fault Detection Method for an Automotive Magneto-Rheological Damper

A Fault Detection Method for anAutomotive Magneto-Rheological Damper

Jorge de Jesus Lozoya-Santos ∗ Juan C. Tudon-Martınez ∗

Ruben Morales-Menendez ∗ Ricardo Ramirez-Mendoza ∗

Luis E. Garza-Castanon ∗

∗ Tecnologico de Monterrey, Campus Monterrey, Av. E. Garza Sada2501, 64849, Monterrey N.L., Mexico

(e-mail: {jorge.lozoya, jc.tudon.phd.mty, rmm,ricardo.ramirez,legarza}@itesm.mx)

Abstract: Oil leakage is a common fault in commercial MR damper. The monitoring ofthe suspension transmissibility (magnitude ratio between the sprung and unsprung massaccelerations) allows to detect a fault in a damper. Two proposed approaches: force sensorbased (FTR) and accelerometers sensor based (ATR) allows to online estimate the suspensiontransmissibility. The concept is validated first in a vertical model of a single vehicle cornershowing the utility of the frequency estimation online. Then, using a Receiver OperatingCharacteristic (ROC ) curves, the best threshold is defined. Early results present less than 26 %average in detection error for ATR approach, which is a 9 % better than FTR approach. Intensivevalidation in a full vehicle model in CarSimTM shows the feasibility of practical implementationof this fault detection system. Moreover, its application to competition and sport vehicles canbe possible since it is an online diagnostic method with low computational cost.

Keywords: Smart Materials, Fault detection, Damper, Oil leakage.

1. INTRODUCTION

The real world problem to solve is focused in fast fault de-tection of automotive dampers in extreme applications orsituations, i.e. racing (car, bike), multiple uses of vehicles(off-road to highway changes). The detection in racing ap-plication will allows to always keep an optimum damping,while in vehicles will decrease the risks of loss of stability athigh speeds / maneouvres after off-road suspension opera-tion. Consumers actually expect safety, security, reliability,comfort, etc. from their vehicles as they do from their otherelectronic products, Bertram et al. [2003]. Advanced FaultDetection and Isolation (FDI ) methods are classified intotwo major groups, those which do not assume any form ofmodel information (process history-based methods) andthose which use accurate dynamic process models (model-based methods), Venkatasubramanian et al. [2003]. Basi-cally, the FDI selection depends on the availability of a re-liable model or process measurements under the consideredfaulty modes of operation. Faults in engineering processesbelong to one of the following categories, Gertler [1998]:faults in sensor and actuator called soft faults or, processfaults where some plant parameters change because ofphysical/mechanical problems.

In Automotive Suspension Control Systems (ASCS ),shock absorbers are the key devices. Its faults are gen-erated by oil evaporation or leakages. The loss of oil byevaporation is for the wear of damper under extremeoperations, Figure 1a. Oil leakage is generated due to the

⋆ Thanks to CONACyT, Mexico for the support under the Post-graduate Cooperation Project 2007-2011.

damaged seals in the damper housing, Figure 1b. The sealsare damaged by wear or high temperature operation.

(a) (b)

OilOil

Fig. 1. Typical faults in automotive dampers: (a) oilevaporation in a bike strut, (b) oil leakage by wornseals in automobile strut.

The recent work in Fault Detection and Isolation (FDI )of automotive suspensions shows model based approacheshave prohibitive computation Kim and Lee [2011] Wangand Song [2011] Gaspar et al. [2010] Fischer and Isermann[2004] Vidal et al. [2010]. A methodology proposes theonline register of data from the condition of the dampersusing mems, and then, through a comparison of the currenttransmissibility function with an ideal one, damper faultis inferred using fast fourier transforms for pseudo-Bodes,Ferreira et al. [2009]. However, mems technology increasethe damper technology. Even aforementioned results fortypical shock absorbers, better and practical FDI systemsfor smart materials based damper are needed.

