# Damage Detection Test of GFRP Composite Civil Materials Based on Piezoelectric Ceramic Sensors

Authors: Yanhua She; Gaojie Cai
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

The piezoelectric ceramic sensor was fixed on Glass Fiber Reinforced Plastic (GFRP) composite civil materials, using the external paste method for damage detection test. The effect of the depth and number of cracks on the surface of the GFRP specimen on the signal received by the piezoelectric ceramic sensor was studied. The time-domain signal graph and energy graph based on wavelet packet were drawn, combining the active induction method and the energy method based on wavelet packet. It is found that the greater the damage degree of GFRP specimens, the smaller the voltage value of the signal, the smaller the energy of the signal, and the greater the damage index based on wavelet packet. The results showed that the active induction method can be used to collect the data of GFRP specimens by piezoelectric ceramic sensor. The collected data are processed by using the damage index principle based on wavelet packet. The maximum voltage value of the specimen, the energy of wavelet packet, and the damage index based on wavelet packet can all accurately judge the damage change of GFRP specimens. The active induction method based on piezoelectric ceramic sensor can detect the damage change of GFRP specimens in real time. It provides an effective method for damage analysis of GFRP composite civil materials.


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## Body

## 1. Introduction

In recent years, the technology of civil engineering structural damage detection [1–4] and health monitoring [5–11] has developed rapidly. In particular, based on the active induction method of piezoelectric effect, the identification and diagnosis of structural damage can be realized by analyzing the difference between the original signal and the current signal [12–21]. Piezoelectric ceramic sensors based on lead zirconate titanate (PZT) have many advantages, such as rapid response, strong energy collection ability, low cost, and easy implementation [22–26]. Roh [27] proposed an active induction monitoring technology, which embeds multiple piezoelectric patches into the composite structure to detect the damage of the composite plate. Subsequently, the technology is widely used in damage detection and structural health monitoring in civil. Du and Kong [28, 29] damaged the pipeline by corrosion and cutting and used piezoelectric ceramic sensors to detect pipelines with different damage levels, to study the change of stress wave after pipeline damage. Feng et al. [30] used piezoelectric ceramic sensors to detect the damage of concrete and found that this method was feasible for detecting cracks in concrete. Zhang et al. [31] took the initiative to cut the wood, resulting in varying degrees of damage. Piezoelectric ceramic sensors were used to detect the changes of stress waves before and after wood damage. Huo et al. and Wang and Hou [32, 33] used piezoelectric ceramic sensors to detect bolt loosening. Yin et al. [34] optimized the active induction method and used piezoelectric ceramic sensors to detect bolt loosening in a washing machine. Song et al. [35] used piezoelectric ceramic sensors to monitor the bolt of rock reinforcement components to ensure that the bolt can play an important role in the normal operation of underground mines. Xu et al. [36] used a homemade piezoelectric ceramic sensor to detect the concrete and found that the strength of the concrete is related to the voltage value obtained by the detection. Feng and Xiao [37] proposed a passive sensing method based on piezoelectric ceramics to detect typical damage types of concrete piles, including partial mud invasion, secondary concrete pouring interface, circumferential cracks, and all mud invasions. Liu et al. [38] buried piezoelectric ceramic sensors in reinforced concrete and used the impedance method to detect the corrosion of steel bars. The results showed that after the annular piezoceramic disk was encapsulated, the resonance of the piezoelectric ceramic under the effects of electric excitation was restricted due to the damping effect of the packaging layer. Kong et al. [39, 40] used piezoelectric ceramic sensors to study soil water content. The experimental results showed that the received signal energy has a certain correlation with soil water content. Rao et al. [41] proposed a new ultrasonic guided wave tomography (GWT) system based on a self-designed piezoelectric sensor for online corrosion monitoring of large plate-like structures. Qin et al. [42] combined the piezoelectric ceramic sensor with the active induction method to detect the bond-slip between steel plate and concrete. However, there are few studies on damage monitoring of Glass Fiber Reinforced Plastic (GFRP) by the active induction method using piezoelectric ceramic sensors.GFRP is a new type of civil composite material based on resin and filled with glass fiber. It has the advantages of light weight, high strength, heat resistance, corrosion resistance, good insulation, low production energy consumption, and environmental protection [43]. Therefore, it is widely used in the field of civil engineering and construction, but GFRP damage detection is rarely done. In order to analyze the damage of GFRP specimens more accurately and effectively, this paper combined the active induction method with the energy based on wavelet packet. On the basis of analyzing the maximum voltage value, the signal energy was further analyzed. The time-domain signal diagram and the energy diagram based on wavelet packet were obtained.


