7/23/2019 Ultrasonics Acoustic emission http://slidepdf.com/reader/full/ultrasonics-acoustic-emission 1/15 Elsevier Editorial System(tm) for Ultrasonics Manuscript Draft Manuscript Number: ULTRAS-D-15-00453 Title: Time-distance domain transformation for Acoustic Emission source localization in thin metallic plates Article Type: Research paper Section/Category: Acoustic emission - ultrasonic domain (A.G. Every) Keywords: Acoustic emission, wave propagation, dispersion,time-distance domain transform, source localization Corresponding Author: Dr. Pawel Packo, Corresponding Author's Institution: AGH Univeristy of Science and Technology First Author: Krzysztof Grabowski, M.Sc.Eng. Order of Authors: Krzysztof Grabowski, M.Sc.Eng.; Mateusz Gawronski, M.Sc.Eng.; Ireneusz Baran, Ph.D.; Wojciech Spychalski, Ph.D.; Wieslaw J Staszewski, Prof.; Tadeusz Uhl, Prof.; T ribikram Kundu, Prof.; Pawel Packo Abstract: Acoustic Emission used in Non-Destructive Testing is focused on analysis of elastic waves propagating in mechanical structures. Then any information carried by generated acoustic waves, further recorded by a set of transducers, allow to determine integrity of these structures. It is clear that material properties and geometry strongly impacts the result. In this paper a method for Acoustic Emission source localisation in thin plates is presented. The approach is based on the Time-Distance Domain Transform, that is a wavenumber-frequency mapping technique for precise event localisation. The major advantage of the technique is dispersion compensation through a phase-shifting of investigated waveforms in order to acquire the most accurate output, allowing for source-sensor distance estimation using a single transducer. The accuracy and robustness of the above process are also i nvestigated. This includes the study of Young's modulus value and numerical parameters influence on damage detection. By merging the Time-Distance Domain Transform with an optimal distance selection technique, an identification-localization algorithm is achieved. The method is investigated analitically, numerically and experimentally. The latter involves both laboratory and large scale industrial tests.
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Structural degradation is a vital problem in operation and maintenance of machines and structures. It is well known that
over time, structural properties of mechanical system deteriorate, possibly leading to failure. Thus evaluation of structural
health - based on scheduled maintenance - not only allows for early damage detection but also prevents costly downtimes or
even catastrophic failures. Various approaches have emerged for structural damage identification for the last few decades.
The majority of these approaches rely in principle on Non-Destructive Testing (NDT) methods for damage detection.
Machines and structures are inspected often periodically. This process - based on disassembling and detailed screening of
components to identify possible failure and material defects - is often ineffective in terms of costs and reliability. Recent
advances in material science, smart sensor technologies, electronics, data processing and rapid miniaturization have led
to the development of new monitoring strategies that fall into the area of Structural Health Monitoring (SHM) [1]. SHM
damage detection methods rely on permanently attached transducers capable of monitoring continuously and globally large
machines and structures. Various NDT and SHM methods are used in practice for inspection. Acoustic Emission (AE) isone of the few well-established NDT techniques that can be implemented for SHM applications.
AE is a passive technique that utilizes elastic waves generated by a sudden energy release in structures. The method
is used not only to detect defects but also to examine growth and location of these defects. Various properties of AE
waveforms are analyzed and characteristic features extracted (e.g. peak-to-peak amplitude, duration or energy) in order to
identify structural damage. Previous research studies and industrial experience gathered for the last few decades show that
this task is not easy due to high complexity and variability of AE waveforms. Therefore a number of signal/data processing
methods have been developed for AE source localization (e.g. [2, 3, 4, 5, 6, 7, 8, 9].