A Magneto-Rheological (MR) damper is a hydraulic devicewhose oil contains metallic micro size particles that changethe rheological properties of the fluid when a magneticfield is applied; this smart material exhibit highly func-

tional and changeable properties, it can be embedded in adamper actuator. An electric current supplied through thedamper coil is used to manipulate the magnetic field. Thevariation of the oil viscosity modifies the damping ratio.Thus, the damping coefficient not only depends on theexcitation frequency, but it also depends on the electriccurrent. This paper is an improved version of the workpresented in Lozoya-Santos et al. [2012] where a processhistory-method of the acceleration of the masses of anautomotive suspension is used to detect a process fault(decreasing of MR force) due to the loss of MR fluidvolume.

The outline of this paper is as follows: Section 2 presentsthe F-class model with a semi-active suspension. Section3 reviews the fundamentals of the original proposal, whilethe Section 4 introduces two new approaches. Results arediscussed in Section 5, and Section 6 concludes the paper.All variables are alphabetically described in Table 1.

Table 1. Variables description

Variable Description

CD, CD(I) Damping factor, CD due to I

cp Passive damping coefficient Ns/m

Fdamping Damping force, N

FMR MR damping force, N

fI Force due to the change of oil viscositycaused by the electric current in N

fr Frequency of the road surface, Hz

fn Resonance frequency of the ms, Hz

f , f(·) Estimated frequency, Hz

I Electric current, A

kq , jq Receding horizon indexes

pi Point in the pseudo-Transmisibility

Q3,Q4 Quartile 75 % and 100 %.

r Frequency ratio, adim

R Sinusoidal amplitude, m

TR, TR Transmissibility and estimated TR, adim

zr Road profile, m

zs, zus Vertical position of the mass ms, mus, m

zs, zus Vertical acceleration of ms, mus, m/s2

z, zdef Piston deflection, m

z, zdef Piston velocity, m/sˆzdef Piston velocity, m/s

z Piston acceleration, m/s2

ϵ Constant that bounds the ρ-value

fµ, fψ Span of algorithm detection

ζ, ζMR Damping ratio, MR damping ratio

|||z|||∞, |||z|||∞ Absolute maximum deflection, velocity

2. F-CLASS VEHICLE MODEL

A F-class car model is used to validate the proposed faultdetection system in CarSimTM , Fig. 2. The suspension isfront and rear independent. The vehicle is equipped withMR dampers at each corner. The parameters of the F-class car are shown in Table 2. They are used for thecomputation of the undamped uncoupled ride frequencyof the suspension fn =

√ktk/(kt + k)ms/2π = 1.71 Hz.

The considered shock absorbers are a commercially smartmaterial based damper ACDelcoTM . This device variesits damping factor CD according to a supplied electriccurrent, I. It is designed to perform a damping ratiovariation with independence of the piston velocity, z,

Fig. 2. F-class car with a semi-active MR damper fromCarSimTM .

Table 2. Parameters of a F-class car inCarSimTM model

Variable Description Value Unit

mbs Sprung mass or body 1823 kg

ms QoV sprung mass 522 kg

mus QoV unsprung mass 50 kg

ks Front spring stiffness 83 N/mm

k Rear spring stiffness 44 N/mm

Front jounce/rebound stops +80/-60 mm

Rear jounce/rebound stops +70/-50 mm

kt Tire stiffness 230 N/mm

Carlson et al. [1995]. The stroke is 60 mm. The maximumabsolute force is 2,500 N with a temperature range of(−40, 150)oC.

The MR damper equation is an extension of the maximumdeflection velocity model, Lozoya-Santos et al. [2010a]and previous work Lozoya-Santos et al. [2010b], basedon the variation of the damping force according to thecharacteristic diagram of a semi-active damper and theapplied electric current, see details, experimental data andidentified parameters in Lozoya-Santos et al. [2012].