## 2. Detection Principle

### 2.1. Active Induction Method

In this experiment, the active induction method was used to detect the damage changes in GFRP specimens by piezoelectric ceramic sensors. The sensor PZT1 generates the stress wave, which will propagate in the whole specimen and be received by another sensor PZT2. When cracks or holes occur in the specimen, the stress wave will reflect the wave generated by the defect, resulting in a decrease in the signal received by the sensor PZT2. The deeper the defect, the less signal the sensor PZT2 receives, as shown in Figure1. In order to quantify the damage of GFRP specimens, the energy method based on wavelet packet is used.Figure 1
Active induction method (unit: mm).


### 2.2. Energy Method Based on Wavelet Packet

The wavelet packet analysis can effectively decompose various time-frequency signals [12]. The energy method based on wavelet packet is usually used to calculate the energy of the received signal in structural analysis. In this study, the energy analysis based on wavelet packet was used to calculate the received wave signal energy under different damage levels in GFRP specimens. The calculation steps are as follows:Firstly, the original signalS received by the sensor is decomposed into 2n signal subsets with different frequency bands by n-level wavelet packet decomposition. Signal subset Xj, where j is the frequency band (j=1,2,⋯,2n) and can be expressed as
(1)Xj=Xj,1,Xj,2,⋯,Xj,m,wherem is the data sampling of the decomposed signal subset.Secondly, the energy of signal subsetEi,j can be defined as
(2)Ei,j=Xj,12+Xj,22+⋯+Xj,m2,wherei is the ith measurement value. The signal energy of the ith measurement can be expressed as
(3)Ei=Ei,1,Ei,2,⋯,Ei,2n.Thirdly, the received signal energy can be calculated as(4)E=∑i=12nEi,j.In this paper, based on the wavelet packet energy method, the received wave energy of GFRP specimens under different damage conditions will be calculated.In the fourth step, the damage index of the structure (DI) is(5)DI=∑j=12nEi,j−Eh,j2∑j=12nEh,j2,whereEh,j is the energy of the j signal of the last layer decomposed by the wavelet packet in the healthy state of the structure. The greater the damage index (DI), the higher the attenuation of the stress wave in the propagation process, and the larger the degree of structural damage.When the damage index (DI) is 0, the specimen is not damaged, and when DI is 1, the specimen is completely destroyed. However, the damage index can only evaluate the damage change of a single specimen, and the damage between multiple specimens cannot be compared. The reasons are as follows: first, the piezoelectric ceramic sensor is highly sensitive and is easily affected by the environment such as temperature and noise, second, the coupling agent between the sensor and the specimen will affect the collected data, third, the parameters of the signal transmitter will affect the signal energy, and fourth, the difference of the sensor itself will have an impact on the received signal.


## 2.1. Active Induction Method

In this experiment, the active induction method was used to detect the damage changes in GFRP specimens by piezoelectric ceramic sensors. The sensor PZT1 generates the stress wave, which will propagate in the whole specimen and be received by another sensor PZT2. When cracks or holes occur in the specimen, the stress wave will reflect the wave generated by the defect, resulting in a decrease in the signal received by the sensor PZT2. The deeper the defect, the less signal the sensor PZT2 receives, as shown in Figure1. In order to quantify the damage of GFRP specimens, the energy method based on wavelet packet is used.Figure 1
Active induction method (unit: mm).


