Due to the high specific strength, high specific stiffness, excellent fatigue resistance, excellent instability resistance and post buckling performance of Carbon Fiber Reinforced Plastic (CFRP) [1–3]. So, it has a wide range of applications in the field of aerospace. At the same time, it not only improves the flight performance, but also helps to reduce the weight of the aircraft. However, in daily use, composite materials are vulnerable to the impact of birds, hail, runway debris, tool falls and other objects [4, 5]. It can cause visible external damage and invisible internal damage. Among them, invisible damage has more potential harm, and inaccurate detection may cause catastrophic events. Therefore, it is necessary to develop new detection means or methods to meet the detection requirements. If your paper is intended for a conference, please contact your conference editor concerning acceptable word processor formats for your particular conference.

With the development of sensor technology and signal processing means, nondestructive testing technology based on.

Lamb wave technology emerges as the times require [6–8]. Because of its excellent performance (such as long-distance transmission, low cost, sensitive to defects, etc.), it has become the focus of many scholars. In order to realize the damage location of CFRP, geometric location method, time of flight method, pattern recognition and other methods have been studied. Based on the combination of multi signal classification (MUSIC) and Lamb wave, Zuo Hao [9] realized the damage location of composite structures.

Due to the influence of structural anisotropy in MUSIC algorithm, there are sensor phase error and sensor position error, which leads to positioning error. Bao Q [10] proposes an anisotropic compensation MUSIC algorithm, which can jointly compensate the phase errors of different types of sensors and improve the positioning accuracy and reliability of music algorithm. The representative method of geometric location is ellipse positioning. Yang B [11] proposes a monitoring system based on Lamb wave technology to realize automatic detection and location of structural damage. The method of coordinate transformation is used to improve the ellipse positioning algorithm. It is applied to online damage location of hydrogen storage tank. In addition, the representative algorithm is time reversal focusing algorithm. Zenghua Liu [12] proposed a multi-channel time reversal focusing method based on the modified time reversal algorithm, and applied this method to the detection of various defects in large diameter and thick-walled pipes. NaokiMori [13] proposes a damage location method based on time reversal focusing of scattered Lamb waves by mode conversion. However, due to the dispersive characteristics of Lamb wave, its propagation velocity is a function of frequency and material thickness, so the wave velocity is not constant. Therefore, the method which depends on wave velocity and time difference has some limitations. In order to not rely on the characteristic parameters of the signal, scholars have developed a damage identification method based on pattern recognition. Based on Lamb wave and artificial intelligence method, A. Mardanshahi [14] proposes an intelligent model for automatic detection and classification of composite matrix cracks. Using the transmission coefficient of Lamb wave and the laser/EMAT ultrasonic signal energy, Lei Yang [15] established an artificial neural network for accurate prediction of weld penetration. The results show that the proposed method can detect the weld of structure quickly. A. De Fenza [16] combines artificial neural network and probability ellipse method to detect structural damage. Based on the wave propagation data, the damage location and damage degree of metal and composite plates are determined. Shengyuan Zhang [17] is based on one-dimensional convolution neural network and Lamb wave technology to realize structural damage identification. However, the method based on pattern recognition needs a large number of sample data, which is an important factor restricting its rapid development.

In addition, when Lamb wave is used for nondestructive testing of structures, the signal inevitably contains noise [18, 19]. Scholars have also done a lot of research on extracting effective information from the original signal. The representative methods are wavelet transform based on denoising method [20], independent component based on signal denoising method [21], empirical mode decomposition based on signal denoising method [22], principal component analysis based on signal denoising method [23]. These methods have achieved good results. However, there are few researches on damage localization without preprocessing. An ideal damage identification algorithm should only be sensitive to damage and not affected by noise. Therefore, how to extract damage features quickly and accurately in strong noise environment is an urgent problem for CFRP damage location and detection function.

In order to solve the above problems, a composite damage imaging localization method based on signal spectrum is proposed. The feasibility of this method is verified by simulation and experiment. The damage was characterized by signal spectrum and the damage factor was calculated. The damage location imaging of composite materials is realized. Finally, the resistant noise characteristic of the proposed algorithm is analyzed, and the results show that the proposed method can achieve structural damage location imaging in strong noise environment.