3. MONITORING THE DAMPER CONDITION

Based on the QoV model, the transmissibility TR equationgiven by output to input magnitude ratio between thesprung and the unsprung mass accelerations (zs, zus) is,Gillespie [1992]:

TR =

∣∣∣∣ zszus∣∣∣∣ =

√1 + (2ζ r)2

(1 + r2)2 + (2ζ r)2(1)

This function depends on frequency, where the dampingratio ζ is

ζ =1

2

CD√ms ks

(2)

and r is the ratio between the excitation frequency fr andthe natural frequency fn given by

r =frfn

(3)

The spring constant ks has little variation during vehi-cle life, vehicle mass ms changes with vehicle load. Thedamping factor CD, so changes due to aging, wear or mal-function of the damper it may be detectable by computingtransmissibility TR function. A system that measures both,zs and zus, accelerations and computes TR, could monitorthe damper condition.

4. FAULT DETECTION SYSTEM

A change in the semi-active and passive damping coef-ficients could represent a fault in the MR damper. This

Front

s

ms

mus

kt

ks

z

Sprung

mass

Unsprung

mass

MRccp+

Road type B

223.2 m @ 40 km/hr

Car direction

Front of carusz

rz

14

75

mm

1265 mm

589 mm

345mm

3165 mm

4450 mm

345mm500 mm

1870 mm

1605 mm

Wheel centers

Fig. 3. Physical dimensions of a F-class car model with a semi-active MR damper.

work proposes the online computing of the transmissibilitysuspension to detect a fault in the MR damper. Twoapproaches are proposed using the estimated frequency ofthe road surface, fr: (a) online computing of the dampingratio, called FTR approach; and (b) the instantaneousratio |zs/zus| using a receding moving maximum valuealgorithm, called ATR approach. The main difference isthe FTR approach utilizes the force from the MR dampermodel as a virtual force sensor, then the instantaneousdamping ratio is computed. ATR approach computes themaximum value of each vertical acceleration measure-ments in a receding sampling horizon of k samples usingtwo accelerometers sensors.

4.1 Heuristic frequency estimation

By assuming a harmonic motion in the damper piston,Worden and Tomlinson [2001], the instantaneous estima-tion of the frequency is, Lozoya-Santos et al. [2012]:

f =1

2π

|||z|||∞ii−jq

|||z|||∞ii−jq

(4)

where the signals z and z are suspension deflection and ve-locity of the damper piston, the infinite norm ||| · |||∞i−jq

defines the maximum value of the measured variable dur-ing the last jq samples in the ith sample. For more detailssee Lozoya-Santos et al. [2012]. This estimation definesthe horizontal coordinate of the online computed pseudo-Bode. i.e. the frequency of the suspension deflection.

4.2 Force-based pseudo-Transmissibility (FTR)

In a shock absorber the damping factor CD, and thedamping ratio ζ, can be obtained as a function of thedamping force and excitation velocity, as shown in Lozoya-Santos et al. [2012], the estimated FTR is:

FTR(I, zdef ) =

√√√√√√√√1 +

(2ρω [ζMR]√

ks/ms

)2

[1− ρ2

ωms

ks

]2+

(2ρω [ζMR]√

ks/ms

)2 (5)

This estimation defines the vertical coordinate of the on-line computed pseudo-Bode, i.e. the magnitude of the es-timated transmissibility when a model of the MR damperor a force sensor is used.

4.3 Accelerometers-based pseudo-Transmissibility (ATR)

Using the infinite norm of the acceleration of the sprungand unsprung masses (zs and zus) in the last jq samples,

the ATR could be computed. The infinite norm of everymass acceleration is:

|z| ∼ |||z|||∞ii−jq

(6)

Then, the ATR is defined as the ratio:

ATR(zs, zus) =|||zs|||∞i

i−jq

|||zus|||∞ii−jq

(7)

This estimation of ATR(zs, zus) defines the vertical co-ordinate of the online computed pseudo-Bode when themagnitude of the estimated transmissibility is based onlyon the acceleration measurements.