## 2.2. Energy Method Based on Wavelet Packet

The wavelet packet analysis can effectively decompose various time-frequency signals [12]. The energy method based on wavelet packet is usually used to calculate the energy of the received signal in structural analysis. In this study, the energy analysis based on wavelet packet was used to calculate the received wave signal energy under different damage levels in GFRP specimens. The calculation steps are as follows:Firstly, the original signalS received by the sensor is decomposed into 2n signal subsets with different frequency bands by n-level wavelet packet decomposition. Signal subset Xj, where j is the frequency band (j=1,2,⋯,2n) and can be expressed as
(1)Xj=Xj,1,Xj,2,⋯,Xj,m,wherem is the data sampling of the decomposed signal subset.Secondly, the energy of signal subsetEi,j can be defined as
(2)Ei,j=Xj,12+Xj,22+⋯+Xj,m2,wherei is the ith measurement value. The signal energy of the ith measurement can be expressed as
(3)Ei=Ei,1,Ei,2,⋯,Ei,2n.Thirdly, the received signal energy can be calculated as(4)E=∑i=12nEi,j.In this paper, based on the wavelet packet energy method, the received wave energy of GFRP specimens under different damage conditions will be calculated.In the fourth step, the damage index of the structure (DI) is(5)DI=∑j=12nEi,j−Eh,j2∑j=12nEh,j2,whereEh,j is the energy of the j signal of the last layer decomposed by the wavelet packet in the healthy state of the structure. The greater the damage index (DI), the higher the attenuation of the stress wave in the propagation process, and the larger the degree of structural damage.When the damage index (DI) is 0, the specimen is not damaged, and when DI is 1, the specimen is completely destroyed. However, the damage index can only evaluate the damage change of a single specimen, and the damage between multiple specimens cannot be compared. The reasons are as follows: first, the piezoelectric ceramic sensor is highly sensitive and is easily affected by the environment such as temperature and noise, second, the coupling agent between the sensor and the specimen will affect the collected data, third, the parameters of the signal transmitter will affect the signal energy, and fourth, the difference of the sensor itself will have an impact on the received signal.


## 3. Test Overview

### 3.1. Specimen Design

According to the different manufacturing process, GFRP produces two different types. The first is the pultrusion type, which has very strong tensile strength, but slightly insufficient compressive strength. The second is the winding type, which is opposite to the former. It has very strong compressive strength and weak tensile strength.In this test, nine GFRP specimens with the same size and different damage degree were designed by using the pultrusion type. As shown in Figure2, the size of each specimen is 600 mm in length, 100 mm in width, 50 mm in height, and 7 mm in wall thickness. As shown in Figure 3, two piezoelectric ceramic sensors were fixed on the surface of each specimen by the external sticking method, and the fixed coupling agent was epoxy resin, which was the connection interface between the piezoelectric ceramic sensor and GFRP. As shown in Figure 4, the sensor PZT-5H is selected in the test. The size of the sensor is 15 mm in diameter and 20 mm in thickness. The piezoelectric ceramic sheet is wrapped by two cylindrical marbles. The marbles protect the piezoelectric ceramic sheet and prevent the violent collision of the outside world. The main parameters of the piezoelectric ceramic sensor are shown in Table 1. There are nine specimens in this test, which are divided into group A with five specimens and group B with four specimens. As shown in Table 2, in group A, the number of crack is 1, and the crack depth is 0, 1, 3, 5, and 7 mm, respectively. In group B, the crack depth is 3 mm, and the number of crack is 0, 1, 3, and 5, respectively. For example, GP-A-1-3 indicates that the number of cracks in Group A is 1 and the depth of cracks is 3 mm. For all test specimens, the crack width is set to 1.5 mm.Figure 2
Schematic diagram of GFRP specimen (unit: mm).Figure 3
The specimen with damage.Figure 4
Piezoelectric ceramic sensors.Table 1
Main performance parameters of piezoelectric ceramic sensors.
Density (g·cm-3)Dielectric constantεElectromechanical coupling coefficientCapacitanceC(nF)Curie temperatureTc (°C)Mechanical quality factorQm7.516001.653.7730080Table 2
Test conditions.
Specimen numberNumber of cracknCrack depthh (mm)Group A (GP-A-n-h)GP-A-0-000GP-A-1-111GP-A-1-313GP-A-1-515GP-A-1-717Group B (GP-B-n-h)GP-B-0-000GP-B-1-313GP-B-3-333GP-B-5-353


