# Acoustic Emission Source Localization System Using Fiber Bragg Grating Sensors and a Barycentric Coordinate-Based Algorithm

Authors: Dandan Pang; Qingmei Sui; Ming Wang; Yaozhang Sai; Rongyao Sun; Yikang Wang
Journal: Journal of Sensors
 (2018)

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## Abstract

Structures and machines are very susceptible to some barely visible defects; acoustic emission (AE) is an effective technique of detecting defects and examining growth and location of these defects. In this paper, a new method was proposed to predict the position of the AE source. The dynamic strain signal from the AE source was acquired by fiber Bragg grating (FBG) sensors. Complex Morlet wavelet transform was used to extract narrowband signals from AE waves. It was proposed that the barycentric coordinate-based localization algorithm can be used to predict the coordinates of the AE source. The validation tests based on the designed AE detection system were performed on a 500 mm × 500 mm × 2 mm Al-alloy plate. The experimental results show that the proposed method is feasible.


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## Body

## 1. Introduction

The degradation of structural properties is well considered as an enormous threat for security and performance of structures and machines. Structural health monitoring (SHM) utilizes several kinds of sensors attached to or embedded in the monitored structures to detect the appearance, location, and severity of damage. Thus, SHM is imperative for damage detection and structural failure. Various methods have been researched for structural damage detection. These methods can be divided into two categories: model-based and signal-based approaches. The former develops suitable model and analyzes changes that relate to damage in the model; the latter extracts features and establishes a relationship between these features and potential damage [1–3]. Acoustic emission (AE) is one of the effective signal-based means implemented for damage detection [4].AE wave is generated by energy release due to a propagating crack or friction in structures. AE technique is used to detect, locate, and assess defects. To obtain AE wave, some AE sensors have been widely used, such as piezoelectric sensors (PZT) and capacitive AE sensors [5–8]. However, the traditional AE sensors have the disadvantages such as complex structure, weak antielectromagnetic interference, and unsuitability for distributed measurement. At present, fiber Bragg grating (FBG) sensors have been expected as an alternative because of their excellent performance. FBG sensors can be easily embedded in the monitored structure without destructive effect, due to their small size and light weight [9]. Furthermore, FBG sensors are immune to electromagnetic interference [10]. In addition, long-distance distributed measurement can be realized by using FBG sensors [11]. Therefore, some scholars have done several researches on AE source localization using FBG sensors [12, 13]. Yu et al. [14] investigated the effective length of the FBG sensor from the AE source on the composite plate. Yu et al. [15] proposed an AE source identification method based on the algebraic reconstruction algorithm and 3D imaging technique.Recently, an increasing number of AE source localization methods was developed based on the intelligent algorithm [16, 17]. Cheng et al. [18] applied an optimized wavelet neural network to realize AE source location in rotating machinery. Sadegh et al. [19] applied the genetic algorithm and artificial neural networks to extract features of AE signals for monitoring lubrication conditions of a journal bearing. However, in the intelligent algorithms used in those studies, lots of training samples were needed, which leaded to inefficiency and complexity of the localization process. Furthermore, AE source localization in plate-like structures usually requires lots of sensors. In particular, those approaches are usually accurate only within the convex area surrounded by sensors.Based on the previous studies, this paper presented a novel AE detection system based on FBG sensors and a new AE source location method. The AE signal was collected by the FBG sensor which was pasted on the structural surface. Barycentric coordinate-based location method was used to predict positioning. Different from the approaches mentioned above, the proposed method was developed based on only range measurements between sensors, not training samples. The AE source is not required to lie inside the convex area formed by sensors. At last, AE source location experiments were carried out to verify this new designed system and localization algorithm. The results show that it is an efficient and feasible method for AE source localization.


