Multi-sensor correlation joint sparse expression steel rail structure health monitoring method

Abstract

The invention discloses a multi-sensor correlation joint sparse expression steel rail structure health monitoring method, which comprises the following steps of: firstly, carrying out multilayer wavelet packet transformation preprocessing on a signal, and then, providing a novel JSR (JavaScript Register) method by utilizing correlation difference among multichannel data so as to realize data fusion and damage information enhancement. In order to improve fusion efficiency and accuracy, a joint sparse adaptive matching pursuit algorithm (SAMP-AS) with adaptive step length is provided, and a joint sparse coefficient weighting algorithm and an adaptive threshold are designed in combination with sparsity difference to enhance real-time damage detection capability. According to the method, a plurality of vehicle-mounted sensors are installed on detection wheels, the limitation of the monitoring range of the sensors is broken through through mobile detection, accurate fusion and denoising of multi-sensor data are carried out by further combining a joint sparse expression algorithm with adaptive step length, and finally, high-precision and large-range steel rail SHM based on the AE technology is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of large-scale structural health monitoring (SHM) of rail tracks, and relates to a multi-channel data fusion and rail damage detection method based on acoustic emission (AE) technology under a noise background. Specifically, it relates to a method of joint sparse representation (JSR) improved based on correlation for large-scale multi-sensor rail SHM. Background Art

[0002] As a key component of the rail transit system, rails will experience fatigue, cracks and fractures over time due to frequent contact with train wheels, thus affecting safety and efficiency. In order to ensure the safety of rail transit and perform timely maintenance, it is imperative to conduct large-scale SHM on rails. Currently, the health monitoring technology based on AE has been favored due to its non-invasive, highly sensitive and simple equipment. However, complex wheel-rail rolling noise (WRRN) will be generated during the contact process between the wheel and the rail, and its frequency band partially overlaps with the damage signal, making it difficult to eliminate through simple filtering methods, reducing the accuracy of damage detection. Therefore, eliminating WRRN from the collected AE signals and avoiding noise drowning out the effective information of damage is an urgent issue in rail SHM. On the other hand, the traditional signal denoising method using a single sensor highly depends on the signal quality of the sensor, cannot cope with situations such as sensor failures, and is limited by the monitoring range of the sensor and cannot achieve large-scale rail SHM. At the same time, due to the high sensitivity of AE signals, their installation positions have a significant impact on the final damage detection accuracy. Summary of the Invention

[0003] Aiming at the problem that the existing rail SHM methods rely on a single sensor with a limited monitoring range and cannot effectively eliminate WRRN, resulting in false detections, the present invention combines multiple on-vehicle AE sensors to break through the detection range limit and provides a multi-sensor correlation joint sparse representation rail structural health monitoring method. This method installs multiple on-vehicle sensors on the detection wheel, breaks through the sensor monitoring range limit through mobile detection, and further combines a joint sparse representation algorithm with an adaptive step size for precise fusion and denoising of multi-sensor data, ultimately realizing high-precision large-scale rail SHM based on AE technology.

[0004] The object of the present invention is achieved through the following technical solutions:

[0005] A multi-sensor related joint sparse representation method for rail structural health monitoring. First, the signal is preprocessed by multi-layer wavelet packet transform (WPT). Then, based on the correlation differences among multi-channel data, a novel JSR method is proposed to achieve data fusion and damage information enhancement. To improve the fusion efficiency and accuracy, a joint sparse adaptive matching pursuit algorithm with adaptive step size (SAMP-AS) is proposed, and a joint sparse coefficient weighting algorithm and an adaptive threshold are designed in combination with the sparsity difference to enhance the real-time damage detection ability. The specific steps are as follows:

[0006] Step 1: Decompose the AE signal in each channel through WPT operation respectively, and reconstruct the preprocessed AE signal through the weighted and screened wavelet coefficients to eliminate random noise;

[0007] Step 2: To fuse the redundant damage information in multi-channel signals and eliminate the remaining WRRN therein, an improved JSR algorithm with correlation constraint is proposed. In this process, the K-order singular value decomposition (KSVD) algorithm is used to train the multi-channel sub-dictionary, and a correlation constraint term is added in the process of solving the dictionary atoms, so as to retain the damaged atoms and eliminate the invalid information atoms;

[0008] Step 3: Starting from the energy perspective, a SAMP-AS algorithm is proposed. This algorithm continuously adjusts the iteration step size through the short-time energy (STE) of the signal segment, shortens the step size in the damaged signal part and increases the step size in the noise part. Finally, the true sparsity of the signal is estimated through this adaptive step size, so as to residual eliminate WRRN and solve the joint sparse coefficient;

[0009] Step 4: According to the sparsity difference between the damage information and the noise, a weighting algorithm and an adaptive threshold based on the sparsity difference are proposed for efficient and accurate damage detection. This algorithm calculates the autocorrelation coefficient S of the multi-channel AE signal X preprocessed by WPT, and constructs the weight ω by using the correlation difference between the autocorrelation coefficient and the joint sparse coefficient, and uses it to weight the joint sparse coefficient Finally, use the weighted joint sparse coefficient Solve the adaptive threshold curve to accurately detect whether there is damage information.