### 3.2. Test Equipment

As shown in Figure5, the test device consists of a data collector (NI USB-6361), a signal transmitter, a laptop, and the GFRP specimens. The sampling frequency of the data acquisition system is 2 MS/s. This parameter means that the data collector can collect 2 million valid data within 1 second. When the stress wave propagates in the material at a certain frequency, the energy of the stress wave will decrease during the propagation process. The frequency of the stress wave affects the propagation of the stress wave in the material. The proper frequency will make the stress wave travel farther, and the signal received by the sensor will be more stable. Signal transmitter adopts the frequency sweep mode, that is, within a cycle, the frequency changes from the start frequency to the stop frequency. A fixed frequency often leads to instability of the signal, so a fixed frequency is not selected. In order to ensure the normal operation of piezoelectric ceramic sensors, appropriate voltage should be set. If the received signal is weak in the test, it is necessary to debug the start frequency and stop frequency of the signal transmitter. The start frequency, stop frequency, voltage value, and period of group A specimens are 10 Hz, 100 kHz, 10 V, and 1 s, respectively. Multiple cracks were cut out on group B specimens, resulting in excessive energy loss. The signal strength received by the sensor of group B was weak. In order to carry out the test smoothly, the frequency was increased to improve the signal strength received by the sensor. Therefore, the start frequency, stop frequency, voltage value, and period of the test pieces in group B are 100 Hz, 500 kHz, 10 V, and 1 s, respectively. To minimize the impact of the environment on the results, all tests were performed in a closed and quiet laboratory.Figure 5
Test device.


### 3.3. Test Process

The piezoelectric ceramic sensors used in this experiment are very susceptible to external temperature and vibration. Therefore, it is necessary to make strict requirements on the environment during the test. Before the formal test, all test-related items should be placed in a closed laboratory for 2 to 3 hours to minimize the impact of temperature. Piezoelectric ceramic sensor collects the stress wave generated by the actuator. In the data collection process, in order to make the test proceed smoothly, the specific test steps are as follows:Step 1: according to the test design, the specimen was cutStep 2: it was found that the surface temperature of GFRP specimens increased significantly, and all specimens were placed on the test bench for 1 hourStep 3: After the temperature of GFRP specimens was stable, the epoxy resin was applied at the designated position, and the two piezoelectric ceramic sensors were fixed. In this way, there was a layer of epoxy resin between the piezoelectric ceramic sensor and the specimen. If the thickness of each epoxy resin was different, it may affect the collected data. Therefore, when fixing the sensor, the thickness of the epoxy resin layer should be the same as far as possibleStep 4: the instrument was switched on for data collection in quiet environmentStep 5: MATLAB was used to process the collected data


