7th Asia-Pacific Workshop on Structural Health Monitoring

November 12-15, 2018 Hong Kong SAR, P.R. China

Creative Commons CC-BY-NC licence https://creativecommons.org/licenses/by/4.0/

Damage Localization in Thin-Walled WGF/Epoxy Composite Laminates

Using Guided Wave by Probabilistic Imaging Algorithm

B. Yang 1*, C. J. Hu 1, Y. Wu 2, Y. X. Xiang 1, F. -Z. Xuan 1

1 School of Mechanical and Power Engineering, East China University of Science and Technology,

Shanghai, China;

Email: y20170063@mail.ecust.edu.cn 2 School of Civil and Architectural Engineering, Nanchang Institute of Technology, Nanchang, Jiangxi,

China.

Keywords: Structural Health Monitoring; Composite Laminates; Piezoelectric Sensors and

Transducers; Damage Localization Algorithm

ABSTRACT

We proposed a probabilistic imaging algorithm to capture the damage location information in woven

glass fabric reinforced epoxy (WGF/Epoxy) composite laminates. The stacking sequence of the

composite laminates is [90o/0o]4. Lamb wave propagation theory, thickness effect and slowness profile

phenomenon were investigated before the damage localization process were performed. Four

piezoelectric wafers were used for exciting and acquiring Lamb wave signals with pitch-catch

configuration. Scattered signals were calculated according to the difference between healthy and

damaged signals. Relying on temporal information of the scattered signal, the algorithm was

constructed to highlight the most possible damage location. Finite element and experimental works

were carried out to verify the feasibility of the algorithm. Results showed that the developed approach

has satisfied application potential in finding the through hole position in WGF/Epoxy laminates.

1. Introduction

Fiber reinforced plastic (FRP) thin-walled composite plates could offer very high strength and stiffness

with low weight[1]. Nowadays, they have been widely employed in several engineering fields[2].

However, thin-walled composite structures are highly susceptible to damages, which are generally

caused by external loads such as impact and fatigue during the service lifespan[3-4]. Effectual damage

evaluation and continuous health monitoring are conducive to reliable service of thin-walled

composite structures. Therefore, the structural failure risk can accordingly be minimized[5]. Structural

health monitoring (SHM) offers a truly viable solution for full-coverage continuous monitoring of

composite structures[6-7]. Lamb wave is a kind of ultrasonic guided wave that propagates inside

thin-walled plates and shallow shells. This wave in thin-walled composite plates can be generated

using conformable piezoelectric (PZT) actuators/sensors. Lamb-wave-based SHM methodologies have

* Corresponding author. E-mail address: yangbin@ecust.edu.cn. Tel./fax: +86-021-64251623.

Mor

e in

fo a

bout

this

art

icle

: ht

tp://

ww

w.n

dt.n

et/?

id=

2403

6

been widely reported to efficiently detecting various types of damages such as fatigue damages[8],

delamination[9], and the barely visible impact damages[10] in composites. The dimension of these

damages is generally comparable to the wavelength and the inspection system consumed very low

energy with only a few transducers. These advantages have lead Lamb-wave-based SHM a desirable

candidate for early and meticulous damage detection in thin-walled composite materials[10-11].

One of the important factors in SHM systems is the amount of data that need to be analyzed[7, 10, 11].

The accuracy and precision of a Lamb-wave-based damage localization approach are highly subject to

the processing and interpretation of signals. The captured Lamb wave signals usually carry

comprehensive information as the interference is exist in the wave propagation path. To enable the

development and optimization of quantitative damage detection and characterization methodologies,

Martin et al.[12] claimed that the understanding of Lamb waves at where the damages frequently initiate

is an essential requirement. Understanding the scattering of guided waves at defects or structural

features such as fastener holes is especially necessary. In the literature, different methods have been

developed to investigate the guided wave propagation behaviors in isotropic and composite laminates.

These references have covered a wide range of signal processing and defect localization algorithms.

