A Mechanical Structure Damage Location Method Based on Near-Field Frequency Space Sparse Decomposition

Abstract

The present invention discloses a mechanical structure damage location method based on near-field frequency space sparse decomposition, comprising the following steps: S1, performing frame-by-frame processing and fast Fourier transform on the original acoustic emission signal to obtain all frequency estimates of the original acoustic emission signal, and dividing sub-bands according to the frequency estimates; S2, constructing an objective function of the near-field frequency space sparse decomposition algorithm based on the particle swarm optimization algorithm; S3, performing L1 norm-singular value decomposition on the acoustic emission sub-bands of multiple snapshots to reduce the number of background noises and redundant snapshots; S4, constructing an array manifold matrix for each sub-band and establishing a product function of an over-complete dictionary array; S5, summing the spatial spectra of all signal sub-bands to obtain the spatial spectrum of the acoustic emission signal, thereby realizing the location of the acoustic emission source. The present invention can comprehensively extract the detailed features of the acoustic emission signal, significantly improve the efficiency and accuracy of location, and can effectively extract the detailed information in the signal.

Description

Technical Field

[0001] The present invention relates to the technical field of structural damage detection, and particularly to a method for locating mechanical structure damage based on near-field frequency-space sparse decomposition. Background Art

[0002] Mechanical structures are usually prone to damage or fracture due to factors such as cyclic loading, stress corrosion, and welding processes. More specifically, local damage to mechanical structures is accelerated by the stress concentration effect, resulting in the shutdown of the entire mechanical system and even casualties in actual engineering applications. In order to reduce maintenance costs and extend the remaining service life, it has become the research focus of scholars and maintenance personnel to propose advanced and effective non-destructive testing (NDT) technologies or structural health monitoring (SHM) methods. In particular, acoustic emission (AE), as the most commonly used structural health monitoring method, has been widely applied to the location and identification of defects (such as fatigue cracks and pitting) in simple mechanical structures.

[0003] Currently, many studies on the location and identification of damage acoustic emission (AE) sources in simple mechanical structures have been successful, mainly including methods such as fast Fourier transform (FFT), empirical mode decomposition (EMD), singular value decomposition (SVD), and empirical wavelet transform (EWT). However, these methods have some obvious deficiencies in analyzing wide-band AE signals generated by complex mechanical structures. Regarding the research on damage acoustic emission source location methods in complex mechanical structures, currently mainly include methods such as deep learning, Bayesian methods, Delta T mapping, and sparse decomposition (SD). In addition, sparse decomposition is a non-linear and non-stationary analysis method that approximates the original signal by constructing a sparse representation to extract detailed information. However, although these methods can generally extract acoustic emission characteristics and locate damage acoustic emission sources in complex mechanical structures, they also have some obvious disadvantages: existing sparse decomposition (SD) methods cannot effectively extract sufficient feature information when processing original acoustic emission signals; due to the need for a large amount of training data sets and the complexity of the algorithm architecture, the algorithm runs slowly, reducing the efficiency of damage acoustic emission source location; the search area is large, resulting in a decrease in source location accuracy; acoustic emission signals in complex mechanical structures often have non-linear and non-stationary characteristics, and traditional linear methods are difficult to effectively process. Specifically, traditional SD methods cannot effectively directly extract acoustic emission characteristics from original acoustic emission signals. Summary of the Invention

[0004] To solve the problems of insufficient acoustic emission extraction, low efficiency, insufficient accuracy, and difficult processing of non-linear and non-stationary acoustic emission signals in the existing damage location of complex mechanical structures, the present invention proposes a mechanical structure damage location method based on near-field frequency space sparse decomposition. By introducing the near-field frequency space sparse decomposition (NFSSD) method, the feature extraction ability, algorithm efficiency, and location accuracy of acoustic emission source location in complex mechanical structures are systematically improved to solve the above problems.

[0005] This application discloses a mechanical structure damage location method based on near-field frequency space sparse decomposition, including the following steps:

[0006] S1. Perform frame-by-frame processing and fast Fourier transform on the original acoustic emission signal to obtain all frequency estimates of the original acoustic emission signal, and divide sub-bands according to the frequency estimates;

[0007] S2. Construct the objective function of the near-field frequency space sparse decomposition algorithm based on the particle swarm optimization algorithm;

[0008] S3. Perform L1 norm-singular value decomposition on the acoustic emission sub-bands of multiple snapshots to reduce the number of background noises and redundant snapshots;

[0009] S4. Construct an array manifold matrix for each sub-band and establish the product function of the over-complete dictionary array;

[0010] S5. Sum the spatial spectra of all signal sub-bands to obtain the spatial spectrum of the acoustic emission signal, thereby realizing the location of the acoustic emission source.