## 3.1. Specimen Design

According to the different manufacturing process, GFRP produces two different types. The first is the pultrusion type, which has very strong tensile strength, but slightly insufficient compressive strength. The second is the winding type, which is opposite to the former. It has very strong compressive strength and weak tensile strength.In this test, nine GFRP specimens with the same size and different damage degree were designed by using the pultrusion type. As shown in Figure2, the size of each specimen is 600 mm in length, 100 mm in width, 50 mm in height, and 7 mm in wall thickness. As shown in Figure 3, two piezoelectric ceramic sensors were fixed on the surface of each specimen by the external sticking method, and the fixed coupling agent was epoxy resin, which was the connection interface between the piezoelectric ceramic sensor and GFRP. As shown in Figure 4, the sensor PZT-5H is selected in the test. The size of the sensor is 15 mm in diameter and 20 mm in thickness. The piezoelectric ceramic sheet is wrapped by two cylindrical marbles. The marbles protect the piezoelectric ceramic sheet and prevent the violent collision of the outside world. The main parameters of the piezoelectric ceramic sensor are shown in Table 1. There are nine specimens in this test, which are divided into group A with five specimens and group B with four specimens. As shown in Table 2, in group A, the number of crack is 1, and the crack depth is 0, 1, 3, 5, and 7 mm, respectively. In group B, the crack depth is 3 mm, and the number of crack is 0, 1, 3, and 5, respectively. For example, GP-A-1-3 indicates that the number of cracks in Group A is 1 and the depth of cracks is 3 mm. For all test specimens, the crack width is set to 1.5 mm.Figure 2
Schematic diagram of GFRP specimen (unit: mm).Figure 3
The specimen with damage.Figure 4
Piezoelectric ceramic sensors.Table 1
Main performance parameters of piezoelectric ceramic sensors.
Density (g·cm-3)Dielectric constantεElectromechanical coupling coefficientCapacitanceC(nF)Curie temperatureTc (°C)Mechanical quality factorQm7.516001.653.7730080Table 2
Test conditions.
Specimen numberNumber of cracknCrack depthh (mm)Group A (GP-A-n-h)GP-A-0-000GP-A-1-111GP-A-1-313GP-A-1-515GP-A-1-717Group B (GP-B-n-h)GP-B-0-000GP-B-1-313GP-B-3-333GP-B-5-353


## 3.2. Test Equipment

As shown in Figure5, the test device consists of a data collector (NI USB-6361), a signal transmitter, a laptop, and the GFRP specimens. The sampling frequency of the data acquisition system is 2 MS/s. This parameter means that the data collector can collect 2 million valid data within 1 second. When the stress wave propagates in the material at a certain frequency, the energy of the stress wave will decrease during the propagation process. The frequency of the stress wave affects the propagation of the stress wave in the material. The proper frequency will make the stress wave travel farther, and the signal received by the sensor will be more stable. Signal transmitter adopts the frequency sweep mode, that is, within a cycle, the frequency changes from the start frequency to the stop frequency. A fixed frequency often leads to instability of the signal, so a fixed frequency is not selected. In order to ensure the normal operation of piezoelectric ceramic sensors, appropriate voltage should be set. If the received signal is weak in the test, it is necessary to debug the start frequency and stop frequency of the signal transmitter. The start frequency, stop frequency, voltage value, and period of group A specimens are 10 Hz, 100 kHz, 10 V, and 1 s, respectively. Multiple cracks were cut out on group B specimens, resulting in excessive energy loss. The signal strength received by the sensor of group B was weak. In order to carry out the test smoothly, the frequency was increased to improve the signal strength received by the sensor. Therefore, the start frequency, stop frequency, voltage value, and period of the test pieces in group B are 100 Hz, 500 kHz, 10 V, and 1 s, respectively. To minimize the impact of the environment on the results, all tests were performed in a closed and quiet laboratory.Figure 5
Test device.