For example, the previous work have covered beam forming[11], neural networks[13-15],

time-reversal-based techniques[16-17], and functional delay and sum[18-19] methods to provide a graphical

representation of damage. These methods have been verified in various structures through the

theoretical, numerical and experimental approaches, respectively. Based on time-of-flight analysis of

scatter waves, we developed an ellipse imaging algorithm in MATLAB[20]. The Lamb wave

propagating behavior was studied, and the probability densities of damage occurrence are calculated in

WGF/epoxy composite laminates. Moreover, to further improve the accuracy of the ellipse imaging

algorithm, Chen et al.[21] proposed a distance coefficient that includes information between sparse

array configuration and defect to select higher signal-to-noise ratio data. Gorgin et al.[22] developed a

damage size characterization algorithm for active SHM using the A0 mode of Lamb waves. The

method was experimentally verified, and it could provide the detailed information about the damage,

such as its location, size, shape and severity in an aluminum plate. Wandowski et al.[23] compared the

damage localization results performed for four sensing network configurations, and their damage

localization algorithm verification experiment was carried out in an aluminum alloy plate. Yu et al.[24]

presented the guided wave field analysis methods for detection and quantification of crack. The

method was then verified experimentally in an aluminum plate. Furthermore, they presented an

analytical investigation of the interaction among piezoelectric wafer active sensor, guided waves, and

host structure[25]. Nazarko et al.[26] investigated the use of artificially deteriorated signals of Lamb

waves in training the detection system for the early damage detection, and an experimental verification

was carried out using an aluminum and composite plates, respectively.

The complex wave propagating mechanism in thin-walled composite laminates makes the damage

imaging process very complicated. More efforts should be made to diagnose the damages in laminated

composites with high accuracy. A paramount challenge in analytically or numerically modeling guided

waves in the anisotropic medium is the comprehensive inclusion of all possible sources of signals[5].

These signals may from both the medium itself and the damages. Moreover, the interpretation on the

modulation mechanism of damage on guided waves is another challenge. Aimed at a systematic

comprehension of guided waves natures in a composites medium, this study is dedicated to develop a

probabilistic imaging algorithm to obtain the damage information in WGF/Epoxy composite laminates.

The Lamb wave characteristics in the composite laminates with various thicknesses were investigated.

Relying on temporal information of the scattered signal, a diagnostic image was constructed to

highlight the through hole location in composite laminates in the finite element (FE) simulations and

experimental measurements. The study provides improved physical insight into the scattering

phenomena at through holes in thin-walled composite laminates, which is essential to develop,

validate and optimize guided wave damage detection and characterization techniques.

2. Fundamental theory

2.1. Governing equations of Lamb wave in composite laminates

x

y

z

Figure 1. Coordinate system of the plate.

Considering the propagation of guided waves along a multilayered panel that with infinite length and

total thickness of h, the panel consists of N layers and we assume each layer was bonded together

perfectly. In the coordinate system in Fig. 1, the x axis coincides with the length, and the z axis is

parallel to the composite panel thickness direction. The consideration of waves implies plane strain

conditions in the xz plane, and negligible variation of the non-vanishing strains and stresses in the

y-direction. Hence, the linear stress-strain constitutive relations for a composite ply are deducted from

the three-dimensional constitutive equations, and the governing equations are given by[27]: [ ]C = (1)

where, σ={σx, σz, σxz}T and ε={εx, εz, εxz}T are the extended stress and strain vectors; σx, σz, and σxz are

the normal and shear stresses. The ply stiffness matrix is:

11 13

13 33

55

0

[ ] 0

0 0

C C

C C C

C

=

(2)

The stress equilibrium equations in the x and z direction provide the equations that describe the motion

of the straight-crested wave.

2.2. Thickness effect on Lamb waves in composite laminates

Lamb waves are highly dispersive and multimodal. The multiple modes propagate simultaneously at

different velocities through all excitation frequencies[28, 29]. The dispersive phenomenon of the Lamb

wave is mainly determined by the center frequency in a special structure. The dispersive phenomenon

would make the signal processing procedure a challenging task if the frequency is not selected

appropriately. This would further affect the damage localization accuracy in composite laminates.

Generally, the velocity of Lamb wave in a plate is dependent on the excited frequency, medium

thickness and the propagation mode. Basically, Lamb wave velocity can be divided into phase

velocities (Cp) and group velocities (Cg) when the wave propagates in the medium. The dispersion

curves of Lamb wave in composite plates with stacking sequence of [90o/0o]4 are calculated by solving

the governing equations of Eq.1. Fig. 2 displays the dispersion curves calculated using DISPERSE

software[30] for Lamb wave propagation in WGF/Epoxy composite laminates. In the test, the plate

thickness is ranging from 0.5 to 3 mm and the scan frequency is between 0 to 10 MHz. As seen from

the figure, there are merely S0 and A0 wave mode when the excitation frequency is smaller than 220

kHz for all the cases. Another aspect, the center frequency of the used PZT wafers in the experiments

also affect the received signal modes. Therefore, we test the center frequency of the PZT wafer in Fig.