Fig. 4 (top plot) shows the QoV model, and the faultdetection system is shown in bottom plot. The schemesconsists of three key elements: frequency estimator, trans-missibility computation, and observable domain switch.Based on the electric current I, measuring the deflectionof the suspension zdef , and computing the velocity of thesuspension deflection zdef , the frequency of the road zr is

estimated: fdef . Then the TR is computed. If the estimated

frequency fdef is into the observable domain, the detection

system is switched on and a comparison TR > TRthis

done for fault detection; otherwise, the detection systemis switched off.

4.4 Fault implementation and driving conditions

The considered faulty condition is a lost of oil in the MRdamper because an oil leakage. It may be detected by mon-itoring the TR. With less MR fluid, the transmissibilityratio changes (increase), Ferreira et al. [2009].

According to the standard ISO 8606:1995, the classifiedroads in types A to H corresponds to roads in goodconditions (i. e. city runways). The evaluation of thedamper condition was done for (1) no fault present, (2)a lost of 25 % and (3) 50 % of the oil volume. The fault issimulated by modifying the damping force. The vehicle wasrunning in a road type B, under the following conditions:speed of 40 km/hr and a distance of 232 m. The faultabruptly appears at t = 10 s.

4.5 Threshold definition

The expected transmissibility TR function will be used forthreshold definition in the fault detection system. The useddata for defining the threshold were generated with 30stochastic simulations in CarSimTM , all of them include

m

m

zc

kt

def

s

us

I

k

zr

zs

zus

..

..

fMR

ATR

FTR

zdef.

fc^

zszus....

fMR

ATR

FTR

zdef.

fc^

YesNo

TR ^

TR > TR ^No faulty

damper

Faulty

damper

φ φ

µ

Observable

domain

switch

f f

f

φ φ

µ

f f

f

TR ^

Yes

NoTR > TR ^ No faulty

damper

Faulty

damper

zdef

Fig. 4. (Top plot)QoV model and instruments and thealgorithms, and (bottom plot) the fault detectionsystem.

the faulty operating conditions in only one MR damper.The transmissibilities FTR and ATR were online com-puted. Several statistics are considered for each discreteinterval (0.05 Hz ) of frequency. The evaluated thresholdswere TRth

= µ+ σ, TRth= µ+ 2σ, and TRth

= Q3.

Using a Receiver Operating Characteristic (ROC ) curves,the best threshold was defined. These tests were done witha constant value of electric current (1.25 A). The ROCcurves show a relation between opportune detection prob-ability Pd versus false alarms probability Pfa. ROC curvesidentify when the statistical threshold captures the nor-mal operating conditions, Spackman [1989]. The detectionprobability considers only the detection system propertyof indicating an abnormal event without considering thefault isolation.

A False Negative (FN ) is when there is a fault, but it isnot detected; while a False Positive (FP) is when there isno fault, but one is detected. True Positive (TP) is whenthere is a fault, and it is detected; while, True Negative(TN) is when there is no fault and no fault is detected.The total faulty cases (TFC ) is TP + FN, and the totalhealthy cases (THC ) is TN + FP . The probability ofdetection Pd = TP

TFC while the probability of false alarms

Pfa = FPTHC .

5. RESULTS

A first step is to do a validation of the transmissibility com-putation under several currents and oil leakage percentagesin a vertical quarter of vehicle. Three simulations are done,for I = {0, 1.25, 2.5} A which has been selected giventhey are the typical values of on-off control techniques forsemi-active suspensions. The simulations are done for thespecified damper conditions. Each simulation obtains thetransmissibility (FTR) for the constant electric current ata given frequency. The change in the transmissibility it isconsistent with the simulated faults and the thresholds areindependent of the applied current, Figure 5. This holds forthe three faults of the damper at different electric currents.

1.8 2 2.2 2.4 2.6

2

4

6

8

10

12

14

16

18

Estimated frequency from z (Hz)

Tra

nsm

issi

bili

ty u

nd

er

failu

re

0 A,10 % Oilleakage

0 A,Healthy

0 A,50 % Oilleakage

1.8 2 2.2 2.4 2.61

2

3

4

5

6

7

8

2.5 A,50 % Oilleakage

2.5 A,10 % Oilleakage

2.5 A,Healthy

1.8 2 2.2 2.4 2.61

2

3

4

5

6

7

8

9

10

1.25 A,50 % Oilleakage

1.25 A,10 % Oilleakage

1.25 A,Healthy

Fig. 5. Sensitivity of transmissibility when theMR damperis under failure state at three levels of electric appliedcurrent when the estimated frequency of z is used.