## 3.3. Test Process

The piezoelectric ceramic sensors used in this experiment are very susceptible to external temperature and vibration. Therefore, it is necessary to make strict requirements on the environment during the test. Before the formal test, all test-related items should be placed in a closed laboratory for 2 to 3 hours to minimize the impact of temperature. Piezoelectric ceramic sensor collects the stress wave generated by the actuator. In the data collection process, in order to make the test proceed smoothly, the specific test steps are as follows:Step 1: according to the test design, the specimen was cutStep 2: it was found that the surface temperature of GFRP specimens increased significantly, and all specimens were placed on the test bench for 1 hourStep 3: After the temperature of GFRP specimens was stable, the epoxy resin was applied at the designated position, and the two piezoelectric ceramic sensors were fixed. In this way, there was a layer of epoxy resin between the piezoelectric ceramic sensor and the specimen. If the thickness of each epoxy resin was different, it may affect the collected data. Therefore, when fixing the sensor, the thickness of the epoxy resin layer should be the same as far as possibleStep 4: the instrument was switched on for data collection in quiet environmentStep 5: MATLAB was used to process the collected data


## 4. Analysis of Test Results

### 4.1. Time-Domain Signal Diagram Analysis

As shown in Figure6, the horizontal coordinate represents the data acquisition time is 1 s, and the vertical coordinate represents the voltage value of the collected signal. The data acquisition system collected 2 million data in 1 s. The voltage value of the signal can reflect the damage degree of the specimen to a certain extent. The greater the damage degree of the specimen, the smaller the voltage value. By comparing the voltage values of different specimens, it is concluded that whether the damage change of specimens is consistent with that of actual specimens.Figure 6
Time domain signal diagram of group A specimens.The number of cracks in group A is 1, and the depth of the crack increases gradually from 0 mm to 7 mm. As shown in Figure6, it can be obviously found that the maximum voltage of specimen GP-A-0-0 is 0.00978 V, which is the largest in group A, followed by specimen GP-A-1-1. The smallest voltage value of group A is GP-A-1-7, which is 0.00395 V. It can be concluded that with the increase of crack depth, the voltage value is gradually reduced.The depth of cracks in group B is 3 mm, and the number of cracks increases gradually from 0 to 5. As shown in Figure7, it can be obviously found that the maximum voltage value of specimen GP-B-0-0 is the largest in group B, which is 0.013 V, followed by specimen GP-B-1-3. The lowest voltage value of group B is GP-B-5-3, which is 0.0051 V. It can be concluded that with the increase of the number of cracks, the voltage value also decreases gradually.Figure 7
Time domain signal diagram of group B specimens.The specific variation of voltage value of group A and B specimens is shown in Figure8. In summary, the change of voltage value can reflect the damage change of the specimen to a certain extent, and the smaller the voltage value is, the greater the damage degree is.Figure 8
Maximum voltage value of GFRP specimens. (a) Group A specimens. (b) Group B specimens.
(a)(b)