A broad group of AE source identification methods is based on the Time-Difference-of-Arrival (TDOA), where - for
a set of transducers - distances from the source to sensors are estimated from threshold crossing times [10]. The TDOA
methods utilize triangulation procedures [2, 6] and the modal AE source localization approach [11]. It appears that many
techniques based on the TDOA are of limited use, due to strict environmental requirements that must be met to achieve
reliable source identification [6]. AE source localization methods work quite well when relatively simple structures - built
from isotropic materials - are monitored. More sophisticated algorithms are needed for complex structures and complex
materials involved. Examples of such methods can be found in references [3, 8, 12, 13]. Often for complex structures a fewbasic concepts or methods are combined to achieve reliable localization [14]. It is inevitable that this combined approach
is always associated with increased computational costs and limitations. Time-consuming calibration before localization is
one of the limitations [15]. This is mainly due to the fact that calibration is often difficult when distorted waveforms - that
result from dispersion or nonlinear behavior - need to be analyzed. The former is common for plate-like structures, where
wave speeds depend on frequency. The latter can be observed in materials that exhibit additionally nonlinear dependence
of wave speed on frequency. Hence, the most commonly used AE calibration procedure - that provides fixed values of
wave velocity - often lead to erroneous and/or misleading identification and localization results.
A new method for AE source localization is presented in this paper. The method originates from the analysis of wave
propagation in plate-like structures. Complex physical mechanisms of wave propagation in such structures require a non-
classical approach to the problem to avoid errors. The Time-Distance Domain Transformation (TDDT) [16, 17] is used for
AE source localization. The TDDT maps signals from the time domain to the distance domain in order to compensate for
dispersion-related wave propagation phenomena. As a result, many problems related to AE source localization in platescan be overcome.
The paper is organized as follows. Section 2 provides the theory for the TDDT procedure, focusing on the core
equations that are needed to present the new localization method. Subsequently, the AE source localization technique based
on the TDDT approach is presented in Section 3. The following section reports numerical simulation and experimental
results of AE source localization. The former - based on the cuLISA3D approach[18] - investigates wave propagation in
an aluminum plate and involves localization sensitivity studies. The latter illustrates the application of the method using
two examples. Firstly, an aluminum plate excited by an artificial acoustic source is investigated. Then, source localization
results from a large gas tank are demonstrated.
2 Mathematical background for the time-distance domain transformation
The TDDT approach transforms a time signal into the distance domain [16, 17] through a mapping characteristic. Themapping characteristic allows for transforming the original signal, represented in the frequency domain, to the spatial
wavelength domain (or equivalently to the wavenumber domain). Subsequently, the mapped signal can be recovered in the
spatial domain. For elastic wave propagation in plates the mapping characteristic is a dispersion curve for a single Lamb
wave mode. Estimation of dispersion curves for isotropic plates is relatively simple and requires only material properties,
namely the Young’s modulus, Poisson’s ratio, density and thickness of the plate. Because of inherent properties of the
TDDT, it is important to note that explicit wave velocity estimation is not needed in this approach.
The time-to-distance mapping in the TDDT results in the compensation of intrinsic dispersion. The reason for signal
compression is that a single frequency component of the input time signal is phase-shifted, according to the corresponding
dispersion relationship for a given mode, which results in a back-propagation projection. A brief explanation of the
mathematical background - essential for the discussion of the localization procedure - is given in this section. For more
detailed information the reader is referred to references [16] and [17].