3. In the test, the emission attenuation is 40 (+60) db, and the receive amplification is 31 db. The

scanning scope is ranging from 100 to 400 kHz. According to the test results in Fig. 3, the center

frequency of the adopted PZT wafer is around 253 kHz. Therefore in the following damage

localization study, we select 210 kHz as the excitation frequency to investigate the guided wave

propagating behavior in the composite laminates.

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

A4A3

A2

A1

S3

S2S1

S0

Ph

ase

vel

oci

ty/(

km

/s)

Frequency/kmz

A0

0 1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

A4

A3A2

A1

S3

S2S1S0

Gro

up

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

(a) Composite laminates thickness=0.5 mm

0 1 2 3 4 50

2

4

6

8

10

A4A3

A2

A1

S3S2S1

S0

Ph

ase

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S3

S2S1S0

A4

A3A2

A1

Gro

up

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

(b) Composite laminates thickness=1 mm

0.0 0.5 1.0 1.5 2.0 2.50

2

4

6

8

10

A4S4

S3S2S1

S0

A3A2

A1

Ph

ase

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

S4

S3

S2S1S0

A4

A3

A2

A1

Gro

up

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

(c) Composite laminates thickness=2 mm

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

A2

A1

S0

S2S1

Ph

ase

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

A2

A1 S2

S1S0

Gro

up

vel

oci

ty/(

km

/s)

Frequency/mkz

A0

(d) Composite laminates thickness=3 mm

Figure 2. Dispersion curves of Lamb waves propagating in WGF/epoxy composite laminates with

different thicknesses.

100 150 200 250 300 350 400-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15Center frequency

Center frequency f0=253 kHz

Am

pli

tud

e

Frequency/kHz

Figure 3. Center frequency of the adopted PZT in the experiments.

2.3. Thickness effect and slowness profiles

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

1

2

3

4

5

6

Am

pli

tud

e

Composites thickness/mm

S0 mode wave

A0 mode wave

X10-4

Figure 4. FE simulation with excitation frequency of 210 kHz.

Numerical studies are performed to investigate the thickness effect and the slowness profile

phenomenon when Lamb wave propagating in WGF/epoxy composite laminates. The numerical

simulation was carried out in ABAQUS/Explicit (Dassault Systems, France). The FE model consists of

a 4-ply [0o/90o] glass fiber reinforced composite laminate with dimensions 490×350×2 mm3. The

material properties of the lamina are summarized in Tables 1 and 2[20]. The excitation consists of a 210

kHz narrow-band 3.5 cycle Hanning window modeled wave. Both composite laminate and PZT

transducers are modeled using three-dimensional eight-node brick elements C3D8R. The boundary of

the model is set as freedom. As the element size should be limited into ten nodes exist per

wavelength[11, 20], therefore, the element size in the model is set as 1 mm in length. Fig.4 shows the

S0/A0 Lamb wave mode amplitude as the function of composite thickness. As can be found in the

results that both the amplitudes show a decrease tendency with increasing of plate thickness. Instead of

decline linearly, the amplitude decreases sharply when the thickness is smaller than 2.5 mm. However,

the curve presents a gentle drop tendency when the thickness is between 2.5 to 4 mm.

0o

90o

180o

270o

A0

S0

0o

90o

180o

270o

A0

S0

(a) [90o/0o]4 (b) [+45o/-45o]4

Figure 5. Slowness profiles of S0 and A0 modes in WGF/epoxy composite laminates with different

stacking sequences.

The slowness profiles is a phenomenon caused by the anisotropy of the material, which results in

different directions of phase and group velocity vectors[31, 32]. This profile is a function of the

reciprocal of direction-dependent propagation velocity. Fig. 5 shows two examples of the slowness

profile phenomenon in WGF/epoxy composite laminates. The stacking sequences of the laminates are

[90o/0o]4 and [+45o/-45o]4, respectively. In isotropic materials, the phase and group velocity vectors

always point in the same direction[33]. However, in the example cases of WGF/epoxy composite plate,

the velocities in directions parallel and perpendicular to the fibers (0o and 90o) are the largest. Due to

this phenomenon, only a projection of the velocity vector is observed in the corresponding

directions[34]. Therefore, it is necessary to adjust the group velocity and stack sequence of the

composite materials before the damaged locating algorithm is performed. As verified in reference[11, 12],

the group velocity is angular dependence and the amplitude of the incident Lamb wave is highly

depended on the stack sequence. It should be noted that the adopted composite laminates in the

following work have the thickness of 2 mm with stacking sequence of [90o/0o]4.

