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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.; Tribikram 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 aset 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 investigated. This includes

the study of Young's modulus value and numerical parameters influence on

damage detection. By merging the Time-Distance Domain Transform with anoptimal 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.



Time-distance domain transformation for Acoustic Emission source

localization in thin metallic plates

Krzysztof Grabowski a, Mateusz Gawronski a, Ireneusz Baran b, Wojciech Spychalski c , Wieslaw J.

Staszewski a

, Tadeusz Uhl a

, Tribikram Kundu d

, Pawel Packo a*

a AGH University of Science and Technology, Krakow, Poland;

bCracow University of Technology, Krakow, Poland;

cWarsaw University of Technology, Warsaw, Poland;

d University of Arizona, Tucson, U.S.A

*Contact author: [email protected]

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 investigated. 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.

Keywords: Acoustic emission, wave propagation, dispersion,time-distance domain transform, source localization

1 Introduction

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].

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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



G(r 0,ω ) = A(r 0,ω )e−iK (ω )r 0 (2)

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

estimation are given in the following section.



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



acoustic source to the sensor (see Figure 2). Figure 1 also shows that the amplitude decreases and the duration of the wave

packet increases when the time offset is increased further above the value corresponding to the actual distance.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45−1.5

−1

−0.5

0

0.5

1

1.5

Distance [m]

A m p l i t u d e

Figure 2. HSU acoustic source signal at the distance of 200 mm after TDDT

When the proposed distance estimation is applied, the localization of AE events is carried out following the triangu-

lation approach described in [6]. The algorithm requires minimum three transducers placed off-line for a 2-D plate setup.

Localization procedures based on triangulation require calculations of differences between arrival times for all relevant

sensors. Then, for a given wave propagation velocity, radii of circles centered at each transducer are calculated and itera-

tively incremented. If a common cross point (or points) for the circles is found, this point is taken as a possible location of

the source. However when the TDDT is used, the distance between the source and the transducer is directly estimated for

each sensor separately. Hence, the entire iterative triangulation procedure can be omitted or used to apply small corrections

only.

To verify the TDDT analytic simulation was performed. Broadband pulse (similar to normalized HSU source) was

used as the source of AE event. For the propagation of the Lamb wave in the materials there was assumed single A0

mode. Material properties of a 2 mm aluminum plate were taken as: Young’s modulus 69 GPa, Poisson’s ratio 0.33 and

the density 2900 kg

m3 . During calculations it was assumed that the propagation distance between the source and the sensor

was equal to 620 mm. The signal was distorted - due to dispersion - as presented in Figure 3a. Furthermore, dispersed

signal was recovered by the TDDT along with time-shifting procedure (in order to find maximum amplitude and shortest

wavepacket after TDDT) as described above. The reconstructed signal in the distance domain is presented in Figure 3b.

Clearly, the signal is compensated and its original shape at the source is preserved. The distance predicted by the TDDT

and time-shifting algorithm is 620 mm and that is equal to the pre-defined distance between the source and the sensor.

The results show that the effectiveness of the applied transformation is excellent, due to the assumed single-mode wave

propagation, which never occurs in practice. Hence, multi-modal signals are investigated in the following section.



0.1 0.2 0.3 0.4 0.5 0.6 0.7

−0.02

0

0.02

Distance [m]

A m p l i t u d e

Dispersion−compensated distance domain signal

0.5 1 1.5 2 2.5

x 10−4

−0.02

0

0.02

Time [s]

A m p l i t u d e

Received signal

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

prone to errors.



0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

m

0.275 0.28 0.285 0.29

0.184

0.186

0.188

0.19

0.192

[m]

[ m ]

SensorPossible AE source area Point representing

localized AE event

Excitation point location

Figure 4. Numerical simulation example of AE source localization. The blue crosses represent sensors, the red area indicates the

estimated location of the AE source. Solid and dashed line circles define areas in which the excitation occurred, their radii are calculated

by the localization algorithm.

The effective localization area changes depending on the threshold value. The results show that the possible AE event

area contains the actual source position. Additionally, source locations calculated for solid and dashed circles crossings

can be used for errors estimation. Localized event in above test case has been placed 4 mm from actual excitation point.

Considering the distances between the source and respective sensors, the error of the method is 6 .6% for the closest

transducer and 3% for the furthest transducer.

4.2 Localization sensitivity study

The final result of the TDDT-based localization procedure depends on dispersion characteristics of investigated material set-

ups, as explained in Sections 2 and 3. Material properties and geometrical features (as thickness) can be easily estimated.