Following the recommendation of Boggs et al. [2006], aroad sequence based in a bounce sine sweep with decre-mental displacement amplitude according to the evaluatedfrequency was implemented for different electric currentusing CarSimTM as a pattern road in order to validatethe fault detection approaches. The frequency is estimatedfrom the suspension deflection, zdef , because there is nota frequency road sensor. A comparison of the real and theestimated frequencies of the road zr shows that the sus-pension is a nonlinear system that filters some frequencies;however, a quasi-linear relation has been observed in the

the estimated frequency interval 1 < fr = fdef < 3 Hz.

Figures 6 and 7 shows different thresholds for each ap-proach: FTR and ATR. It is important to note that thetransmissibilities thresholds ATR has a lower resonancefrequency. This can be due to the mechanical motion ratio.

According to the TR function, an observable domain switch(shade area) in Fig. 8 was proposed to improve theefficiency of the detection system. By defining fµ = 1.4Hz and fϕ = 0.35 Hz in the observable domain switch(shown in Fig. 4), the fault detection system is activatedapproximately the 50% of time into the suspension highersensibility range. If the frequency is higher or lower,the probability of right detection decreases because thetransmissibility functions are closer.

Figure 9 shows the ROC curve of different thresholds whena damper of a vehicle model has an oil leakage of 25%(top plot) and 50% (bottom plot), by taking into accountonly the time when the fault detection system is activated.

1.2 1.4 1.6 1.8 2 2.2

2

4

6

8

10

12

14

Estimated frequency [Hz]

Tra

nsm

issib

ility

2 σ, 50 % 2 σ, 25 %

2 σ, 0 %

1 σ, 25 %

1 σ, 0 %

1 σ, 50 %

Fig. 6. Possible transmissibilities (FTR approach) thresh-olds when a vehicle runs in a type B road for threestates of the damper: 0 % no fault, 25 % lost oilvolume and 50 % lost oil volume.

1 1.5 2 2.5 3

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Tra

nsm

issib

ility

Estimated frequency [Hz]

25 % 2 σ

25 % σ

50 % 2 σ

50 % σ

0 % 2 σ

0 % 1 σ

Fig. 7. Possible transmissibilities (ATR approach) thresh-olds when a vehicle runs in a type B road for threestates of the damper: 0 % no fault, 25 % lost oilvolume and 50 % lost oil volume.

0.2 0.8 1.4 2 2.60

1

2

3

4

f [Hz]

I = 1. 25 A

Observable domain

TRThresholdTR

25 % lost oil

volume

Estimated frequency

Tra

nsm

issib

ility

fµφf

def

Fig. 8. Transmissibility vs frequency. Dashed line is for afaulty damper, lower line is for damper without faults.

These plots correspond to ATR approach; however, similarresults were obtained with FTR approach.

Based in these plots, the best detection performance isobtained when the mean value (TR) is used as thresholdline for both approaches. For instance, by using ATR

approach the probability of detection (Pd) of an oil leakageof 50% is up to 85 % with a false alarm rate (Pfa) of 25%;and Pd = 73 % with Pfa = 24 % if the leakage is of 25 %volume. On the other hand, using the thresholds of (1 or2) σ and 3rd Quartile (Q3) had regular performances.