[0011] Preferably, the S1 includes the following steps:

[0012] According to the non-stationarity of the acoustic emission signal, perform frame-by-frame processing on the original acoustic emission signal to obtain multi-snapshot signals, and obtain an L-frame data set X l (t) (l = 1, 2,..., L), where each frame can be regarded as a short-time stationary signal. Subsequently, approximately obtain all frequency estimates of the data set X l (t) through fast Fourier transform, and divide sub-bands according to these frequency estimates, where the center frequency of the sub-band corresponds to each frequency point. Convert the frame of the time-domain signal obtained by the acoustic emission sensor through the array into a model in the frequency domain, and the expression is as follows:

[0013] X l (f) = A Nl (x, y, f)S Nl (f) + N l (f); (1)

[0014] Among them,

[0015]

[0016] X l (f) and S Nl (f) is the array received data set after fast Fourier transform for each frame, N l (f) is the noise vector, A Nl (x, y, f) is the direction matrix at each discrete point of each frame data set on N grids, x is X l (f) is the row index of the matrix, y is the number of sampled frequency points, that is, the number of discrete points of the signal spectrum in the frequency domain, f is the acoustic emission signal with noise, m is X l (f) is the number of rows of the matrix, and N0 is the number of subbands.

[0017] Preferably, the S2 includes the following steps:

[0018] Based on the ability of the particle swarm optimization algorithm to perform global search in continuous space, the particle swarm optimization algorithm is used to construct the objective function of the near-field frequency space sparse decomposition (NFSSD) algorithm, thereby improving the 1-matching performance of the best matching element. Specifically, the particle swarm optimization algorithm regards the individuals in the population as particles searching in multi-dimensional space, and characterizes these particles through position, velocity, and fitness function.

[0019] Let f = f s + f n , where f s is the original acoustic emission waveform, and f n is the original acoustic emission noise. Therefore, the objective function can be defined as:

[0020]

[0021] where, g i represents traversing the elements in the dictionary D.

[0022] After the objective function is initialized, the position information and velocity of the particles will be continuously updated according to the fitness function during the iteration process. Specifically, when the number of iterations increases, the dimension of the best over-complete dictionary gradually increases, thereby significantly increasing the complexity of the algorithm. Therefore, the Hermitian inversion method is used to reconstruct the signal, and the expression is as follows:

[0023]

[0024] where, H k is the Hermitian matrix represented in partitioned form, 0 k is the zero vector, ρ k is the scalar regularization term, and η kis the key component for recursively updating the matrix, d yk is the error vector, and the superscript T represents the transpose;

[0025] When an inverse matrix is defined as Equation (5) can be rewritten in a new form as:

[0026]

[0027] where represents the inverse matrix at the (k - 1) step, h k is the gradient vector, b k is the intermediate vector of the update direction.

[0028] It can be clearly seen from Equation (5) that when signal reconstruction is performed, the current matrix inversion can be expressed as a linear combination of the previous inversion results, thus improving the efficiency of matrix inversion. Let the overcomplete dictionary be transformed into the currently updated matrix D Δk =[D Δk- 1g yk , where g yk is the best - matching element after the current iterative update. Therefore, the update relationship of the matrix D Δk is Θ Δk =[Θ Δk-1 d yk , where Θ Δk =φψ Δk and d yk =φg yk , φ is the observation matrix, and ψ Δk is the transformation matrix.

[0029] Therefore, let be constructed in a cascaded manner, and finally the following Hermitian matrix is obtained:

[0030]

[0031] According to Equation (5), we get Thus, by substituting H k into Equation (6) to calculate the inverse recursive formula, the matrix for signal reconstruction by the near - field frequency - space sparse decomposition algorithm is obtained.

[0032] Preferably, S3 includes the following steps:

[0033] Suppose there are P given acoustic emission sources located at coordinates (x p , y p ), p = 1, 2,..., P. The original acoustic emission signal is decomposed by the fast Fourier transform at point N0 to obtain N l (f), where X l(f) is equivalent to the frequency snapshot after each sub - band decomposition, denotes the center frequency of the N0 - th sub - band;

[0034] Therefore, the P acoustic emission source direction matrices with dimensions of m×p are represented as follows:

[0035]

[0036] where, A p (x, y, f j )'s column vector is an m×1 steering vector. By sampling the original acoustic emission signal in the frequency domain, multiple narrow - band data sets corresponding to different center frequencies f j (j = 1, 2, …, N0) are obtained;

[0037] Introduce the narrow - band characteristic acoustic emission signal X(f j ) to determine the location of the acoustic emission source. Based on the sparsity of the acoustic emission source, sample N grids in the entire near - field region, and construct an over - complete sparse array popular basic matrix A N (x, y, f j ) for the sampling points in the x - direction and y - direction. The expression is as follows:

[0038]

[0039] where, α m (x N , y N , f j ) represents the amplitude function of the signal, x N represents the abscissa of the N - th spatial position, and y N represents the ordinate of the N - th spatial position.