The current research shows that Lamb wave will produce scattering wave when it encounters damage, which leads to the change of the direct wave response signal obtained by the sensor passing through the damage path compared with the undamaged signal. Lamb wave tomography can locate and image the damage based on this change.

Lamb wave tomography [24, 25] is a kind of technology which depends on the difference between signals to realize damage localization and imaging. It does not need parameters such as wave velocity and arrival time, and does not understand the complex multimodal propagation characteristics of Lamb wave. The damage location process is divided into two parts: signal comparison and image reconstruction. When comparing the signals, the frequency spectrum of the reference signal and the damage signal is calculated, and the damage factor ( D F f ) is determined according to the frequency spectrum before and after the damage. The calculation is defined as follows: D F f = 1 − min ( F u , F d ) max ( F u , F d ) (1) Where F u and F d involve the peak values of the frequency spectrum obtained by the response signal of Lamb wave without damage or damage, respectively.

According to the corresponding D F f value of each sensor path, the damage probability distribution of adjacent area is reconstructed. In order to locate the damage more accurately, all the sensing paths corresponding to the probability distribution map are superposed to obtain the damage probability distribution of any point (x, y) in the detection area of N sensing paths: P ( x , y ) = ∑ i = 1 N − 1 ∑ j = i + 1 N D F f * S i j ( x , y ) (2)

S i j ( x , y ) is called the spatial distribution function. Finally, using the obtained damage factor, a probabilistic imaging algorithm is used to realize the imaging of the damage location.

The damage factor in Eq. 1 is calculated as follows.

The frequency components and frequency distribution range of dynamic signal can be obtained by spectrum analysis, and the amplitude distribution and energy distribution of each frequency component can be obtained. The frequency values of the main amplitude and energy distribution are obtained.

Frequency spectrum analysis uses Fourier transform to decompose the time domain signal and expand it according to the frequency to make it a function of frequency, and then study and process the signal in the frequency domain.

The forward Fourier transform is shown in Eq. 3 and the inverse transform is shown in Eq. 4. F ( ω ) = ∫ − ∞ + ∞ f ( t ) e − j ω t d t (3) f ( t ) = 1 2 π ∫ − ∞ + ∞ F ( ω ) e j ω t d ω (4) Where F ( ω ) is the continuous spectrum of f ( t ) ; f ( t ) is time domain signal; ω is the angular frequency.

The above is the Fourier transform of continuous signal. Since most of the signals collected in practical engineering are discrete signals, Discrete Fourier Transform (DFT) is used in practical application. The forward transform of DFT is shown in Eq. 5 and the inverse transform is shown in Eq. 6. X ( k ) = ∑ n = 0 N − 1 x ( n ) e − j 2 π n k / N ( n = 0,1,2 , … , N − 1 ) (5) x ( n ) = 1 N ∑ k = 0 N − 1 X ( k ) e j 2 π n k / N ( n = 0,1,2 , … , N − 1 ) (6) Where N is the number of sampling points; n is the sequence number of discrete values in time domain; and k is the serial number of discrete values in frequency domain.

Figure 1 is a flow chart for damage location and imaging identification in composite materials. The method can be divided into seven steps as follows:

1) The Lamb wave damage detection experiment is carried out through simulation and experiment.

In order to verify the feasibility of the proposed algorithm, a simulation study was first put forward. Using ABAQUS software (ABAQUS company, CA, United States), the damage of composite materials was simulated by finite element method. The geometric dimension of the composite is 600 mm × 600 mm × 2 mm, and the laying mode is [0°/90°]₈. The parameters of structural materials are shown in Table 1. The actuator and sensor are responsible for sending and receiving Lamb wave signal respectively. The signal is a lamb wave signal with center frequency of 50 kHz modulated according to Eq. 7 [26]. The time domain and frequency domain waveforms are shown in Figure 2B. The location of the actuator and sensor on the CFRP is shown in Figure 2A. The grid element size is 1 mm × 1 mm, and the type is SC8R. A = 1 2 [ 1 − cos ( 2 π f c t n ) sin ( 2 π f c t ) ] (7)

F _c refers to the frequency; n denotes the number of cycles in the signal window (n = 5); t represents the duration of wave propagation.