[0010] Compared with the prior art, the present invention has the following advantages:

[0011] 1) An improved JSR algorithm with correlation constraints is proposed. By using the correlation difference, irrelevant dictionary atoms are filtered out, the damage information is enhanced, and the WRRN in the signal is eliminated at the same time.

[0012] 2) The SAMP-AS algorithm is innovated. By continuously adjusting the step size through the instantaneous energy, the sparsity information is accurately estimated, which is used to efficiently and accurately solve the joint sparse coefficients, laying a foundation for subsequent high-precision damage detection.

[0013] 3) By using the sparsity difference, a unique sparse coefficient weighting algorithm and an adaptive threshold are designed, bypassing the reconstruction process of the traditional JSR algorithm, and improving the accuracy and efficiency of damage detection.

[0014] 4) Through the analysis of experimental data, the optimal installation angle of vehicle-mounted sensors is determined, providing theoretical support for the design of mobile rail inspection vehicles and guiding the large-scale rail safety monitoring. Description of the Drawings

[0015] Figure 1 It is a conceptual schematic diagram of the multi-sensor correlated joint sparse representation rail structure health monitoring method.

[0016] Figure 2 It is a wheel-rail rolling experimental platform, (a) detection wheel and vehicle-mounted AE sensor, (b) AE data acquisition system.

[0017] Figure 3 It is a connection diagram of the installation positions of vehicle-mounted multi-sensors and AE signal acquisition experimental equipment.

[0018] Figure 4 It is the time-domain waveform and spectrum of multi-channel AE data collected at a 120-degree angle, (a) time-domain waveform of the signal of sensor one, (b) spectrum of the signal of sensor one, (c) time-domain waveform of the signal of sensor two, (d) spectrum of the signal of sensor two.

[0019] Figure 5 It is the time-domain signals of two sensors after WPT preprocessing at 120 degrees, (a) preprocessed signal of sensor one, (b) preprocessed signal of sensor two.

[0020] Figure 6 It is the autocorrelation coefficient of the original AE signal and the sparse coefficient vector collected by sensor one (the angle between the two sensors: 120 degrees).

[0021] Figure 7 It is the PSNR and KURT of the reconstructed fusion signal at the installation angle of each sensor.

[0022] Figure 8Comparison of the number of iterations required for SAMP-AS and traditional SAMP to achieve the target sparsity.

[0023] Figure 9 is the weighted joint sparse coefficient.

[0024] Figure 10 Adaptive thresholds and weighted joint sparse coefficients at different sensor angles, (a) 30 degrees, (b) 60 degrees, (c) 90 degrees, (d) 120 degrees, (e) 150 degrees, (f) 180 degrees. Detailed implementation manners

[0025] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0026] The present invention provides a multi-sensor related joint sparse representation method for rail structural health monitoring. First, the multi-channel AE signals collected are preprocessed by multi-layer WPT to eliminate the additive random noise in the signals. In order to enhance the damage information and eliminate WRRN, an improved JSR algorithm with correlation constraint is proposed for multi-channel data fusion and denoising. Subsequently, in order to improve the computational efficiency of the sparse process and the solution accuracy of the sparse coefficient, a new SAMP-AS algorithm is proposed. The prior information of sparsity is accurately estimated through automatic conditional iteration steps. In order to further improve the detection accuracy and real-time performance of the SHM system, a weighted algorithm based on sparsity difference and an adaptive threshold are innovated to accurately and efficiently detect the damage signals. In addition, through data analysis, the optimal installation angles between multiple vehicle-mounted AE sensors are given, providing support for the design of subsequent mobile rail damage detection vehicles and guidance for the practical application of large-scale rail SHM. As Figure 1 shown, the specific steps are as follows:

[0027] Step 1: For the rail structural health monitoring based on vehicle-mounted multi-sensors, the frequency distribution of AE signals is between 0.1 and 900 kHz. In these data, the damage signals are mixed with the modulation effect generated by WRRN during the wheel-rail rolling contact process. In WRRN, the noise distributed in the low-frequency part and obeying the Gaussian distribution is called random noise, and the other part is distributed in the high-frequency part, with a frequency band overlap with the effective damage information. The present invention first decomposes the AE signals in each channel through WPT operation, and reconstructs the preprocessed AE signals through the weighted and screened wavelet coefficients respectively to eliminate the random noise. The specific steps are as follows:

[0028] Step 1.1: For a multi-channel AE signal Among them, represents the signal corresponding to the z-th channel, where z represents the channel serial number of the signal, and Z c is the total number of channels, M is the number of elements in each column, N is the number of columns, i and j are the row serial number and column serial number in the entire matrix respectively, and the multi-layer WPT process can be formulated as follows:

[0029]

[0030] Among them, represents the wavelet space corresponding to the v-th scale coefficient, and t rans represents the translation variable, and ψ v is the parent function of which represents the positive integer domain.