## 2. Theoretical Principle

### 2.1. FBG AE Sensing Principle

The dynamic strain field along the FBG generated by AE wave can be simplified as a time-dependent cosine-Gauss function:(1)εAEt=AAEe−t−t02/a2cos2πλAEz−ωAEt,where AAE is the amplitude of AE wave propagating in a material to be monitored, λAE is the wavelength of AE wave, ωAE is the angular frequency of AE wave, t0 is the arrival time, and a is the duration of AE wave.The alternation of wavelength of FBG is mainly attributed to two factors: one is the modulation of the grating periodΛ (geometric effect), which causes the axial deformation of FBG, and the other is the change of the effective refractive index of FBG n¯eff (photoelastic effect).In consideration of the geometric effect and photoelastic effect, the expression of the effective refractive index of FBG under AE wave is obtained:(2)neff‴z′,t=neff0−Δnsin2πΛ0z−neff032⋅P12−νP11+P12⋅AAEe−t−t02/a2cos2πλAEz′−ωAEt,where z′=z+∫0zεξdξ, P11 and P12 are the photoelastic coefficients of FBG, and v is Poisson’s ratio [20].Based on the mentioned theory above, the spectrum characteristics of FBG under AE waves are simulated and analyzed. When the wavelength of AE waveλAE is 100 mm, the length of grating L is 10 mm and the amplitudes of AE waves AAE are 15 με, 50 με, 100 με, 150 με, and 300 με, respectively. Relation between AAE and reflectivity and wavelength of FBG is shown in Figure 1. The center of FBG shifts towards the longer wavelength as AAE increases when λAE is greater than L. Results also show that there is a good linear relation between central wavelength and AAE. The maximum reflectivity of the FBG reflection spectrum keeps invariant as the change of AAE.Figure 1
Relation betweenAAE and reflectivity and wavelength of FBG.


### 2.2. Complex Morlet Wavelet Transform

The collected AE waves often contain some mutation-shaped peaks or nonstationary components. Morlet wavelet transform is employed to extract the narrowband signal of AE waves.The continuous wavelet transform of AE waveεAEt can be defined as
(3)Wεα,τ=1α∫−∞+∞εAEtϕ¯t−ταdt,where 1/αϕ¯t−τ/α is the complex conjugate of the scaled wavelets 1/αϕt−τ/α obtained by zooming and panning the mother wavelet, α is the zoom factor, and τ is the shift factor.The complex Morlet wavelet can be expressed as [21, 22]
(4)ϕt=1πfbe−t2/fbei2πfct.The Fourier transform of the above function is defined by(5)φω=e−π2fbω−fc2,where fb and fc are the bandwidth factor and center frequency of the complex Morlet wavelet, respectively. The wavelet is a complex exponential function with the shape of a Gaussian window. Hence, the narrowband signal with center frequency fc can be extracted by Morlet wavelet transform. The bandwidth is limited in the range of ωc−ωb/2,ωc−ωb/2. The complex Morlet wavelet filter can be constructed as
(6)WTfb,fc=F−1EAEωφ¯ω,where F−1 denotes the inverse Fourier transform, EAEω and φω are the Fourier transform of εAEt and ϕt, respectively.When considering the propagation distancez, the AE wave εAEz,t can be express as
(7)εAEz,t=e−jn1z−ω1t+e−jn2z−ω2t,where n1 and n2 are the wave numbers. Denote
(8)n1+n22=n0,n1−n22=Δn,ω1+ω22=ω0,ω1−ω22=Δω,φ¯αω=φ¯αω1=φ¯αω2.The module value of AE wave is acquired by the complex Morlet wavelet transform(9)WTz,α,τ=2aφαω01+cos2Δnz−2Δωτ.Whenτ=Δnz/Δω=z/V, the module value is maximum, where V is the group velocity of AE wave. Therefore, the arrival time difference Δt can be obtained by finding the peak values of the module values:
(10)Δt=τ1−τ2.According to the arrival time difference and the distance difference, the wave velocityvAE can be calculated on the monitored material:
(11)vAE=ΔzΔt.