Table 1. Elastic properties of WGF/epoxy composites used in the simulation (GPa).

E11 E22 E33 G12 G13 G23 v12 v13 v23

11.8 11.8 0.58 4.82 4.82 4.82 0.05 0.24 0.24

Table 2. Strength properties of WGF/epoxy composites used in the simulation (MPa).

XT YT ZT S12 S13 S23 XC YC ZC

485.05 488.91 52.14 108.4 108.4 108.4 59.94 59.58 52.14

3. Damage localization in WGF/Epoxy composite laminates

3.1. The probabilistic imaging algorithm description

Collecting Lamb wave signals of the

hea l thy and damaged compos i te

specimens

Calculating the signal difference

between the two signals after Hilbert

transform

Finding out the TOF of the scattered

signal peak, calculating the distance

between actuator-damage-sensor, and

drawing the ellipse

Calculating the probability of all the

gr ids to the e l l ipse by Cumulative

distribution function

Adding all the corresponding grids

and imaging

Figure 6. Flowchart of the proposed damage location and imaging algorithm used in composite

laminates.

When Lamb wave is incident on damage, wave scattering occurs at the damage boundary. Accordingly,

by determining the location of wave scattering sources for different sensing paths, some points on the

damage boundary, and subsequently the shape and size of damage, can be defined[13, 20]. We compiled a

probabilistic imaging algorithm in MATLAB software (MathWorks, USA) to fulfill the damage

localization process in the WGF/Epoxy composite laminates. The Lamb-wave-based damage detection

methodology for anisotropic materials is based on the fundamental idea of probabilistic imaging

algorithm. Briefly, the defect localization algorithm consists of five main steps that includes: signal

generation and acquisition, calculating the scattered signal, Time-of-Flight of the scattered signal,

localization by probabilistic method, grid data processing and defect imaging. The procedure for the

proposed algorithm is summarized in Fig. 6. In the program, the probabilistic function was set as the

subroutine in the program, and the possibility of damage on the node is determined by the cumulative

distribution function F(z), defined as following:

( ) ( )z

ij ijF z f z dz−

= (3)

where 2

1( ) exp[ ]

22

ij

ij

iji j

zf z

z = − is the Gauss distribution function, and zij is the distance defined

as: 2 2( ) ( )ij m ij m ijz x x y y= − − − . For a given zij, the occurrence probability of the defect at point (xm,

ym) is:

( , ) 1 [ ( ) ( )]m m i j i j i jI x y F z F z= − − − (4)

To acquire the signal features associated with damage, an active sensor network, consisting of 4 PZT

wafers corresponding to pitch-catch configurations will be carried out. Each of the transducers can act

as both actuator and sensor for excitation and measurement, respectively. A sequential scan for

detecting damage in large structures can thus be performed by exciting one of the transducers to

generate a Lamb wave while the rest of the transducers are used for measuring the impinging waves.

This results in a total of N(N−1) actuator/sensor signal paths. However, it should be noted that the

developed algorithm merely need N(N−1)/2 groups of the signals, and this advantage makes the data

processing relatively easier. For the PZT configurations with 4 PZT wafers in Fig.7, there are totally 6

groups of signals used in the algorithm. In the following work, we named the signals according to the

wave path as AB, AC, AD, BC, BD, and CD.

3.2. Through hole location with the data obtained in FE simulation

PZT-A PZT-B

PZT-CPZT-D

490 mm

35

0 m

m

(150, 170) (350, 170)

(100, 70) (400, 70)Defect

(245, 125)

0o

90o45o

Fiber direction

Figure 7. Geometric dimension of the composite laminates used in the FE and experiments.

