Defect Identification Method of CMC Bonding Structure based on Dynamic Time Warping and Simulation Analysis

In this work, a new defect identification method has been proposed in an attempt to detect the bonding quality of ceramic matrix composites. The method is based entirely on dynamic time warping (DTW) and simulation analysis. Aiming at two different characteristic defects of the glue layer (I) and glue layer (II) of CMC, the transfer matrix method is employed to model and simulate the defects in the bonding structure. On the basis of this, a dynamic time warping algorithm is used to regularize the simulation waveform and the actual waveform in time sequence, and the correlation coefficient is employed for the estimation of waveform similarity after regularization. In comparison with the traditional similarity evaluation standard of the DTW algorithm, the improved DTW algorithm has better waveform classification ability for the glue layer (I) and glue layer (II). The classification accuracy of debonding defects of the glue layer (I) is more than 95%, and that of the glue layer (II) exceeds 90%. Additionally, compared with the conventional terahertz imaging method, correlation imaging is appropriate for different characteristics of defect signals and has an improved defect-recognition effect.


INTRODUCTION
Ceramic matrix composite (CMC) is a composite material composed of various fiber-reinforced ceramic substrates 1 . The key attributes of CMCs are their high stiffness, high-temperature resistance, lightweight and corrosion resistance, all of which hold immense importance in the aerospace field. Usually, a five-layer glue structure is formed using CMC, glue layer (I), insulating felt, glue layer (II), and metal substrate 2 . Therefore, the hidden debonding defects are understandably harmful to the bonding strength, and the detection accuracy and accuracy of these defects are the important standards to determine the system protection effectiveness in CMC materials. Nondestructive testing (NDT) technology is required to detect defects. The traditional nondestructive testing technologies include ultrasonic 3 , eddy current 4 , X-ray 5 , etc., each having its own set of advantages and disadvantages. For example, the ultrasonic testing method may require a liquid coupling, and the detection resolution is relatively poor whereas eddy current technology is only able to detect surface and near-surface defects in conductive materials. X-ray method, on the other hand, is unsafe for the human body due to the involvement of the use of harmful radiation 6 .
Terahertz wave is a kind of electromagnetic wave with a frequency ranging between 0.1 to 10 terahertz and as such lies between traditional microwave and infrared light waves 7 . THz time-domain spectroscopy (TDS) is one of the most popular THz methods. Owing to its strong penetrability and low photon energy radiation, it has great potential in the internal imaging of non-conductive and non-polar materials. These materials also include multilayer composites, which are opaque under visible and infrared light 8 . Besides, the inner layer thickness, the hidden defects, and inhomogeneity within these materials can be determined by the analysis using THz radiation. It is worth noting that terahertz radiation provides a non-destructive, non-ionizing, and non-contact method for material evaluation 9 .
There has been much research in recent years on nondestructive testing of CMC bonding structures using THz TDS. For the quality detection of glue layer of CMC bonding structure, the maximum value of the time-domain signal, flight time, variance, and other parameters are used for nondestructive testing signal analysis 10,11 , whereas Fourier transforms, wavelet transform, EMD, and other methods are used to enhance weak signal 2,12 , for improving the efficiency of defect identification. Simultaneously, in recent years, there have been some researches on the nondestructive detection of debonding defects of CMC materials using neural network intelligent recognition algorithm 1  Therefore, in an attempt to find a solution to the above problems, this paper proposes a defect identification method based on dynamic time warping and simulation analysis, the TMM is used to simulate the sampling waveform of the sample. The simulation was employed to obtain the characteristic interval of the defect in the terahertz time domain. The DTW algorithm is used to time sequence the simulated waveform in the normal area. The actual waveform is then collected, and then the waveform similarity is calculated after regularization, which is utilized as the index of terahertz imaging.

PRINCIPLE Terahertz Transmission Matrix Simulation
Because the test sample is usually a structure comprising multi-layers, considering the complexity of the structure, TMM is used to simulate. Each layer of TMM is modeled by the following two matrices: The first matrix represents the behavior of terahertz signals at each interface between two media with different optical material constants, including the corresponding Fresnel coefficients 16 .
where  is the angular frequency, c is the speed of light, and i n  is the complex refractive index of the layer ( i i i n n j    ). The whole theoretical transfer function ( ) R  is obtained by 6 multiplying two matrices as follows: 11 12 Finally, the simulated terahertz time-domain signal can be obtained using the following formula 17 : where, F E t is the Fourier transform of incident THz pulse and 1 F  is the inverse Fourier transform.