### 2.3. Barycentric Coordinate-Based Location Algorithm

In 1827, the barycentric coordinate was developed to characterize the relative position of a point with respect to other points [23–26]. In the plane, for a point k and other three points l, m, and n, the barycentric coordinate of point k with respect to points l, m, and n can be defined as {akl, akm, and akn} that satisfies
(12)pk=aklpl+akmpm+aknpn,where pk, pl, pm, and pn are the Euclidean coordinates of points k, l, m, and n, respectively.Consider an AE eventk occurs on the plate with three sensors l, m, and n nearby, the AE signal is detected by each of the sensors. Then, the absolute values of the barycentric coordinates akl, akm, and akn can be computed as
(13)akl=SΔkmnSΔlmn,akm=SΔknlSΔlmn,akn=SΔklmSΔlmn,where SΔkmn, SΔknl, SΔklm, and SΔlmn are the signed areas of the corresponding triangles Δkmn, Δknl, Δklm, and Δlmn. These areas can be solved according to
(14)SΔkmn2=−116011110dkm2dkn21dmk20dmn21dnk2dnm20,where dkm, dkn, and dmn are the distance measurements among the AE source k and sensors m and n, respectively.In the plane, three adjacent sensorsl, m, and n are not collinear to avoid the case that SΔlmn=0. Thus, it remains to determine the sign patterns of the barycentric coordinates for obtaining the barycentric coordinates. In addition, note that akl+akm+akn=1. Therefore, given akl, akm, and akn, the problem of determining the sign of the barycentric coordinate is equated with solving the following equation:
(15)σklakl+σkmakm+σknakn=1,where σkl, σkm, and σkn take values of either 1 or −1. The available information to determine the sign patterns should be limited to the pairwise distance measurements between the AE source k and sensors l, m, and n.As shown in Figure2, there are only 7 possible sign patterns (σkl, σkm, and σkn) of the barycentric coordinates (as the pattern (−1, −1, −1) is not a possible solution for (15)). Therefore, the plane can be divided into 7 zones: I (1, 1, 1), II (1, −1, −1), III (1, 1, −1), IV (−1, 1, −1), V (−1, 1, 1), VI (−1, −1, 1), and VII (1, −1, 1). It turns out that sometimes the sign pattern can be uniquely determined from (15), but sometimes this cannot be done. When the sign pattern cannot be uniquely solved from (15), we consider two cases in the following.Figure 2
7 sign patterns for (σkl, σkm, and σkn).In the first case, one ofakl, akm, and akn equals to zero. That is, the AE source k lies on the line aligned with one of the three edges of the triangle formed by the three adjacent sensors, according to (13). Without loss of generality, say akl=0. For this case, we can take σkl=1 (without loss of generality). Then, the other two signs σkm and σkn can be determined according to the following criterion.
(16)σkl,σkm,σkn=1,1,1ifakm,akn≤1,1,1,−1ifakm>1,akm>akn,1,−1,1ifakn>1,akn>akl.In the second case, one ofakl, akm, and akn, saying akl, satisfies akl=1 and akm=akn≠0. For this case, suppose ∠lmn is an acute angle, the sign pattern (σkl, σkm, and σkn) can be determined according to the following criterion.
(17)σkl,σkm,σkn=−1,1,1ifdmk=dln,dnk=dlm,dlk2=2dlm2+2dln2−dmn2,1,1,−1ifdmk2<dlm2+dlk2,1,−1,1ifdmk2>dlm2+dlk2.