As the theoretical solutions cannot capture the Lamb wave feature well in the composite laminates by

solving the wave equation such as Eq.1, researches on Lamb wave propagating characteristics in

composite laminates by FE before experiments are essential[27, 35]. In this work, the FE simulation is

performed to study Lamb wave propagating feature in both the healthy and damaged WGF/epoxy

composite laminates, respectively. For the damaged laminates, a through hole with diameter of 3 mm

was adopted to simulate the defect. For the composites plate with plane dimensions shown in Fig. 7,

numerical simulations are performed by the explicit time integration algorithm. The material

properties of the WGF/epoxy are listed in Tables 1 and 2. Fig. 8 shows the Lamb wave structure in the

simulation. As can be seen in Fig. 8, the Lamb wave in WGF/epoxy forms a rhombic-like shape and its

propagating velocity along fill (90o) and warp (0o) directions of the composite laminates is larger than

other directions. The wave velocity along 45o fiber direction is the lowest among all the directions.

The simulation result matches the wave propagating theory and the slowness profiles as described in

Section 2.3. This phenomenon can be explained as following: The fibers in the WGF/epoxy composite

laminates are along 90o/0o direction, and the strength and modulus along fiber direction are much

higher than other directions in the woven fabric composites. The particle elastic motions of Lamb

wave in fiber direction are stronger and this mechanism finally leads to the high wave amplitude in the

simulation. Fig. 8 also shows the energy distribution of the Lamb wave interacting with through hold

in the composites plate. As seen, mode converse and scattering would be generated when the incident

wave interacts with the defect. Based on this phenomenon, the damage localization process by the

developed probabilistic imaging algorithm will be performed. The scattered Lamb wave signal is

obtained using baseline subtraction, as following[11]:

S D I

ab ab abU U U= − (5)

Where S

abU and I

abU are the vectors of the scattered and incident signals, respectively, and D

abU is

the signal vector for the damaged structure. The proposed Lamb-wave-based damage detection

methodology utilizes the scattered wave signals S

abU to reconstruct a damage localization image.

Scattered signal

Defect

Wave frontBoundary

reflection

Figure 8. The defect reflection phenomenon in the composite laminates.

Fig. 9 are the resulted Lamb wave signals obtained in the simulation. In the figure, we compared two

groups of signals that includes the healthy and damaged specimens. It should be noted that the wave

signals were excited by PZT-A in Fig. 7 and received by the other 3 PZTs. As seen in the figure, the

two signals in Fig. 9a are very similar. However, signals in the other cases are very different. As

discussed above, this is due to the slowness profiles of WGF/epoxy composite laminates. Because the

wave path in Fig. 9a is on the fiber direction, while the other wave propagating paths have to go across

the crossed ply layers, which will consume the wave energy by wave scattering during the propagating

process in the plate. When comparing the signals obtained in healthy and damaged specimens, the

main difference is the wave amplitude due to the defect scattering effects. Fig. 10 is the scattered wave

calculated by Eq.5 from Fig. 9. We marked the duration in Fig. 10 which was used in the proposed

probabilistic imaging algorithm descripted in Section 3.1.

0 50 100 150 200-30

-20

-10

0

10

20

×10-5

Am

pli

tud

e

Time/μs

Healthy

Damaged

0 50 100 150 200

-6

-4

-2

0

2

4

6

8 Healthy

Damaged

×10-5

Am

pli

tud

e

Time/μs

0 50 100 150 200

-4

-3

-2

-1

0

1

2

3

4

5×10-5

Am

pli

tud

e

Healthy

Damaged

Time/μs

(a) (b) (c)

Figure 9. Typical damage and healthy signal in the simulation with PZT-A as activated and PZT-B, C,

D as received sensors, respectively.

0.0000 0.0001 0.00020

4

80

20.0

0.5

1.00

1

0

2

0

2

4

Time/s

ab

ac

ad

Am

pli

tud

e

bc

bd

cd

Figure 10. Typical scattered wave with its duration.