[0040] Preferably, the S4 includes the following steps:

[0041] Solve the spatial spectrum of each sub - band signal in the entire spatial domain, and construct a convex optimization model to process A N (x, y, f j ) to achieve the joint estimation of different frequency - domain snapshots at a single frequency point. The expression is as follows:

[0042]

[0043] where, ‖·‖ F represents the Frobenius norm, X sv (f j ) represents the spatial - domain signal observation matrix at the center frequency f j , and S sv (f j ) represents the spatial - domain signal observation matrix at the center frequency f jThe sparse signal estimation coefficient matrix under, λ is the regularization parameter, represents the center frequency f j of the regularization norm solution.

[0044] Preferably, the S5 includes the following steps:

[0045] By combining the non-sparse 2-norm with frequency-domain multi-snapshot sampling and using the sparse 1-norm for spatial sampling, the spatial spectrum of each sub-band signal in the entire spatial region is calculated by the following formula:

[0046] P(x,y,f j ) = |S N (x,y,f j )| 2 ; (11)

[0047] Sum all the spatial spectra calculated by formula (11) and find the spectral peak, so as to realize the acoustic emission source localization, that is:

[0048]

[0049] wherein, S N (x,y,f j ) represents the signal spectral component at the position (x,y) and the center frequency f j .

[0050] Advantages of the present invention:

[0051] (1) The present invention can deeply fuse frequency information and sub-band information at multiple scales, comprehensively extract the detailed features of acoustic emission signals, and solve the problem of insufficient feature extraction in traditional methods.

[0052] (2) By parallel integrating frequency information and sub-band decomposition, the present invention optimizes the algorithm structure, significantly improves the running efficiency of the localization algorithm, and overcomes the defect of low efficiency in existing methods.

[0053] (3) The present invention can accurately construct the array manifold matrix and effectively solve the spatial spectrum, significantly narrow the search range, improve the localization accuracy, and solve the problem of insufficient localization accuracy in traditional methods.

[0054] (4) The NFSSD method proposed by the invention, as a non-linear and non-stationary analysis method, can effectively extract detailed information in signals by constructing sparse representations, overcoming the limitations of traditional methods in dealing with non-linear and non-stationary signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a schematic flow chart of the mechanical structure damage localization method based on near-field frequency space sparse decomposition according to an embodiment of the present invention;

[0056] Figure 2 This is the overall framework of the test platform for the embodiments of the present invention;

[0057] Figure 3 This is a schematic diagram of the time-domain waveform and Fourier spectrum of the acoustic emission (AE) signals from sensor 1 to sensor 6 for the embodiments of the present invention;

[0058] Figure 4 This is a schematic diagram of the decomposition results of the acoustic emission (AE) signals from sensor 1 to sensor 6 for the embodiments of the present invention;

[0059] Figure 5 This is a schematic diagram of the acoustic emission (AE) count history of the first laser cladding layer from sensor 1 to sensor 6 for the embodiments of the present invention;

[0060] Figure 6 This is a schematic diagram of the reconstructed time-domain waveform and Fourier spectrum of the acoustic emission (AE) signals from sensor 1 to sensor 6 for the embodiments of the present invention;

[0061] Figure 7 This is a schematic diagram of the coordinate-based positioning results of the acoustic emission (AE) sources during laser cladding under different process parameters for the embodiments of the present invention: (a) overview, (b) the first laser cladding layer, (c) the second laser cladding layer, (d) the third laser cladding layer, (e) comparison results;

[0062] Figure 8 This is a schematic diagram of the comparison results with traditional positioning methods for the embodiments of the present invention: (a) PAC AE acquisition system, (b) triangulation method, (c) deep learning, (d) Bayesian method, (e) SD, (f) SD-SVD;

[0063] Figure 9 This is a schematic diagram of the root mean square (RMS) positioning errors of different methods for the embodiments of the present invention. Detailed implementation manners

[0064] To make the objectives, technical solutions and advantages of the present application clearer and more understandable, the following provides embodiments with reference to the accompanying drawings and further elaborates on the present application in detail.

[0065] Sparse decomposition (SD) is essentially equivalent to an over-complete dictionary (OCD) with narrowband and broadband characteristics. The basic principle of SD is considered to be solving the signal representation problem. The representation methods of the SD architecture mainly include two stages: orthogonal matching pursuit (OMP) and basis pursuit (BP). Specifically, compared with BP, OMP is an effective weak signal feature extraction method, especially suitable for signals with strong background noise. Therefore, the embodiments of the present application mainly focus on the sparse decomposition of acoustic emission signals based on OMP.

[0066] An embodiment of the present application discloses a mechanical structure damage location method based on near-field frequency space sparse decomposition. The process is as follows Figure 1 as shown, including the following steps:

[0067] S1. Perform frame-by-frame processing and fast Fourier transform (FFT) on the original acoustic emission signal to obtain all frequency estimates of the original acoustic emission signal, and divide subbands according to the frequency estimates.