## 2.1. FBG AE Sensing Principle

The dynamic strain field along the FBG generated by AE wave can be simplified as a time-dependent cosine-Gauss function:(1)εAEt=AAEe−t−t02/a2cos2πλAEz−ωAEt,where AAE is the amplitude of AE wave propagating in a material to be monitored, λAE is the wavelength of AE wave, ωAE is the angular frequency of AE wave, t0 is the arrival time, and a is the duration of AE wave.The alternation of wavelength of FBG is mainly attributed to two factors: one is the modulation of the grating periodΛ (geometric effect), which causes the axial deformation of FBG, and the other is the change of the effective refractive index of FBG n¯eff (photoelastic effect).In consideration of the geometric effect and photoelastic effect, the expression of the effective refractive index of FBG under AE wave is obtained:(2)neff‴z′,t=neff0−Δnsin2πΛ0z−neff032⋅P12−νP11+P12⋅AAEe−t−t02/a2cos2πλAEz′−ωAEt,where z′=z+∫0zεξdξ, P11 and P12 are the photoelastic coefficients of FBG, and v is Poisson’s ratio [20].Based on the mentioned theory above, the spectrum characteristics of FBG under AE waves are simulated and analyzed. When the wavelength of AE waveλAE is 100 mm, the length of grating L is 10 mm and the amplitudes of AE waves AAE are 15 με, 50 με, 100 με, 150 με, and 300 με, respectively. Relation between AAE and reflectivity and wavelength of FBG is shown in Figure 1. The center of FBG shifts towards the longer wavelength as AAE increases when λAE is greater than L. Results also show that there is a good linear relation between central wavelength and AAE. The maximum reflectivity of the FBG reflection spectrum keeps invariant as the change of AAE.Figure 1
Relation betweenAAE and reflectivity and wavelength of FBG.


## 2.2. Complex Morlet Wavelet Transform

The collected AE waves often contain some mutation-shaped peaks or nonstationary components. Morlet wavelet transform is employed to extract the narrowband signal of AE waves.The continuous wavelet transform of AE waveεAEt can be defined as
(3)Wεα,τ=1α∫−∞+∞εAEtϕ¯t−ταdt,where 1/αϕ¯t−τ/α is the complex conjugate of the scaled wavelets 1/αϕt−τ/α obtained by zooming and panning the mother wavelet, α is the zoom factor, and τ is the shift factor.The complex Morlet wavelet can be expressed as [21, 22]
(4)ϕt=1πfbe−t2/fbei2πfct.The Fourier transform of the above function is defined by(5)φω=e−π2fbω−fc2,where fb and fc are the bandwidth factor and center frequency of the complex Morlet wavelet, respectively. The wavelet is a complex exponential function with the shape of a Gaussian window. Hence, the narrowband signal with center frequency fc can be extracted by Morlet wavelet transform. The bandwidth is limited in the range of ωc−ωb/2,ωc−ωb/2. The complex Morlet wavelet filter can be constructed as
(6)WTfb,fc=F−1EAEωφ¯ω,where F−1 denotes the inverse Fourier transform, EAEω and φω are the Fourier transform of εAEt and ϕt, respectively.When considering the propagation distancez, the AE wave εAEz,t can be express as
(7)εAEz,t=e−jn1z−ω1t+e−jn2z−ω2t,where n1 and n2 are the wave numbers. Denote
(8)n1+n22=n0,n1−n22=Δn,ω1+ω22=ω0,ω1−ω22=Δω,φ¯αω=φ¯αω1=φ¯αω2.The module value of AE wave is acquired by the complex Morlet wavelet transform(9)WTz,α,τ=2aφαω01+cos2Δnz−2Δωτ.Whenτ=Δnz/Δω=z/V, the module value is maximum, where V is the group velocity of AE wave. Therefore, the arrival time difference Δt can be obtained by finding the peak values of the module values:
(10)Δt=τ1−τ2.According to the arrival time difference and the distance difference, the wave velocityvAE can be calculated on the monitored material:
(11)vAE=ΔzΔt.