Fig. 11 is the damage localization result obtained by the proposed probabilistic imaging algorithm with

the data achieved in the FE simulation. As shown in the figure, the probably damage location is very

close to the real damage area in the model. The color bar is given in the plot, and we use it to represent

the probability density map. In details, the damage appearance probability F(z) in the specimens is

between 0 to 1. F(z)=0 and 1 represent that the damage is not appear and appear, respectively. As

shown, the real through hole is located at (0.245, 0.12), while the algorithm predicated two possible

damage locations (where F(z)=1) in the figure with the coordinate of (0.245, 0.1155) and (0.235,

0.1085), respectively. Fig. 12 shows sectional view of the damage probability density along the x and y

axis through the actual damage position. Also, the relation between the percentage error between the

estimation and the real damage using the proposed methodology was calculated. The figure shows that

the proposed methodology is able to predict the damage location along x direction with locating error

below ±5%, and the error is smaller than 10% along y direction. This further highlights the robustness

of the proposed damage detection methodology. The location error is due to uncertain material

parameters in the modeling for the theoretical prediction. Another aspect, unlike the real composites,

the interface between different neighbor composite layers play very important role during the guided

wave propagating process. Since the model in the simulation did not content the interface property, the

resulted scattered wave and its duration are smaller than the real situation. All the mentioned factors

lead to the damage location deviation calculated by the probabilistic imaging algorithm. To further

verify the algorithm, we would carry out the experimental study in the following section.

Figure 11. Damage location results with data from the FE simulation.

0.0 0.1 0.2 0.3 0.4 0.50.5

0.6

0.7

0.8

0.9

Pro

ba

bil

ity

den

sity

x/m

(0.245,0.1155)

(0.235,0.1085)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.5

0.6

0.7

0.8

0.9 (0.245,0.1155)

(0.235,0.1085)

Pro

bab

ilit

y d

ensi

ty

y/m

(a) x error: 0; 4.08% (b) y error: 3.75%; 9.58%

Fig. 12. Sectional view of the damage probability density along the (a) x and (b) y axis through the

actual damage position.

3.3. Defect localization with the data in experiments

The researched WGF/epoxy composite laminates are manufactured by vacuum assisted resin injection

(VARI) processing. The polymer used as matrix in the processing is vinyl ester epoxy resin. This resin

can be cured at room temperature in the presence of hardening agent and accelerating agent. The

hardening agent is Methyl Ethyl Ketone Peroxide (MEKP), and the accelerating agent is

Dimethylaniline. The resin is mixed with accelerating agent and hardening agent at mass ratio of

100:1:0.01. The reinforced material is plain woven glass fabric clothes. The woven glass fabrics are

the two-dimension orthogonal plain woven fabric clothes with surface mass density of 700 g/m2. The

strand width of the fabric is 4 mm, while the gap between each adjacent strand is 1 mm. The detailed

manufacturing procedure can be found in our previous work in reference[3]. In the experiments,

through hole was made by an electric drill on the composite plate, and the diameter of the hole is 3

mm and the location is in according with the simulation. The plate dimension in the experiments is

490×350×2 mm3. A hanning-windowed signal is generated from the Tektronix AFG 3012C single

channel arbitrary function generator. Then the signal is powered up to 20 times of the initial value by a

linear high-voltage amplifier (Model EPA-104, Piezo Systems, Inc.). The data are recorded at 2.5 GS/s

through a Tektronix MDO 3012 mixed domain oscilloscope. In terms of the PZT array arrangement,

non-circular PZT wafers are used. The diameter of the PZT wafer is 10 mm with the thickness of 1

mm.

0 50 100 150 200 250-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Wave

am

pli

tud

e

Time/μs50 75 100 125 150

-0.1

0.0

0.1

0.2

0.3

0.4

Wa

ve

am

pli

tud

e

Time/μs

Healthy Signal

Damaged Signal

(a) (b)

Figure 13. Time-domain presentation and typical amplitude profiles of a typical lamb wave signal

acquired in the health and damaged composites.

Using the above manufactured WGF/epoxy composites and the guided wave monitoring system, the

damage localization experiment was performed and analyzed. As a representative, Fig. 13a shows the

time-domain presentation of a typical Lamb wave signal in the WGF/epoxy composite laminates in the

experiments. In order to extract the required signal features that can be used in the developed

probabilistic imaging algorithm. Fig. 13b showed the typical signal difference between the healthy and

the damaged specimens. It should be noted that the window size of ToF is chosen below 150 μs such that sufficient details of both time and frequency information of the signal could be retained. From Fig.

13b, one can extract the amplitude profiles at fundamental and double frequencies as a respective

function of propagation time. In accordance with the algorithm flowchart in Fig. 6, the final defect

location result is shown in Fig. 14. The percentage error along x and y direction in the composite plate

is 0 and 4%, respectively. The predicted damage location matches the real defect location well. The

accuracy of damage localization of thin-walled glass/epoxy composite laminates in the experiment is

higher than that of simulation data. This further verified the feasibility of the developed probabilistic

imaging algorithm in the real WGF/epoxy composite laminates with stacking sequence of [90o/0o]4.