[0068] According to the non-stationarity of the acoustic emission signal, perform frame-by-frame processing on the original acoustic emission signal to obtain multi-snapshot signals, and obtain an L-frame dataset X l (t) (l = 1, 2, …, L), where each frame can be regarded as a short-time stationary signal. Subsequently, approximately obtain all frequency estimates of the dataset X l (t) through fast Fourier transform, and divide subbands according to these frequency estimates, where the center frequency of the subband corresponds to each frequency point. Convert the frame of the time-domain signal obtained by the acoustic emission sensor array into a model in the frequency domain, and the expression is as follows:

[0069] X l (f) = A Nl (x, y, f)S Nl (f) + N l (f); (1)

[0070] where

[0071]

[0072] X l (f) and S Nl (f) are the array reception datasets after fast Fourier transform for each frame, N l (f) is the noise vector, A nl (x, y, f) is the direction matrix of each discrete point of each frame dataset on N grids, x is the row index of the X l (f) matrix, y is the number of sampled frequency points, that is, the number of discrete points of the signal spectrum in the frequency domain, f is the acoustic emission signal with noise, m is the number of rows of the X l (f) matrix, and N0 is the number of subbands.

[0073] S2. Construct the objective function of the near-field frequency space sparse decomposition algorithm based on the particle swarm optimization algorithm (PSO).

[0074] Since in traditional sparse decomposition (SD), each orthogonal matching pursuit (OMP) iteration requires traversing the dictionary D = {g i, all elements in {i = 1, 2, …, Q} are searched to find the best - matching elements of the remaining signals, and the Gabor dictionary obtained by parameter discretization is usually selected as the over - complete dictionary (OCD). Therefore, the computational cost increases significantly, thus reducing the redundancy of the Gabor dictionary. To solve this problem, the embodiment of this application constructs the objective function of the near - field frequency - space sparse decomposition (NFSSD) algorithm by using the particle swarm optimization algorithm based on its ability to perform global search in the continuous space, thereby improving the matching performance of the best - matching elements. Specifically, the particle swarm optimization algorithm regards the individuals in the population as particles searching in the multi - dimensional space, and characterizes these particles through position, velocity, and fitness function. The construction process of the objective function of the near - field frequency - space sparse decomposition algorithm is as follows:

[0075] Let f = f s + f n , where f s is the original acoustic emission waveform and f n is the original acoustic emission noise. Therefore, the objective function can be defined as:

[0076]

[0077] where g i represents traversing the elements in the dictionary D.

[0078] After the objective function is initialized, the position information and velocity of the particles are continuously updated according to the fitness function during the iteration process. Specifically, when the number of iterations increases, the dimension of the best over - complete dictionary gradually increases, thus significantly increasing the complexity of the algorithm. Therefore, the Hermitian inversion method is used to reconstruct the signal, and the expression is as follows:

[0079]

[0080] where H k is the Hermitian matrix represented in partitioned form, 0 k is the zero vector, ρ k is the scalar regularization term, and η k is the key component of the recursively updated matrix, d yk is the error vector, and the superscript T represents the transpose;

[0081] When an inverse matrix is defined as , Equation (5) can be rewritten in a new form as:

[0082]

[0083] where, Denote the inverse matrix at the (k - 1) - step as \(h\). k and \(b\) is the gradient vector k and \(b\) is the intermediate vector of the update direction.

[0084] It can be clearly seen from Equation (5) that when signal reconstruction is performed, the current matrix inversion can be expressed as a linear combination of the previous inversion results, thus improving the efficiency of matrix inversion. Let the over - complete dictionary be transformed into the currently updated matrix \(D\). Δk \(=\left[D_{1g}\right]\), where \(g\) Δk- is the best - matching element after the current iterative update. Therefore, the update relationship of the matrix \(D\) is \(\Theta\) yk \(=\left[\Theta_{d}\right]\), where \(\Theta\) yk \(=\varphi\psi\), \(d\) Δk \(=\varphi g\), \(\varphi\) is the observation matrix, and \(\psi\) Δk is the transformation matrix. Δk-1 \(d\) yk \(=\varphi g\), \(\varphi\) is the observation matrix, and \(\psi\) Δk \(=\varphi\psi\), \(d\) Δk \(=\varphi g\), \(\varphi\) is the observation matrix, and \(\psi\) yk \(=\varphi g\), \(\varphi\) is the observation matrix, and \(\psi\) yk is the transformation matrix. Δk is the transformation matrix.

[0085] Therefore, let be constructed in a cascaded manner, and finally the following Hermitian matrix is obtained:

[0086]

[0087] According to Equation (5), we get Thus, by substituting \(H\) into Equation (6) to calculate the inverse recursive formula, the matrix for signal reconstruction of the near - field frequency - space sparse decomposition algorithm proposed in this application is obtained. k

[0088] S3. Perform L1 - norm - singular value decomposition on the acoustic emission sub - frequency bands of multiple snapshots, effectively reducing the background noise and the number of redundant snapshots.