## 2.3. Barycentric Coordinate-Based Location Algorithm

In 1827, the barycentric coordinate was developed to characterize the relative position of a point with respect to other points [23–26]. In the plane, for a point k and other three points l, m, and n, the barycentric coordinate of point k with respect to points l, m, and n can be defined as {akl, akm, and akn} that satisfies
(12)pk=aklpl+akmpm+aknpn,where pk, pl, pm, and pn are the Euclidean coordinates of points k, l, m, and n, respectively.Consider an AE eventk occurs on the plate with three sensors l, m, and n nearby, the AE signal is detected by each of the sensors. Then, the absolute values of the barycentric coordinates akl, akm, and akn can be computed as
(13)akl=SΔkmnSΔlmn,akm=SΔknlSΔlmn,akn=SΔklmSΔlmn,where SΔkmn, SΔknl, SΔklm, and SΔlmn are the signed areas of the corresponding triangles Δkmn, Δknl, Δklm, and Δlmn. These areas can be solved according to
(14)SΔkmn2=−116011110dkm2dkn21dmk20dmn21dnk2dnm20,where dkm, dkn, and dmn are the distance measurements among the AE source k and sensors m and n, respectively.In the plane, three adjacent sensorsl, m, and n are not collinear to avoid the case that SΔlmn=0. Thus, it remains to determine the sign patterns of the barycentric coordinates for obtaining the barycentric coordinates. In addition, note that akl+akm+akn=1. Therefore, given akl, akm, and akn, the problem of determining the sign of the barycentric coordinate is equated with solving the following equation:
(15)σklakl+σkmakm+σknakn=1,where σkl, σkm, and σkn take values of either 1 or −1. The available information to determine the sign patterns should be limited to the pairwise distance measurements between the AE source k and sensors l, m, and n.As shown in Figure2, there are only 7 possible sign patterns (σkl, σkm, and σkn) of the barycentric coordinates (as the pattern (−1, −1, −1) is not a possible solution for (15)). Therefore, the plane can be divided into 7 zones: I (1, 1, 1), II (1, −1, −1), III (1, 1, −1), IV (−1, 1, −1), V (−1, 1, 1), VI (−1, −1, 1), and VII (1, −1, 1). It turns out that sometimes the sign pattern can be uniquely determined from (15), but sometimes this cannot be done. When the sign pattern cannot be uniquely solved from (15), we consider two cases in the following.Figure 2
7 sign patterns for (σkl, σkm, and σkn).In the first case, one ofakl, akm, and akn equals to zero. That is, the AE source k lies on the line aligned with one of the three edges of the triangle formed by the three adjacent sensors, according to (13). Without loss of generality, say akl=0. For this case, we can take σkl=1 (without loss of generality). Then, the other two signs σkm and σkn can be determined according to the following criterion.
(16)σkl,σkm,σkn=1,1,1ifakm,akn≤1,1,1,−1ifakm>1,akm>akn,1,−1,1ifakn>1,akn>akl.In the second case, one ofakl, akm, and akn, saying akl, satisfies akl=1 and akm=akn≠0. For this case, suppose ∠lmn is an acute angle, the sign pattern (σkl, σkm, and σkn) can be determined according to the following criterion.
(17)σkl,σkm,σkn=−1,1,1ifdmk=dln,dnk=dlm,dlk2=2dlm2+2dln2−dmn2,1,1,−1ifdmk2<dlm2+dlk2,1,−1,1ifdmk2>dlm2+dlk2.


## 3. AE Source Location Experiments

In this work, all the experiments are performed on a 6061 aluminum alloy (Al-alloy) plate. The dimension of the Al-alloy plate is 500 mm × 500 mm × 2 mm. The diagram of the experimental setup is shown in Figure3. The data sampling frequency is set at 2 MHz. Three FBGs are glued on the preselected points of the Al-alloy plate, whose coordinates are A = 100 mm, 200 mm; B = 400 mm, 200 mm; and C = 250 mm, 350 mm. A normalized pencil lead break source (HSU) is used as an AE source.Figure 3
The schematic of the experimental setup.According to Section2.3, the location method based on barycentric coordinates needs the distance measurements among AE source S, point A, point B, and point C. The AE source location geometry is shown in Figure 4. As the distance measurements between three sensors (A, B, and C) are known before the experiment, there are three unknown distances, dSA, dSB, and dSC.Figure 4
The AE source location geometry.Because of the isotropic characteristic of the Al-alloy plate, the AE wave travels at the same speed in all directions. As shown in Figure4, AE wave velocity measurement is carried out at point P. Point P is laid on the line BC and the coordinate is (200, 200). When there is an AE event happens at point P, the AE signals obtained by FBGs (B and C) are shown in Figure 5. The frequency responses of FBG signals are shown in Figure 6. It is known that the AE signal is a broadband signal with a range from 50 kHz to 300 kHz. The Morlet wavelet transform is utilized to extract a narrowband signal with central frequency of 100 kHz. As shown in Figure 7, the module values of the extracted narrowband signals are obtained and the first peaks of the module values are used to compute the time difference Δt between FBGs (B and C). Depending on the time difference and the distance difference measured between PB and PC, the AE wave velocity vAE can be obtained. In order to reduce the measurement error, the same experiment is repeated for 10 times and the results are shown in Figure 8. Based on the above method, the average wave velocity is 2454.1 m/s and the estimation error is less than 0.25%.Figure 5
AE waves detected by FBGB and FBGC.Figure 6
Frequency response of the detected signal.Figure 7
Module values of the extracted narrowband signals.Figure 8
Measurement results of wave velocity.The threshold value method is an effective and simple technique to obtain the arrival times. At the beginning, according to the detected velocityvAE and the arrival time of the AE wave from point P to point C, tPC is calculated as tPC=dPC/vAE. In Figure 7, the absolute module value corresponding to tPC is set as the threshold value. In the next experiment, when the module value of the FBG signal is greater than the preset threshold value, this moment is the arrival time of the AE wave. Based on this process, arrival times (t1, t2, and t3) of AE waves in Figure 4 can be computed.