Figure 14. Damage localization results in the experiments (through hole diameter: 3 mm).

4. Conclusions

This paper performed finite element analysis and experimental methods to investigate the guided wave

propagating characteristics and damage localization method in WGF/epoxy composite laminates. The

results show that the amplitude of Lamb wave decreases with increasing of composite thickness. Due

to the anisotropic material property, the slowness profile effect could affect the damage localization

results in both the FE and experiments. Results showed satisfactory consistency of the developed

probabilistic imaging algorithm approach to locate the through hole in the WGF/Epoxy laminates.

This study facilitates the deployment of structural health monitoring which is capable of identifying

damages in the composites materials.

Acknowledgments:

This work was supported by National Natural Science Foundation of China (No.11702097) and

Special Research Foundation of Young Teachers (No. 222201714015).

References

[1] B Yang, ZQ Wang, LM Zhou, JF Zhang, WY Liang, “Experimental and numerical investigation of

interply hybrid composites based on woven fabrics and PCBT resin subjected to low-velocity

impact”, Compos Struct 132, pp 464-476, 2015.

[2] H Cheng, Y Li, KF Zhang, WQ Mu, BF Liu, “Variation modeling of aeronautical thin-walled

structures with multi-state riveting”, J. Manuf Syst 30(2), pp 101-115, 2011.

[3] B Yang, ZQ Wang, LM Zhou, JF Zhang, LL Tong, WY Liang, “Study on the low-velocity impact

response and CAI behavior of foam-filled sandwich panels with hybrid facesheet”, Compos Struct

132, pp 1129-1140, 2015.

[4] HS Lei, K Yao, WB Wen, H Zhou, DN Fang, “Experimental and numerical investigation on the

crushing behavior of sandwich composite under edgewise compression loading”, Compos Part B 94, pp 34-44, 2016.

[5] M Hong, ZQ Su, Q Wang, L Cheng, XL Qing, “Modeling nonlinearities of ultrasonic waves for

fatigue damage characterization: Theory, simulation, and experimental validation”, Ultrasonics 54,

pp 770–778, 2014.

[6] CR Farrar, K Worden, NAJ Lieven, G Park, “Nondestructive Evaluation of Structures, in:

Encyclopedia of Aerospace Engineering”, John Wiley & Sons, Ltd, 2010. [7] MQ Le, JF Capsal, M Lallart, Y Hebrard, AVD Ham, N Reffe, L Geynet, PJ Cottinet, “Review on

energy harvesting for structural health monitoring in aeronautical applications”, Prog Aerosp Sci

79,pp 147–157, 2015.

[8] CC Tao, HL Ji, JH Qiu, C Zhang, Z Wang, WX Yao, “Characterization of fatigue damages in

composite laminates using Lamb wave velocity and prediction of residual life”, Compos Struct

166, pp 219-228, 2017.

[9] NP Yelve, M Mitra, PM Mujumdar, C Ramadas, “A hybrid method based upon nonlinear Lamb

wave response for locating a delamination in composite laminates”, Ultrasonics 70, pp 12-17, 2016.

[10] M Hong, Z Mao, MD Todd, ZQ Su, “Uncertainty quantification for acoustic nonlinearity parameter

in Lamb wave-based prediction of barely visible impact damage in composites”, Mech Syst Signal

Pr 82, pp 448-460, 2017.

[11] CT Ng, M Veidt, “A Lamb-wave-based technique for damage detection in composite laminates”, Smart Mater Struct 18, pp 074006, 2009.

[12] M Veidt, CT Ng, “Influence of stacking sequence on scattering characteristics of the fundamental

anti-symmetric Lamb wave at through holes in composite laminates”, J. Acoust Soc Am 129, pp

1280-1287, 2011.

[13] A Koyuncu, E Cigeroglu, HN Özgüven, “Localization and identification of structural nonlinearities

using cascaded optimization and neural networks”, Mech Syst Signal Pr 95, pp 219-238, 2017.

[14] JF Wang, LX Tian, "Global Lagrange stability for inertial neural networks with mixed time varying

delays”, Neurocomputing 235, pp 140-146, 2017.