[0089] Suppose there are \(P\) given acoustic emission sources located at coordinates \((x_{p},y_{p})\), \(p = 1,2,\cdots,P\). The original acoustic emission signal is decomposed by fast Fourier transform at point \(N_{0}\), and \(X(f)\) is obtained, where p \(y_{p}\), p \(X(f)\) is equivalent to the frequency snapshot after the decomposition of each sub - band. Here, \(N_{0}\) is the number of sub - bands, l and \(\omega_{N_{0}}\) \(X(f)\) is equivalent to the frequency snapshot after the decomposition of each sub - band. Here, \(N_{0}\) is the number of sub - bands, l and \(\omega_{N_{0}}\) represents the center frequency of the \(N_{0}\) - th sub - band. represents the center frequency of the \(N_{0}\) - th sub - band.

[0090] Therefore, the acoustic emission source direction matrix with \(P\) dimensions of \(m\times P\) is expressed as follows:

[0091] ​

[0092] Among them, A p (x, y, f j ) has column vectors that are m×1 steering vectors. The principle of the embodiments of the present application is to sample the original acoustic emission signal in the frequency domain to obtain multiple narrowband data sets corresponding to different center frequencies f j (j = 1, 2, …, N0).

[0093] Meanwhile, a narrowband characteristic acoustic emission signal X(f j ) is introduced to determine the location of the acoustic emission source. Based on the sparsity of the acoustic emission source, N grids are sampled in the entire near-field region. Therefore, an overcomplete sparse array popular basic matrix A N (x, y, f j ) is constructed for the sampling points in the x and y directions, and the expression is as follows:

[0094]

[0095] Among them, α m (x N , y N , f j ) represents the amplitude function of the signal, x N represents the abscissa of the Nth spatial position, and y N represents the ordinate of the Nth spatial position.

[0096] S4. Construct an array popular matrix for each subband and establish the product function of the overcomplete dictionary array.

[0097] Solve the spatial spectrum of each subband signal in the entire spatial domain, and construct a convex optimization model to process A N (x, y, f j ) to achieve the joint estimation of different frequency-domain snapshots at a single frequency point, and the expression is as follows:

[0098]

[0099] Among them, ‖·‖ F represents the Frobenius norm, X sv (f j ) represents the spatial domain signal observation matrix at the center frequency f j , S sv (f j ) represents the sparse signal estimation coefficient matrix at the center frequency f j , λ is the regularization parameter, represents the regularization norm solution at the center frequency f j .

[0100] S5. By summing the spatial spectra of all signal subbands, the spatial spectrum of the acoustic emission signal is obtained, thereby realizing the localization of the acoustic emission source. Subsequently, non-sparse 2-norm is combined with frequency-domain multi-snapshot sampling, and sparse 1-norm is used for spatial sampling. Therefore, the spatial spectrum of each subband signal in the entire spatial region is calculated by the following formula:

[0101] P(x,y,f j )=|S N (x,y,f j )| 2 ;(11)

[0102] Sum all the spatial spectra calculated by Equation (11) and find the spectral peak, thereby realizing the localization of the acoustic emission source, that is:

[0103]

[0104] where S N (x,y,f j ) represents the signal spectral component at the position (x,y) and the center frequency f j .

[0105] In a specific embodiment, the effectiveness of the method proposed in this application for locating the damage acoustic emission source is verified through the laser cladding mechanical structure damage acoustic emission experimental dataset. The detailed coordinates of the acoustic emission sensors are summarized in Table 1 as follows:

[0106] Table 1 Coordinates of acoustic emission sensors (mm)

[0107]

[0108] To evaluate the performance of the method proposed in the embodiments of this application, a 16-channel SH-II type acoustic emission (AE) instrument is used to collect the damage acoustic emission signals generated during the laser cladding process of the mechanical structure. In the experiment, the laser cladding experiment is completed by an AFS-C1280 coaxial powder feeding laser material manufacturing device. To collect the acoustic emission signals, 6 PK15I piezoelectric acoustic emission sensors are used, with a resonant frequency of 150 kHz, and CG-88 vaseline is used as the acoustic coupling agent to fix the sensors on the experimental mechanical structure. Figure 2Shows the acquisition process of the acoustic emission signal during laser cladding, including acoustic emission sensors 1 - 6, the experimental mechanical structure (laser nozzle, sample), and the computer (acquisition terminal). In addition, by setting the frequency range of the band - pass filter to 10 kHz to 500 kHz and the threshold to 40 dB according to the Shannon sampling theorem, environmental noise can be effectively eliminated. It should be noted that the sampling frequency of the acoustic emission signal is set to 1 MHz to ensure the integrity of the acoustic emission signal transmission. In addition, the experimental sample uses a 316L stainless - steel mechanical structure with dimensions of 400 mm × 400 mm × 8.5 mm.