Figure 10 shows the average detection error when the faultdetection system is activated and the MR damper has anoil leakage of 50% of volume, by using the TR thresholdand the ATR approach for computing the transmissibilityfunction. For the 50% lost oil volume, the error of the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Detection Limit

0

0.2

0.6

0.8

1.0

0.4

Detection Limit

Probability of false alarms (pfa)

0

0.2

0.6

0.8

1.0

0.4

TR = Q3Th

TR = TRTh

TR = TR+ σ_

Th

TR = TR+ σTh

TR = Q3Th

TR = TR_

Th

25 %

50 %

Pro

ba

bili

ty o

f d

ete

ctio

n (

pd)

_

_

_

Fig. 9. ROC curve for different thresholds by consideringan oil leakage of 25% (top) and 50% (bottom).

ROC curve was (100 - Pd = 15 %). Figure 10 shows theaverage parameters of the ROC curve. These parametersare better (mean and variance) for ATR compared withFTR approach. In general, the algorithm is slightly betterfor detecting the TP cases than the TN because TP isgreater than TN in both faulty scenarios; while, the casesassociated to bad detections (FN and FP) have similaraverage values.

TP FN TN FP

10

2030

4050

GlobalFaulty

MR damperMR damper

without faults

2025303540

15

Dete

ction

err

or

[%]

Outc

om

es for

the

bin

ary

dete

ction [%

]

Fig. 10. Average parameters of ROC for a F-class vehicleconsidering an oil leakage of 50 % volume.

Figure 11 shows the thresholds for ATR approach; there-fore based on the expected average of transmissibilityATR,if a suspension system has a transmissibility TR > TR, itis almost sure that the MR damper is faulty.

1 1.2 1.4 1.6 1.8 20

0.5

1

Estimated frequency [Hz]

Threshold: 0 % of lost oil volume

Tra

nsm

issi

bil

ity

50 % lost oil volume 25 % lost oil volume

Fig. 11. Selected threshold for the TR vs the estimatedfrequency of a semi-active suspension.

Figure 12 (top plot) shows a detailed example of the onlineestimated ATR and threshold TR transmissibility for atype B road sequence shown in bottom plot. Transmis-sibility ATR was estimated using eqn (7), and thresholdTR was recalled based on the estimation of the frequencyof road zr through the frequency of deflection of thesuspension zdef using eqn. (4).

Considering the detection error as the time steps havingwrongly detected damper condition between the totalnumber of time steps (in percentage), the example inFigure 12 has 10% in error detection during 20 s. Ifthe detection error considers only the time where thedetection system was active, the global detection error was18%. Using the TR as a threshold ATR approach has anaverage 26 % in error detection while FTR has 34 % (andhigher variance) based on more than 30 random tests usingCarSimTM . The ATR outperforms the FTR approach. If adiagnosis about the volume of the lost oil is needed, morethresholds can be integrated for the isolation capability.

Tra

nsm

issib

ility

AT

TR threshold

(lower limit)

Road t

ype

B [cm

]

online estimated TR

Damper free of faults Faulty damper

0

0.5

1

1.5

2R

−2

−1

0

1

2

Time [secs]

0 5 10 15 20

Fig. 12. (Top plot) Transmissibilities (computation andestimation) vs time for a Type B road sequence shownin bottom plot.

6. CONCLUSION

Smart materials such as Magneto Rheological (MR) fluidsexhibit highly functional properties. An MR oil embeddedin a damper is an excellent actuator. However it is a highlynonlinear system; this complex behavior complicates itsanalysis in fault tolerant control systems. Oil leakage is acommon fault in commercial MR damper. The monitoringof the suspension transmissibility (magnitude ratio be-tween the sprung and unsprung mass accelerations) allowsto detect a fault in a damper. Two proposed approaches:force sensor based (FTR) and accelerometers sensor based(ATR) allowed to online estimate the suspension trans-missibility. The concept was validated first in a verticalmodel of a single vehicle corner showing the utility ofthe frequency estimation online. Then, using a ReceiverOperating Characteristic (ROC ) curves, the best thresh-old was defined. Early results presented less than 26 %average in detection error for ATR approach, which is a9 % better than FTR approach. Intensive validation in afull vehicle model in CarSimTM showed the feasibility ofpractical implementation of this fault detection system.Moreover, their application to competition and sport ve-hicles can be possible since it is an online diagnostic withlow computational cost.

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