When a source signal V a propagates through a plate and is received by a sensor, the relationship between respectiveFourier spectra is given in the form
V (ω ) = E a(ω ) E s(ω )G(r 0,ω )V a(ω ) (1)
where V a(ω ) is the excitation signal, V (ω ) is the received signal, E a(ω ) is the electro-mechanical efficiency coefficient
for the source, E S (ω ) - mechanical-electro efficiency coefficient of the receiving transducer, G(r 0,ω ) - structure transfer
function (output strain at the sensor to input strain at the actuator), r 0 - propagation distance, and ω denotes the angular
frequency. The structure transfer function, G(r 0,ω ), can be further taken as
where A(r 0,ω ) is the amplitude and K (ω ) is the dispersion relationship. Equation (2) indicates that - due to propagation
in the plate - a frequency component is shifted by the phase-delay factor eiK (ω )r 0 . Using Eqs. (1) and (2) yields
V (ω ) = E a(ω ) E s(ω ) A(r 0,ω )e−iK (ω )r 0V a(ω ) = H (ω )V a(ω ) (3)
with H (ω ) = E a(ω ) E s(ω ) A(r 0,ω )e−iK (ω )r 0 denoting the transfer function between the output and the input signal. More-
over E a(ω ) E s(ω ) A(r 0,ω ) can be treated as amplitude of H (ω ). For a narrowband excitation signal V a(ω ), the amplitude
of the signal can be simplified to ’1’ and denoted as
H (ω ) ≈ e−iK (ω )r 0 (4)
Although AE events generate broadband signals, the following discussion does not include the frequency-dependent am-
plitude term. Extension of the following reasoning to the general case is straightforward.
Eqs. (3) and (4), immediately show that the phase of the received signal is changed proportionally to K (ω )r 0. Moreover,
V (ω ) can be presented a complex function dependent on the dispersion curve
V (k ) = V [K (ω )] = e−ikr 0 |k =K (ω )V a(k ) (5)
Furthermore, it is clear that different frequency components of the signal will have different phase offsets due to dispersive
character of Lamb waves in plates. Thus, a mapping through interpolating V (ω ) with the dispersion curve can be written
as
K (ω ) = Ω−1(k ) (6)
V (k ) = V [Ω−1(k )] (7)
where Ω−1(k ) is the inverse of the dispersion curve linearly spaced in the wavenumber domain. Finally, following themapping (Eqs. (6) and (7)) and recorded signal by the sensor, V a (Eq. (3)), the signal in the spatial domain can be written
as
V a(k ) = V a[K (ω )] = eikr 0 |k =K (ω )V (k ) (8)
The inverse spatial Fourier transform of Eq. (8) yields
va( x) =
V (k )eikr 0 eikxdk (9)
which in practice, using inverse fast Fourier transform finally can be simply noted as
va( x) = IFFT [V [Ω−1(k )]] (10)
Eqs. (1) to (10) introduce the procedure of mapping from the time to the distance domain. Following Eq. (5), for
proper distance signal reconstruction the distance between the source and the sensor, r 0, must be known. However, for AE
source this parameter is generally unknown, hence additional signal analysis is necessary. Details on the source distance
3 Acoustic Emission source localization technique based on the Time-Distance Domain Transformation
The TDDT procedure - introduced in Section 2 - is a key element of the proposed AE source localization technique. This
procedure transforms a signal from the time domain to the distance domain. However, when the method is applied for AE
source localization it is important that data acquisition systems used are triggered by AE events, i.e. data acquisition starts
when AE events are generated. The exact timings of these events are unknown and thus need to be estimated.
In typical AE measurements signals are acquired when amplitudes of the waves arriving to the first sensor are abovethe pre-defined threshold level. Then the localization is accomplished when differences of arrival times of these waves are
correlated, assuming that wave propagation velocities are constant. In practice distances from the AE source to sensors
cannot be estimated accurately. It is clear that imprecise distances and dispersion contribute to poor localization results.
However, once dispersion is compensated, original wave packets can be reconstructed and distances traveled by acoustic
waves can be estimated using the TDDT. The procedure requires the following assumption. If the AE source signal
recording starts exactly at the same time as the event occurs, the shortest wave packet of the highest peak-to-peak amplitude
will be acquired after the reconstruction in the distance domain. However, in practice precise time when AE event occurred
is unknown. Hence, the unknown time delay between the AE event and the acquisition of the data can be estimated through
the time-shifting of the acquired data and searching for the most compressed distance-transformed signal.
In the presented case the acquisition started when the amplitude of the signal crossed a pre-defined threshold value.
Performing the TDDT at this moment would produce an error, since the precise time of generation of AE event is unknown.