Although, it is relatively easy to determinate material properties and geometrical features for metallic plates, the sensitivity

of the method to an error in spectral characteristics should be evaluated. The problem is important when the method

is implemented for practical industrial applications. It is clear that the applicability of the method will depend on its

localization sensitivity.

The localization sensitivity is investigated using the wave propagation model from Section 3. The AE source was

placed 200mm from the sensor. Wave propagation in the aluminium plate was investigated using three sets of dispersion

curves corresponding to the three sets of properties which varied as explained below.

(1) Young’s modulus reduced by 10% (from 69 GPa to 62 GPa)

(2) Young’s modulus increased by 10% (from 69 GPa to 76 GPa)

(3) mesh resolution increased twice (change in properties due to numerical dispersion)

The (1) and (2) scenarios will be used to determine the localization sensitivity due to errors associated with elastic

properties estimation. It was assumed that the influence of the Poisson ratio on dispersion properties is small [25], and that

the density and thickness can be accurately measured. The (3) scenario aims at investigating the influence of numerical



model properties on localization results. The latter is an important factor when numerical simulations are employed for the

development of new AE localization approaches.

Dispersion curves used in the localization method were calculated using the semi-analytical method described in [24].

Subsequently, the responses were processed following the TDDT-based localization procedure. The results are given in

Fig. 5.

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38−5

−4

−3

−2

−1

0

1

2

Distance [m]

A m p l i t u d e

Correct resultDenser mesh

0.2 0.25 0.3 0.35 0.4

−4

−3

−2

−1

0

1

Distance [m]

A m p l i t u d e

Correct result−10% Young modulus

+10% Young modulus

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.



0 10 20 30 40 50 60 700

5

10

15

[m]

[ m ]

Sensor

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.



0 2 4 6 8 10

0

1

2

3

4

5

6

7

[m]

[ m ]

5 5.5 6

0

0.5

1

[m]

[ m ]

SensorLocalized eventExcitation point

~0.7 m

TDOA method localization result ~1.2 m from original excitation point

Figure 8. AE source localization results for the gas tank

Source localization using an in-built TDOA-based procedure was carried out for comparison. The TDOA-based local-

ization produced an error of 24% (1.2 m). Subsequently, the TDDT-based method was employed. The results show that

for the TDDT-based localization error is approximately 0.7 m which corresponds to approximately 14% error. In the case

of the TDDT method, the results also show that the horizontal accuracy for source positioning is of the order of a few

millimeters; the major discrepancy corresponds to the vertical direction. This clearly shows that thickness variation is an

important parameter in this case.

5 Conclusions

AE source localization technique in plates based on the time-distance transformation technique was proposed and investi-

gated. The method was validated using four test cases, namely an analytic study for a single Lamb wave mode, a numerical

simulation of a plate structure considering multiple modes with no measurement noise, a laboratory test, and a field study

on a small and large scale objects. Moreover, in order to verify the method’s sensitivity to input parameters two studies

were carried out. The first one was devoted to the threshold setting sensitivity and provided additional means to quantify

localization accuracy by using localization rings. The second one was of particular practical importance and examined the

localization sensitivity to material properties used for dispersion curves calculation.

An analytical and numerical studies presented here confirm the accuracy and feasibility of the TDDT-based localization.

The results show that even highly dispersed waveforms can be compensated to the form of the source signal, and can be

effectively used to find the source location. Certain parameters were found to be crucial for AE source localization,

especially in practical applications. The errors were mainly attributed to large sensors’ spacing, variable thickness of the

structure, and material properties used for dispersion curves calculation. The sensitivity of the method was found relatively

low, indicating that slight uncertainty in estimation of material properties of a medium does not destroy the localization

procedure.

In contrast to other localization approaches, the proposed method uses the full AE waveforms. Only the basic geometry

and material parameters of monitored structures are required in this localization procedure. Since these parameters are

relatively easy to evaluate, the method provides a versatile tool for industrial applications. The key aspect of spatial

representation of a signal greatly improves the localization part of the method and improves proper distance calculation

from recorded signals. The results show that the transformation reconstructs the source signal, hence the method can be

used for source evaluation.



It is important to emphasize that this method aims at excluding specific input parameters’ tuning or calibration in order

to localize an AE source. The proposed approach requires only physical parameters which can be estimated accurately. It

should be mentioned that the errors associated with the input data do not influence the localization result significantly as

observed in the sensitivity study. The proposed technique for acoustic emission source localization and analysis creates new

possibilities in the identification process and allows for more accurate damage localization. The dispersion phenomenon is

accounted for and utilized in localization process due to the time-distance mapping.

ACKNOWLEDGMENTS

The work presented in this paper was supported by the Polish National Centre for Research and Development (NCBiR)

under the Grant No. PBS1/A9/10/2012.



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