## 4. Results

Impact is applied on the plate using a steel ball at randomly selected location ofS (400 mm, 300 mm), as shown in Figure 4. The AE waves detected by FBGs are shown in Figure 9. After complex Morlet wavelet transform, the narrowband signals are illustrated in Figure 10. According to the narrowband signals, the arrival times of AE signals are computed. Based on the calculated velocity vAE, the distance measurements among AE source S, point A, point B, and point C are dAB=1502, dAC=1502, dBC=300, dAS=5010, dBS=10010, and dCS=100, respectively. Then, absolute values of the barycentric coordinates aSA, aSB, and aSC are calculated. According to (15), (16), and (17), the sign patterns (σSA, σSB, and σSC) can be deduced as (1, −1, 1); therefore, the position of impact is correctly found at the zone VII. The Euclidean coordinate pS of the AE source S is calculated.Figure 9
AE waves detected by FBGs.Figure 10
Narrowband signals extracted from the detected signals.In each zone, two positions are randomly selected to verify the results of the proposed location method. The location results are presented in Figure11 and Table 1. The results show that the average and maximum location errors that correspond to the horizontal direction are, respectively, 3.6 and 7 mm. The average and maximum location errors that correspond to the vertical direction are 3.9 and 7 mm, respectively. Also, mean square deviation is employed to calculate the AE source location error using the proposed localization method.
(18)E=xp−xa2+yp−ya2,where xp,yp is the Euclidean coordinate of the predicted AE source and xa,ya is the Euclidean coordinate of the actual AE source. The location errors based on the proposed location method are indicated in Figure 12. The results show that the average and maximum location errors are 5.4 and 9.2 mm, respectively.Figure 11
The localization results.Table 1
Location results in 7 zones.
Actual position (mm)
Predicted position (mm)
I
(250, 250)
(253, 254)
(300, 225)
(305, 231)
II
(250, 425)
(246, 423)
(225, 450)
(228, 445)
III
(150, 350)
(152, 348)
(100, 400)
(97, 402)
IV
(25, 175)
(32, 181)
(25, 150)
(20, 143)
V
(200, 125)
(198, 126)
(350, 100)
(352, 102)
VI
(450, 175)
(454, 168)
(475, 175)
(470, 181)
VII
(425, 300)
(423, 298)
(400, 400)
(397, 403)Figure 12
The AE source localization errors.


## 5. Conclusions

In this paper, we have introduced an easy realizable AE source localization method based on the AE waves obtained by FBG sensors. The edge filter method-based FBG interrogation system is used to satisfy the high-speed signal demodulation needs. To realize the barycentric coordinate-based location method, the Morlet wavelet transform is utilized for velocity and arrival time calculation. Then, the AE source location method based on barycentric coordinates is proposed. In the end, impact experiments with random selected positions are carried out for verification of the proposed location method. This research provides an easy and efficient method to safety monitoring of structures.



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*Source: 9053284-2018-08-15.xml*