Therefore, the signal was time-shifted by zero-padding and then the TDDT was employed to calculate the transformed dis-tance domain response. The time offset corresponding to the best dispersion-compensated waveform was used to calculate
the spatial shift of the signal. Therefore after employing the TDDT, the source distance was evaluated using the data only
from a single transducer. Figure 1 presents results from the time shifting procedure applied to a pencil lead break source
(HSU) time signal. The results show that the amplitude and duration of the waveform in the distance are strongly correlated
and the respective maximum and minimum occur for exactly the same time offsets.
Time Shift [µs]0 50 100 150 200 250 300
P e a k - t o - p e a k a m p l i t u d e
[ - ]
×10-3
0
2
0 50 100 150 200 250 300
L e n g t h o f t h e w a v e p a c k e t [ m m ]
0
500
Peak-to-peak amplitude
Length of the wavepacket
Figure 1. Peak-to-peak amplitude and duration of the wave packet in the distance domain (i.e. after the TDDT) plotted against the time
shift applied to the time-domain signal received by a sensor.
Figure 1 shows that the reconstructed distance-domain signal reaches the maximum amplitude and the shortest duration
after approximately 28µ s, as indicated by the vertical red line. After applying the TDDT to this identified offset value the
distance-domain transformed signal was positioned at exactly 200 mm which corresponds to the exact distance from the
Figure 3. Time-distance domain transform algorithm example - the upper waveform represents a signal recorded by a transducer, the
lower waveform is the same signal after compensation by the TDDT shown in the distance domain
4 Results
This section presents three application examples of the TDDT-based AE source localization procedure. Firstly, a numerically-
simulated example is presented. Then, two experimental case studies are investigated. The experimental work involves
laboratory experiments with the normalized HSU source and field measurements from a large gas tank.
4.1 Numerical simulations
Numerical simulations - based on the Local Interaction Simulation Approach (LISA) [19, 20, 21] - were performed to
illustrate the performance of the TDDT-based AE source localization procedure. The work utilized the application of thecuLISA3D software [18, 22]. Wave propagation in a 570×370×2mm aluminum plate was investigated. Material properties
of aluminium were assumed as: the Young’s modulus 69 GPa, the Poisson’s ratio 0.33, and the density 2900 kg/m3. The
plate was meshed using 0.5mm cuboid elements, resulting in four elements through the plate thickness. The time step was
set to ∆t = 0.05 µ s. The excitation was placed in the center of the plate. An identified source signal - which corresponds
to the HSU-Nielsen source [23] - was applied as a prescribed out-of-plane displacement.
Data responses were acquired by three sensors, as shown in Figure 4. Acquired waveforms were processed following
the TDDT-based localization procedure as described in Section 3. All relevant source distances were estimated using
the proposed method, and the circles corresponding to the identified distances from the sensors to possible location of
AE events were drawn. Exact numerical dispersion curves for the model were used instead of analytically calculated
ones [24]. The solid circles indicate source distances estimated with predefined threshold value. In order to verify the
localization sensitivity, dashed circles were drawn. Dahsed lines represent source distances estimated using perturbed
threshold levels in the localization procedure. Namely, threshold levels were increased by 5% before distance calculation.Areas between concentric solid and dashed circles indicate possible source locations. Hence, areas instead of single points
are considered for localization. Such approach increases resistance of system to errors due to inaccuracies present in all
types of approximations. The crossing areas of the three rings indicate the estimated location of the AE source. Localization
quality can be assessed by analyzing rings’ thicknesses, i.e. if the variability (the ring thickness) is high, the localization is
Figure 5. Example of sensitivity studies results for the proposed method. Clearly, the reconstructed waveform depends on applied
dispersion curves. The upper figure presents sensitivity of the method to strictly numerical parameter - mesh density, which changed
alone without proper dispersion curve fitting results in computational errors. The lower part presents method vulnerability to value
change of the Young’s modulus. Differencies in amplitude, phase shift and spatial emplacement are visible.