[15] O Abdeljaber, O Avci, S Kiranyaz, M Gabbouj, DJ Inman, “Real-time vibration-based structural

damage detection using one-dimensional convolutional neural networks”, J. Sound Vib 388,pp

154-170, 2017.

[16] VRN Santos, FL Teixeira, “Study of time-reversal-based signal processing applied to polarimetric

GPR detection of elongated targets”, J. Appl Geophys 139, pp 257-268, 2017.

[17] E Amitta, D Givolia, E Turkel, “Combined arrival-time imaging and time reversal for scatterer

identification”, Comput Methods Appl Mech Engrg 313, pp 279-302.

[18] ZG Chua, Y Yang, LB Shen, “Resolution and quantification accuracy enhancement of functional

delay and sum beam forming for three-dimensional acoustic source identification with solid

spherical arrays”, Mech Syst Signal Pr 88,pp 274-289, 2017.

[19] Y Yang, ZG Chu, LB Shen, ZM Xu, “Functional delay and sum beam forming for

three-dimensional acoustic source identification with solid spherical arrays”, J. Sound Vib 373, pp

340-359, 2016.

[20] B Yang, FZ Xuan, SJ Chen, SP Zhou, Y Gao, B Xiao, “Damage localization and identification in

WGF/epoxy composite laminates by using Lamb waves: Experiment and simulation”, Compos

Struct 165, pp 138-147, 2017.

[21] SJ Chen, SP Zhou, Y Li, YX Xiang, MX Qi, “Distance-coefficient-based imaging accuracy

improving method based on the Lamb wave”, Chin Phys Lett 34, pp 044301,2017.

[22] R Gorgin, ZJ Wu, DY Gao, YS Wang, “Damage size characterization algorithm for active

structural health monitoring using the A0 mode of Lamb waves”, Smart Mater Struct 23, pp

035015, 2014.

[23] T Wandowski, PH Malinowski, WM Ostachowicz, “Circular sensing networks for guided waves

based structural health monitoring”, Mech Syst Signal Pr 66-67, pp 248-267, 2016.

[24] LY Yu, ZH Tian, CAC Leckey, “Crack imaging and quantification in aluminum plates with guided

wave wavenumber analysis methods”, Ultrasonics 62, pp 203-212, 2015.

[25] LY Yu, GB Santoni, V Giurgiutiu, “Shear lag solution for tuning ultrasonic piezoelectric wafer

active sensors with applications to Lamb wave array imaging”, Int J Eng Sci 48, pp 848-861, 2010.

[26] P Nazarko, L Ziemianski, “Damage detection in aluminum and composite elements using neural

networks for Lamb waves signal processing”, Eng Fail Anal 69, pp 97-107, 2015.

[27] KB Antigoni, DA Saravanos , “A layerwise semi-analytical method for modeling guided wave

propagation in laminated and sandwich composite strips with induced surface excitation”, Aerosp

Sci Technol 51, pp 118-141, 2016.

[28] YZ Hai, PC Ya, JB Yu, HC Xian , “Time reversal and cross correlation analysis for damage

detection in plates using Lamb waves”, In: IEEE, pp 1516-1520, 2010.

[29] JR Zhang, HY Ma, WG Yan, ZJ Li, “Defect detection and location in switch rails by acoustic

emission and Lamb wave analysis: A feasibility study”, Appl Acoust 105, pp 67-74, 2016.

[30] B Pavlakovic, “Lowe M Disperse user’s manual, version 2.0, Imperial College London, UK”.

[31] AH Nayfeh, “Wave propagation in layered anisotropic media with applications to composites”, Elsevier, New York, 1995.

[32] JL Rose, “Ultrasonic Waves in Solid Medi”, Cambridge University Press, New York, 1999.

[33] O Putkis, RP Dalton, AJ Croxford, “The anisotropic propagation of ultrasonic guided waves in

composite materials and implications for practical applications”, Ultrasonics 65, pp 390-399, 2016.

[34] G Neau, M Deschamps, M Lowe, “Group velocity of lamb waves in anisotropic plates: comparison

between theory and experiments”, Aip Conf Proc 557, pp 81-88, 2010.

[35] CAC Leckey, MD Rogge, FR Parker, “Guided waves in anisotropic and quasi-isotropic aerospace

composites: Three-dimensional simulation and experiment”, Ultrasonics 54, pp 385-394, 2014.