In the experimental study, the size of the composite is 600 mm × 600 mm × 2 mm, and the stacking order is [0°/90°]⁸. 12 sensors with a diameter of 30 cm are evenly arranged on the surface around the centre point. The sensor arrangement is consistent with the simulation, as shown in Figure 3.

The experimental system is shown in Figure 11. It consists of an arbitrary function generator (Rigoldg5252) for sending signals, a linear broadband power amplifier (Krohn-Hite 7602M) for amplifying signals, a multichannel oscilloscope (Tektronix MDO4034B-3) for signal acquisition, and a computer.

The damage is simulated by changing the local strain field of the structure by mass block [9, 26]. For a single damage, a mass block of 30 mm × 10 mm × 40 mm is pasted at the coordinate position (315.00, 375.00). For multiple damages, paste a 20 mm high cylinder block based on a single damage at coordinates (295.00, 220.00). The signal from the signal generator is consistent with the simulation, and the excitation frequency is also 50 k Hz. In the process of signal acquisition, the sampling frequency of oscilloscope is 10 M Hz. The lamb waves are inevitably disturbed by noise. In order to get the effective signal, the wavelet method is used to filter the signal noise.

Figures 12A,B show the signals collected by sensors on the sensing channels S1–S7 and S5–S9 before and after damage. It can be seen that the direct waves of signals on S1–S7 sensor channel have great changes before and after damage. This is because the damage located in the sensor channel scatters part of the direct wave. However, there is no damage on the S5–S9 sensor channel, so the signal changes little before and after the damage.

The frequency spectrum of the four signals in Figure 12 was calculated, and the results in Figure 13 were obtained. It can be seen that the damage causes the frequency spectrum of the signal to change, and the damage information can be characterized by calculating the damage factor.

The frequency spectrum of all sensor channel signals is calculated. Damage factor is calculated according to Eq. 1. Finally, the structural damage localization imaging as shown in Figure 14 is obtained.

The result of imaging location coordinate is (321.10, 375.80), According to Eq. 8, the radial error is 6.15 mm.

In the same way, the multi damage location method is the same as that of single damage location. Figure 15 is a simultaneous interpreting sensor signal on different sensing channels. Calculate the frequency spectrum of the signal, as shown in Figure 16. It can be seen that the presence of damage leads to the change of signal and its frequency spectrum.

The damage factor of each channel is calculated and the damage location imaging is carried out. The results are shown in Figure 17.

The coordinates of the two damages are (310.30, 379.10) and (304.00, 217.20) respectively. The radial errors are 6.24 mm and 9.43 mm, respectively.

Any detection technology in nature will inevitably be affected by the environment. Noise has a certain impact on the accuracy of detection data and damage identification and location. The proposed damage factor calculation method must have a certain resistant noise characteristic analysis to have practical engineering significance.

Since it is difficult to obtain the signal under strong noise in the laboratory environment, the noise (SNR = 3 dB) is loaded into the effective signal to simulate the signal collected in the strong noise environment.

In this paper, the experimental data are analyzed. Strong noise is added to the four signals in Figure 12, and the frequency spectrum of each signal is calculated, as shown in Figures 18–21, respectively.

It can be seen from Figures 18–21 that the maximum value of spectrum with and without noise signal is basically the same. Then the damage factors of all channel signals are calculated. Single damage location imaging of structure in noise environment is realized, as shown in Figure 22.

In Figure 22, the specific location of the damage is (320.80, 376.10). According to Eq. 8, the damage location error is 5.90 mm.

It can be seen from Figures 23–26 that the noise has little effect on the maximum value of the frequency spectrum of the signal. Then the damage factor is calculated, and finally the damage location imaging is realized, as shown in Figure 27.

In Figure 27, the exact coordinates of the two damages are (321.30, 376.10) and (308.60, 216.00). The radial positioning errors are 6.40 mm and 14.18 mm, respectively.

In this paper, a composite damage location and imaging method based on Lamb wave spectrum detection is proposed. The spectrum of signal is used to represent the damage information, and Lamb wave tomography is used to locate and image the damage. The results show that the proposed method can achieve damage location and imaging. The main conclusions are as follows:

1) The damage factor calculation method based on signal spectrum proposed in this paper is effective and feasible.