The results show that changing the value of Young’s modulus does not affect the shape of identified signal in significant
way, although it is also not perfectly preserved. Noticeable variation of peak-to-peak amplitude was observed in accordance
with the discussion presented in Section 3. Those results are in line with ones acquired during correct distance estimation
tests indicating that finding propagation distance of the wave can be achieved by investigating the amplitude of signal
after the TDDT. There is also no significant change in the spatial placement of the output signal, the crucial parameter
for AE source localization. Analysis of output using increased mesh resolution has also proven that during numerical
simulations, the actual numerical dispersion curves must be used in order to acquire most reliable results. Figure 5 presents
that incorrectly matched numerical dispersion curves affect the spatial emplacement and amplitude values of transformed
waveform.
4.3 Experimental validation4.3.1 Normalized HSU source in aluminum plate
For the first test case, an aluminum plate which is the same as in the numerical experiment study, was taken. Dimensions of
the plate were 500×420×2 mm. Material properties for dispersion curves calculation were taken as E = 69 GPa, ν = 0.3and ρ = 2900 kg/m3. A normalized HSU source at two distinct locations were used as an acoustic source. Data acquisition
was synchronized for all sensors i.e. it was triggered by one of the transducers once the signal exceeded the predefined
threshold value at any of the sensors. The plate was instrumented with three resonant surface-bonded Vallen VS150-M
transducers, as shown in Figure 6. AEP4H preamplifiers, an ASIP-2 preprocessor module and an AMSY-6 system were
used for data acquisition, filtering and processing.
After the signals were acquired, the TDDT-based localization procedure was followed to estimate the location of the
acoustic source. The results are given in Figure 6 for the two HSU excitation points used.
Figure 6. HSU source location in an aluminium plate. Plus signs and cross signs indicate the estimated and actual acoustic source
locations.
The results show that good agreement between the estimated (cross signs) and exact (plus signs) source locations was
achieved. Estimated localization produced 4.3%(4 mm)a n d 6.5% (13 mm) errors for the two artificial sources. Localization
discrepancies can be attributed to material properties that were assumed in the calculation procedure. Additional errors
can be related to the threshold crossing procedure in the localization algorithm. Both issues were discussed in previous
sections.
4.3.2 Source localization in a large gas tank
Finally, the proposed AE source localization method was investigated in a large gas tank shown in Figure 7. The steel tank
had the diameter of 20 m and was 16.5 m high. The walls of the tank were made from plates with thickness decreasing
from bottom (10 mm) to the top (8 mm). All together 64 VS150-M type AE resonant sensors with AEP4 preamplifiers were
attached to the outer surface of the tank. The Vallen ASIP-2 preprocessor modules and an AMSY-6 system were used for
data acquisition, filtering and processing. Figure 7 illustrates locations of sensors on the tank. The vertical and horizontalspacing between the sensors was approximately 5 m and 4.8 m, respectively.
Figure 7. Steel gas tank (top) and the sensor network (bottom)
In all experimental tests, a single transducer was used as an acoustic emitter, to model an AE source. The source signal
was a broadband pulse similar to the excitation employed in numerical simulations. Since the thickness of the walls varied
across the height, only sensors adjacent to the artificial source were used for localization. Sensors used for localization are
indicated in Figure 8.
The response signals were acquired with the sampling rate of 3.33 MHz. Altogether 131 072 samples per signal were
recorded. The measurements were 300 samples pre-triggered. The waveforms were acquired synchronously and were
triggered by the sensor that first detected the preset threshold crossing.Once the dispersion curves for the medium were calculated, the acquired data were processed following the TDDT-
based localization procedure described in Section 3. The A0 mode was considered in these calculations. The calculations
of dispersion curves assumed constant thickness of 9 mm of the tank’s plates in the considered area. Nominal material
parameters for steel were taken in these calculations, i.e. the Young’s modulus 180 GPa, the Poisson’s ratio 0.33, and the
density 7850 kg
m3 . The localization results are presented in Figure 8.
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