[0109] To ensure the uniformity between the medium and the substrate when the acoustic emission signal propagates in the laser - clad layer, 316L stainless - steel powder similar to the experimental mechanical structure is used as the cladding material. The parameter configuration of the laser - cladding experiment is shown in Table 2. In particular, to ensure the effectiveness and stability of the laser - cladding additive - manufacturing equipment and the acoustic - emission acquisition system, the acoustic - emission signal is collected in advance under no - load conditions (i.e., without additional laser - cladding powder). In addition, the acoustic - emission signals of laser cladding under changing process parameters are also collected to study the generalization ability of the proposed method. The technical parameters of three groups of laser - cladding experiments are shown in Table 3. Specifically, in this experiment, an acoustic - emission damage dataset generated under different processing conditions is collected, three groups of laser - cladding acoustic - emission signals are collected, and in the laser - clad layer. Compared with the first and second groups of laser - clad layers (showing characteristics of insufficient cladding and slag inclusion), the third group of laser - clad layers is flat and plump, indicating that the process parameters of the third group of experiments are more suitable for actual industry.

[0110] Table 2 Parameter settings of the laser - cladding experiment

[0111]

[0112] Table 3 Process parameters of three groups of laser - cladding experiments

[0113]

[0114] To verify the effectiveness of the near - field frequency - space sparse decomposition (NFSSD) method proposed in this application, first, data points in the first laser - clad layer are selected for acoustic - emission source localization of damage. The NFSSD is used to extract the acoustic - emission features of the original signal and obtain the frequency - domain distribution. For intuitive analysis, taking one acoustic - emission source as an example, the original acoustic - emission time waveforms and Fourier spectra of six sensors are obtained by FFT analysis, and the analysis results are as Figure 4 = 3 shown. From Figure 3It can be seen that it is difficult to directly identify the characteristics of acoustic emission signals by observing time-domain waveforms and Fourier spectra because the acoustic emission dataset of laser cladding has a certain self-similarity, which is not conducive to signal identification. In addition, for the collected laser cladding acoustic emission signals, the acoustic emission events generated by all sensors must be separated first, usually by setting a threshold voltage to directly extract the acoustic emission events. However, due to the influence of various non-linear factors (such as high energy, large amplitude, and violent fluctuations), the laser cladding acoustic emission signals generated by mechanical metal structures usually have non-linearity and non-stationarity, and their fault characteristics are easily submerged by strong background noise. Therefore, it is difficult to determine the effectiveness and accuracy of the threshold voltage selected for each sensor. The NFSSD proposed in this application is an intelligent acoustic emission source localization method without prior knowledge, which can effectively extract the acoustic emission characteristics of laser cladding and reduce the dependence on human factors.

[0115] Figure 4 The results of decomposing the acoustic emission signals of sensors 1 to 6 by the method S2 proposed in this application are shown. As Figure 4 shown, since the acoustic emission characteristic information of the mechanical metal structure is mainly concentrated in the high-frequency part, only the mode components of four different channels are extracted from each acquisition channel by the method proposed in this application. In addition, according to S3 of the method proposed in this application, Figure 5 The ring-down count history of the laser cladding acoustic emission signals collected by six acoustic emission sensors in the first laser cladding layer is shown. From Figure 5 it can be seen that there is no significant correlation between the acoustic emission count and the peak frequency of the acoustic emission signal, which indicates that the activity of the acoustic emission source is relatively independent of the type of acoustic emission waveform, thus revealing the necessity of extracting the frequency-domain characteristics of the acoustic emission signal. Specifically, there is a certain lag between the acoustic emission signal and the laser cladding process, that is, there is a time mismatch between the acquisition of the acoustic emission signal and the laser trajectory. At the same time, the complexity and uncertainty of the laser cladding experiment make it difficult to accurately calibrate the peak frequency and depict the periodic nodes of the acoustic emission signal by analyzing only a set of signals, thus reducing the recognition accuracy. Generally speaking, the method proposed in this application can accurately record the change trend of the laser cladding acoustic emission count. These results prove the effectiveness of the method proposed in this application for acoustic emission feature extraction under different processing conditions. In addition, by executing S4 of the method proposed in this application, Figure 6 The reconstructed time-domain waveforms and Fourier spectra of sensors 1 to 6 are shown. From Figure 6 it can be seen that the frequency band of the laser cladding acoustic emission signal is mainly between 75 kHz and 200 kHz. Subsequently, Figure 7 The coordinate-based acoustic emission source localization results in (b) show that after the processing of S5 of the method proposed in this application, the root mean square (RMS) localization error is 14.8 mm (see Figure 7In (e)). Specifically, the positioning coordinates of the damaged acoustic emission source are not exactly close to the actual coordinates of the current laser cladding point, indicating that the acoustic emission waveform may not be generated immediately after the laser stimulates the sample, but there is a certain time difference.