Algorithm
During the sample preparation process, the inhomogeneity of materials and the mutual penetration of glue layers leads to terahertz echo position shifting forward and backward in different regions. Traditional similarity calculation methods such as correlation coefficient, Manhattan distance, and Euclidean distance cannot be employed for calculation. Therefore, a similarity calculation method based on dynamic time warping is proposed in this paper. DTW is an algorithm to estimate the similarity between two sequences. The purpose of this measurement is to find the shortest path by twisting and bending a time series 18 .
In the classic DTW algorithm, a local distance measure is defined to obtain the similarity between training samples and multiple test samples by finding the optimal path 19 . Assuming that there is a standard template r with length I and a training template t with length J , the optimal path is found through the Euclidean distance of each point of the standard template r and the training template t , resulting in finding the nonlinear matching between the two templates 20 , as shown in Fig. 1. The distance function ( , ) d i j is Euclidean distance, which is usually employed for the measurement of similarity. The regularized path D can be described as follows: Boundary conditions, continuity, monotonicity, and slope constraints have to be satisfied when selecting the path 21 . The similarity ( , ) Dist t r between the training template and test template can be obtained using the path D . The minimum total distance of the regular path is the best alignment between the test sample and the training sample.
Among them, the shortest distance regular path rw and tw can be found through the normalization coefficient by backtracking 22 . However, the uncertainty in the actual manufacturing process of materials gives rise to a morphological difference between the actual and simulation waveform. The conventional 8 method of calculation of Euclidean distance will result in a large difference between the normal and the simulation waveform, which is hard to be distinguished from the defective waveform.
Therefore, this paper focuses on calculating the Pearson correlation coefficient of the regular path rw and tw as the final measure of similarity between the standard template and the training template 23 , The formula is as follows.

Sample Production and Signal Analysis
The sample employed in this paper is a ceramic matrix composite bonding sample      3 shows the reflection of the theoretical THz wave at each interface of the specimen. 10 The above TMM matrix is used to obtain the simulation waveforms of the defect and normal region as shown in Fig. 4. In the figure, the simulation waveform simulates the time-domain waveform reflected from the samples with and without defects, which carries the major portion of the information from the time-domain. Generally speaking, when an electromagnetic wave is reflected from the interface between incident material and reflective material with a higher refractive index than incident material, phase inversion will occur. When the incident wave encounters a reflective material with a lower refractive index than the incident material, the phase change of the reflected wave interface will not occur 25 . Due to the thickness of the sample, the time delay of the reflected wave 1 E from the upper surface usually exceeds the maximum time delay (320 ps) of our system upon focusing on the glue layer. Then, the reflected signal 2 E from CMC material to the glue layer (I) is the most obvious signal. 3 deepening of the back valley of 5 E and is the fuzzy feature.

Terahertz Signal Classification and Recognition
The terahertz time- warping, as shown in Fig. 5 and Fig. 6, and it is evident that dynamic time warping has a certain regularization effect on glue layer (I) and (II). A better matching effect can be achieved because the local waveform can align the position of the characteristic peaks, which, for subsequent data processing is more convenient. For the glue layer (I), 9.5ps-10ps has a good regularity effect; for glue layer (II), a good regularity effect exists in the range of 4ps-5ps.
However, when the flight time deviates from the optimal regularization range, the traditional DTW method using Euclidean distance to evaluate waveform similarity can be no longer applied. Therefore, this paper makes use of the Pearson correlation coefficient as a means to evaluate the waveform similarity after regularization.   It is evident that in case of obvious defect characteristics, such as debonding defect of the glue layer (I), there isn't an overall obvious difference between the traditional maximum value imaging and correlation imaging, however, the correlation imaging has a good recognition effect for the four side defects, while the maximum value imaging manifests a poor recognition effect for upper and lower defects, which may be the result of the unknown maximum value characteristics caused by the difference in materials used for the preparation of samples.
Obviously, for the debonding defects of the glue layer (II), the defect characteristics are fuzzier, and the defect identification is more influenced by the material inhomogeneity and dispersion.
imaging method can make up for this defect, and also exhibits a good recognition effect for debonding defects of the glue layer (II).

CONCLUSIONS
In this study, a defect identification method based on dynamic time warping and simulation analysis is proposed, which primarily aims at two different types of defect detection in ceramic matrix composite glue materials. The defect characteristics and characteristic intervals of the simulation waveform analyzer are obtained based on the TMM method. The method not only provides theoretical support for terahertz non-destructive testing but also reduces the dependence of traditional nondestructive testing on standard samples. Besides, to solve the problem of position shift of terahertz echo caused by material non-uniform penetration and scattering, a DTW algorithm based on Pearson correlation coefficient is proposed. Compared with the traditional DTW algorithm, the improved method is more suitable for terahertz signals and shows a better classification effect in the process of defected waveform recognition. It has higher defect-recognition rate. Finally, a new imaging recognition algorithm has been proposed in this paper which focuses on the identification of debonding defects existing in the glue layer (I) and glue layer (II) in the CMC bonding structure. Pearson correlation coefficient is used to carry out correlation imaging. Compared with traditional THz single feature imaging, the correlation imaging method has better imaging recognition ability for debonding defects of glue layer (I) and glue layer (II). However, for defect detection, the edge recognition ability still needs to be improved.