### 4.2. Energy Analysis

As shown in Figure9, in order to analyze the change of stress wave energy, the energy method based on wavelet packet is used to estimate the energy of the received signal. In group A, the crack depth increases gradually from 0 mm to 7 mm, while the energy index based on wavelet packet decreases gradually from 142.8 to 24.1. With the increasing number of cracks in group B, from 0 crack to 5 cracks, the voltage value gradually decreased from 242.9 to 52.9. The test results showed that the decrease of energy based on wavelet packet can reflect the damage trend of GFRP specimens to a certain extent.Figure 9
Energy based on wavelet packet. (a) Group A specimens. (b) Group B specimens.
(a)(b)In addition, in terms of the maximum voltage value and the energy based on wavelet packet, the specimen GP-B-0-0 is greater than that of the specimen GP-A-0-0, which is due to the different input parameters on the signal transmitter. The stop frequency of group A is 100 kHz, while that of group B is 500 kHz. Similarly, the difference between specimen GP-A-1-3 and specimen GP-B-1-3 is also the reason.The time domain signal graph analysis, voltage value analysis, and energy analysis based on wavelet packet can only analyze the damage change of the specimen and cannot judge the specific degree of specimen damage. Therefore, the damage index (DI) based on wavelet packet is introduced, which is presented and discussed in the previous paper. As shown in Figure10, it is based on the change of wavelet packet damage index. It can be seen from Figure 10(a) that in group A specimens, the corresponding damage indexes of the specimens with crack depth of 0 mm, 1 mm, 3 mm, 5 mm, and 7 mm are 0, 0.11, 0.25, 0.82, and 0.92, respectively, that is, the damage degrees of the specimens are 0, 11%, 25%, 82%, and 92%, respectively. It shows that the deeper the crack depth of the specimen, the greater the damage index and the greater the damage degree. Similarly, as shown in Figure 10(b), group B specimens are analyzed. The more cracks in the specimen, the greater the damage index and the greater the damage degree.Figure 10
Index based on wavelet packet. (a) Group A specimens. (b) Group B specimens.
(a)(b)The damage index of the specimens GP-A-1-3 and GP-B-1-3 is different. The possible reasons are as follows: (1) the output frequencies of the signal transmitters of the two are different, resulting in different collected signals. (2) The difference of the sensor itself will have an impact on the collected data. (3) GFRP materials are not homogeneous materials, and their own differences will affect the collected data. Based on the above influencing factors, the wavelet packet damage index can only evaluate specimens in the same group and cannot compare specimens in different groups.The above experimental results show that the piezoelectric ceramic sensor is expected to be used to detect the damage change of GFRP by the active induction method. However, some shortcomings of the active induction method are also exposed in the test. Although the change trend of structural damage of GFRP can be judged by the change of the maximum voltage value and the energy value based on the wavelet packet, the degree of structural damage and the specific location of damage cannot be specifically identified. Before practical application, it is necessary to consider the distance between the sensor producing stress waves, the sensor receiving stress wave, and the temperature of the working environment. In addition, the types of GFRP and its working environment will also have a great impact on the test data.


## 4.1. Time-Domain Signal Diagram Analysis

As shown in Figure6, the horizontal coordinate represents the data acquisition time is 1 s, and the vertical coordinate represents the voltage value of the collected signal. The data acquisition system collected 2 million data in 1 s. The voltage value of the signal can reflect the damage degree of the specimen to a certain extent. The greater the damage degree of the specimen, the smaller the voltage value. By comparing the voltage values of different specimens, it is concluded that whether the damage change of specimens is consistent with that of actual specimens.Figure 6
Time domain signal diagram of group A specimens.The number of cracks in group A is 1, and the depth of the crack increases gradually from 0 mm to 7 mm. As shown in Figure6, it can be obviously found that the maximum voltage of specimen GP-A-0-0 is 0.00978 V, which is the largest in group A, followed by specimen GP-A-1-1. The smallest voltage value of group A is GP-A-1-7, which is 0.00395 V. It can be concluded that with the increase of crack depth, the voltage value is gradually reduced.The depth of cracks in group B is 3 mm, and the number of cracks increases gradually from 0 to 5. As shown in Figure7, it can be obviously found that the maximum voltage value of specimen GP-B-0-0 is the largest in group B, which is 0.013 V, followed by specimen GP-B-1-3. The lowest voltage value of group B is GP-B-5-3, which is 0.0051 V. It can be concluded that with the increase of the number of cracks, the voltage value also decreases gradually.Figure 7
Time domain signal diagram of group B specimens.The specific variation of voltage value of group A and B specimens is shown in Figure8. In summary, the change of voltage value can reflect the damage change of the specimen to a certain extent, and the smaller the voltage value is, the greater the damage degree is.Figure 8
Maximum voltage value of GFRP specimens. (a) Group A specimens. (b) Group B specimens.
(a)(b)