[0116] In addition, to study the influence of processing conditions on the positioning performance of the proposed method, the experiment in this embodiment also analyzed the coordinate positioning of the laser cladding acoustic emission source collected under different process parameters (see FIGS. 7(c) and (d)). The results show that the root mean square (RMS) errors of the method proposed in this application for the positioning of the acoustic emission sources in the second and third layer laser claddings are 21.3 mm and 19.4 mm respectively (see FIG. 7(e)). In summary, the experimental results preliminarily verify the effectiveness and accuracy of the method proposed in this application for the positioning of damaged acoustic emission sources in complex mechanical structures under different laser cladding processing conditions.

[0117] To further verify the effectiveness and superiority of the method proposed in this application, this embodiment compares two traditional acoustic emission source localization methods (i.e., PAC acoustic emission acquisition system and triangulation method), and four representative methods in the acoustic emission source localization of complex mechanical structures (i.e., deep learning, Bayesian method, sparse decomposition (SD), sparse decomposition - singular value decomposition (SD - SVD)). Comparative analysis of all methods is carried out based on the above experimental data, and the main details of the comparison results are summarized as follows: (1) In Method 1 (PAC acquisition system), the time difference between sensors is directly calculated using the original acoustic emission signal. Due to the influence of strong background noise, the localization accuracy of the acoustic emission source is low. (2) In Method 2 (triangulation method), as the number of acoustic emission sensors increases, the computational complexity increases. Therefore, this method is limited in high - precision acoustic emission source localization and has poor generality. (3) In Method 3 (deep learning), there are two drawbacks: A. When the number of layers or nodes is too small, the deep network is prone to underfitting; B. When the number of layers or nodes is too large, the training and calculation time increase, and the deep network is prone to overfitting. (4) In Method 4 (Bayesian method), the waveform propagation speed and time difference are effectively corrected. However, the strong fluctuation of the acoustic emission energy during laser cladding leads to an increase in the absolute error at the impact moment, thus reducing the accuracy of this method for acoustic emission source localization. (5) In Method 5 (SD), directly applying SD for acoustic emission source localization has two obvious deficiencies: A. When the distance between the acoustic emission source and the sensor increases, the source localization accuracy drops significantly; B. The computational complexity is high when performing acoustic emission source localization, making it difficult to apply to cases with a large number of acoustic emission sources or grids. (6) In Method 6 (SD - SVD), first, SVD is applied to decompose the original acoustic emission signal to obtain the signal subspace, and then SD is applied to constrain the noise term and perform acoustic emission source localization. However, for the acoustic emission source localization calculation in the near - field range, a sparse manifold matrix of two parameters (direction angle and distance) needs to be jointly constructed, resulting in a large computational complexity for this method.

[0118] Figure 8 The results of damage acoustic emission source localization using all analysis methods are shown. Among them, for the six comparison methods of (a) PAC acoustic emission acquisition system, (b) triangulation method, (c) deep learning, (d) Bayesian method, (e) SD, and (f) SD - SVD, the average RMS errors of acoustic emission source localization for the three laser cladding layers are 44.5 mm, 52.9 mm, 51.5 mm, 56.6 mm, 58.4 mm, and 41.8 mm respectively. Although these six methods can roughly locate the laser cladding acoustic emission source, their RMS localization errors are significantly higher than the method proposed in this application (18.5 mm, see Figure 8 in (e)), and the method proposed in this application has the lowest average absolute error compared with these methods.

[0119] More specifically, the comparison results of the RMS positioning errors of the seven methods are shown in Figure 9 . It can be clearly seen from Figure 9 that the method proposed in this application has the highest positioning accuracy for the damaged acoustic emission source compared with other comparison methods. Therefore, these comparison results further prove the advantages of the proposed method in the positioning of damaged acoustic emission sources in complex mechanical structures (i.e., laser cladding mechanical structures).

[0120] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A mechanical structure damage location method based on near-field frequency space sparse decomposition, characterized in that, It includes the following steps: S1. Perform frame-by-frame processing and fast Fourier transform on the original acoustic emission signal to obtain all frequency estimates of the original acoustic emission signal, and divide sub-bands according to the frequency estimates; S2. Construct the objective function of the near-field frequency space sparse decomposition algorithm based on the particle swarm optimization algorithm; S3. Perform L1 norm-singular value decomposition on the acoustic emission sub-bands of multiple snapshots to reduce the background noise and the number of redundant snapshots; S4. Construct an array manifold matrix for each sub-band and establish the product function of the over-complete dictionary array; S5. Sum the spatial spectra of all signal sub-bands to obtain the spatial spectrum of the acoustic emission signal, thereby realizing the localization of the acoustic emission source.