## 4.2. Energy Analysis

As shown in Figure9, in order to analyze the change of stress wave energy, the energy method based on wavelet packet is used to estimate the energy of the received signal. In group A, the crack depth increases gradually from 0 mm to 7 mm, while the energy index based on wavelet packet decreases gradually from 142.8 to 24.1. With the increasing number of cracks in group B, from 0 crack to 5 cracks, the voltage value gradually decreased from 242.9 to 52.9. The test results showed that the decrease of energy based on wavelet packet can reflect the damage trend of GFRP specimens to a certain extent.Figure 9
Energy based on wavelet packet. (a) Group A specimens. (b) Group B specimens.
(a)(b)In addition, in terms of the maximum voltage value and the energy based on wavelet packet, the specimen GP-B-0-0 is greater than that of the specimen GP-A-0-0, which is due to the different input parameters on the signal transmitter. The stop frequency of group A is 100 kHz, while that of group B is 500 kHz. Similarly, the difference between specimen GP-A-1-3 and specimen GP-B-1-3 is also the reason.The time domain signal graph analysis, voltage value analysis, and energy analysis based on wavelet packet can only analyze the damage change of the specimen and cannot judge the specific degree of specimen damage. Therefore, the damage index (DI) based on wavelet packet is introduced, which is presented and discussed in the previous paper. As shown in Figure10, it is based on the change of wavelet packet damage index. It can be seen from Figure 10(a) that in group A specimens, the corresponding damage indexes of the specimens with crack depth of 0 mm, 1 mm, 3 mm, 5 mm, and 7 mm are 0, 0.11, 0.25, 0.82, and 0.92, respectively, that is, the damage degrees of the specimens are 0, 11%, 25%, 82%, and 92%, respectively. It shows that the deeper the crack depth of the specimen, the greater the damage index and the greater the damage degree. Similarly, as shown in Figure 10(b), group B specimens are analyzed. The more cracks in the specimen, the greater the damage index and the greater the damage degree.Figure 10
Index based on wavelet packet. (a) Group A specimens. (b) Group B specimens.
(a)(b)The damage index of the specimens GP-A-1-3 and GP-B-1-3 is different. The possible reasons are as follows: (1) the output frequencies of the signal transmitters of the two are different, resulting in different collected signals. (2) The difference of the sensor itself will have an impact on the collected data. (3) GFRP materials are not homogeneous materials, and their own differences will affect the collected data. Based on the above influencing factors, the wavelet packet damage index can only evaluate specimens in the same group and cannot compare specimens in different groups.The above experimental results show that the piezoelectric ceramic sensor is expected to be used to detect the damage change of GFRP by the active induction method. However, some shortcomings of the active induction method are also exposed in the test. Although the change trend of structural damage of GFRP can be judged by the change of the maximum voltage value and the energy value based on the wavelet packet, the degree of structural damage and the specific location of damage cannot be specifically identified. Before practical application, it is necessary to consider the distance between the sensor producing stress waves, the sensor receiving stress wave, and the temperature of the working environment. In addition, the types of GFRP and its working environment will also have a great impact on the test data.


## 5. Conclusions

In this paper, piezoelectric ceramic sensors are used to detect the damage of GFRP, and the collected data are processed by the active induction method based on wavelet packet and the principle of damage index. It is found that as the crack depth changes from 0 to 7 mm, the time domain signal diagram of the group A specimens changes significantly. The voltage value is reduced from 0.00978 V to 0.00395 V, and the energy based on wavelet packet is reduced from 142.8 to 24.1. The damage index based on wavelet packet increases from 0 to 0.92. It can be seen that as the depth of the specimen crack increases, the voltage value decreases, the energy decreases, and the damage index increases. In the same way, analyzing the group B specimens, it can be obtained that as the number of cracks in the specimens increases, the voltage value decreases, the energy decreases, and the damage index increases. The experimental results show that the maximum voltage value of the specimen, the energy based on wavelet packet and the damage index based on wavelet packet can accurately judge the damage change of the specimen. The active induction method based on piezoelectric ceramic sensors can detect the damage change of GFRP specimens in real time. It provides an effective method for damage analysis of GFRP composite civil materials.



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*Source: 5850187-2022-09-10.xml*