2. The mechanical structure damage location method based on near-field frequency space sparse decomposition according to claim 1, wherein The S1 includes the following steps: Process the original acoustic emission signal frame by frame to obtain an L-frame dataset X with a length of T and a frame shift of T / 2 l (t) (l = 1, 2, …, L), where each frame can be regarded as a short-time stationary signal; Obtain the data set X approximately through fast Fourier transform l All frequency estimates of (t), and divide sub-bands according to the frequency estimates, where each frequency point corresponds to the center frequency of the sub-band; Convert the frame of the time-domain signal obtained by the acoustic emission sensors through the array into a model in the frequency domain, and the expression is as follows: X l f = A Nl (x, y, f)S Nl f + N l f;(1) Where, X l (f) and S Nl (f) is the array received data set after fast Fourier transform for each frame, N l (f) is the noise vector, A Nl (x, y, f) is the direction matrix at each discrete point of each frame data set on N grids, x is X l (f) is the row index of the matrix, y is the number of sampling frequency points, that is, the number of discrete points of the signal spectrum in the frequency domain, f is the acoustic emission signal with noise, m is X l (f) is the number of rows of the matrix, N0 is the number of sub-bands.

3. The method for mechanical structure damage location based on near-field frequency space sparse decomposition according to claim 2, wherein The S2 includes the following steps: The particle swarm optimization algorithm regards the individuals in the population as particles searching in the multi-dimensional space, and characterizes these particles through position, velocity and fitness function; Let \(f = f\) s + f n , where \(f\) s is the original acoustic emission waveform, and \(f\) n is the original acoustic emission noise. Define the objective function as follows: Among them, g i represents traversing the elements in dictionary D; Reconstruct the signal by using the Hermitian inversion method, and the expression is as follows: Among them, H k is a Hermitian matrix represented in partitioned form, 0 k is a zero vector, ρ k is a scalar regularization term, and η k is a key component for recursively updating the matrix, d yk is an error vector, and the superscript T represents the transpose; When an inverse matrix is defined as Equation (5) is rewritten as: Among them, represents the inverse matrix at the (k - 1)th step, h k is the gradient vector, b k is the intermediate vector of the update direction; Let the overcomplete dictionary be converted into the currently updated matrix D Δk =[D Δk-1 g yk , where g yk is the best matching element after the current iterative update. Therefore, the update relationship of matrix D Δk is Θ Δk =[Θ Δk-1 d yk , where Θ Δk =φψ Δk , d yk =φg yk , φ is the observation matrix, and ψ Δk is the transformation matrix; Let be constructed in a cascaded manner, and finally the following Hermitian matrix is obtained: According to Equation (5), we get Thus, by substituting H k into Equation (6) to calculate the inverse recursive formula, a matrix for signal reconstruction using the near-field frequency-space sparse decomposition algorithm is obtained.

4. The mechanical structure damage location method based on near-field frequency space sparse decomposition according to claim 3, characterized in that The S3 includes the following steps: Suppose there are P given acoustic emission sources located at coordinates (x p , y p ), where p = 1, 2, …, P. The original acoustic emission signal is decomposed by fast Fourier transform at point N0, obtaining N l (f), where X l (f) corresponds to the frequency snapshot after decomposition of each subband, and represents the center frequency of the N0th subband; Therefore, the acoustic emission source direction matrix with P dimensions of m×P is expressed as follows: Among them, A p (x, y, f j ) has a column vector that is a guiding vector of m×1. By sampling the original acoustic emission signal in the frequency domain, multiple narrowband data sets corresponding to different center frequencies f j (j = 1, 2, …, N0) are obtained; Introduce the narrowband characteristic acoustic emission signal X(f j ), to determine the location of the acoustic emission source. Based on the sparsity of the acoustic emission source, sample N grids in the entire near-field region, and construct an over-complete sparse array popular basis matrix A N (x, y, f j ), and the expression is as follows: Among them, α m (x N , y N , f j ) represents the amplitude function of the signal, x N represents the abscissa of the Nth spatial position, and y N represents the ordinate of the Nth spatial position.

5. The mechanical structure damage location method based on near-field frequency space sparse decomposition according to claim 4, wherein The S4 includes the following steps: Solve the spatial spectrum of each sub-band signal in the entire spatial domain and construct a convex optimization model to process A N (x, y, f j ), to achieve the joint estimation of different frequency-domain snapshots at a single frequency point. The expression is as follows: Among them, ‖·‖ F denotes the Frobenius norm, X sv (f j ) represents the spatial domain signal observation matrix at the center frequency f j , S sv (f j ) represents the sparse signal estimation coefficient matrix at the center frequency f j , λ is the regularization parameter, represents the regularization norm solution at the center frequency f j .

6. The mechanical structure damage location method based on near-field frequency space sparse decomposition according to claim 5, characterized in that The S5 includes the following steps: By combining the non-sparse 2-norm with frequency-domain multi-snapshot sampling and using the sparse 1-norm for spatial sampling, the spatial spectrum of each sub-band signal in the entire spatial region is calculated by the following formula: P(x, y, f j ) = |S N (x, y, f j )| 2 ; (11) Sum all the spatial spectra calculated by formula (11) and find the spectral peak, thereby realizing the localization of the acoustic emission source, that is: Among them, S N (x, y, f j ) represents the signal spectrum component at the position (x, y) and the center frequency f j .

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