[0031] Step 1.2: In order to eliminate the low-frequency part in WRRN, the gradient change based on the energy ratio of wavelet coefficients is used to track the change trend between noise and effective information, and it is judged whether the wavelet coefficients of the corresponding nodes should be retained. The formula is as follows:

[0032]

[0033] In the formula, is the weight of the wavelet coefficients at the -th scale, and τ c is the number of layers of WPT decomposition, and a total of wavelet nodes are generated.

[0034] Step 1.3: The wavelet coefficient nodes used for reconstructing the signal can be screened through the obtained wavelet coefficient weights , and then the inverse WPT operation is used to reconstruct the preprocessed multi-channel acoustic emission signal X for subsequent fusion and analysis. The formula is as follows:

[0035]

[0036] X = [X 1 , X 2 ,..., X z

[0037] In the formula, is the inverse wavelet packet transform, Ψ WPT represents the wavelet basis function, and X z represents the AE signal after WPT preprocessing of the z-th channel. Then, based on the wavelet coefficient nodes screened by weighting, the random noise in the multi-channel AE signal X after WPT preprocessing can be eliminated.

[0038] ​Step 2: To fuse the redundant damage information in multi-channel signals and eliminate the remaining WRRN, the present invention innovates an improved JSR algorithm with correlation constraints. In this process, the KSVD algorithm is used to train the multi-channel sub-dictionary, and a correlation constraint term is added in the process of solving the dictionary atoms, so as to retain the damaged atoms and eliminate the invalid information atoms. The specific steps are as follows:

[0039] The core idea of using SR theory for data fusion is to represent the original signal by searching for a set of sparse bases with the minimum error. For the AE signal X after WPT preprocessing in the z-th channel z , there exists a dictionary and a sparse coefficient matrix where, represents the k-th column dictionary atom in D z , K is the total number of dictionary atoms, and φ j z represents the j-th column sparse coefficient vector in Φ z . Then the input signal can be represented as follows:

[0040]

[0041] where ε is the regularization coefficient. The first term in the above formula is the error term, indicating that the reconstructed signal obtained by multiplying the dictionary and the sparse coefficient matrix should be as close as possible to the original signal. The second term is the sparsity constraint term, indicating that the sparse coefficients should have fewer non-zero elements to eliminate the redundant information in the signal.

[0042] Step 22: Considering the wheel rolling process, due to the modulation effect of the complex structure, the noise is attenuated inside the wheel. Due to the large energy consumption, more noise is collected by the sensor near the wheel-rail contact point; while the damage signal generated by lattice fracture has a small attenuation due to the concentrated energy release. The damage signals in multi-channel data have higher similarity or correlation than the noise. Therefore, as a supplementary information constraint, the cross-correlation between multi-channel data is added as a constraint term to the SR process, and the formula is as follows:

[0043]

[0044] where C(·) represents the cross-correlation function, j1 and j2 are the serial numbers of different sparse vector columns respectively, and are different sparse vectors respectively, and ε1 and ε2 are different constants. The third term in the above formula indicates that the algorithm searches for the global optimal solution in the direction of higher correlation during the solution process.

[0045] Step 3: Aiming at the problem that the traditional SR algorithm needs to preset parameters according to the prior information of signal sparsity, and the speed and accuracy of signal reconstruction cannot meet the requirements of a large-scale rail SHM system, the present invention starts from the energy perspective and proposes a SAMP-AS algorithm. This algorithm continuously adjusts the iteration step size through the STE of signal segments, shortens the step size in the damaged signal part to improve the detail resolution of the SR process, and increases the step size in the noise part to improve the calculation efficiency and avoid interference information. Finally, the true sparsity of the signal is estimated efficiently and accurately through this adaptive step size, so as to residual eliminate WRRN and solve the joint sparse coefficient. The specific steps are as follows:

[0046] Step 31: For the AE signal X after WPT preprocessing of the z-th channel z , set the initial residual where and are the N-th columns of the residual matrix and the signal matrix X z respectively, and then construct the candidate set Let the iteration number t = 1.

[0047] Step 32: Calculate the short-time energy f for each column signal in each channel of X E , and the formula is as follows:

[0048]

[0049] where represents the j-th column of the preprocessed signal X of the z-th channel z , and Γ represents the window function of the Hamming window. Subsequently, calculate the adaptive step size L a , and the formula is as follows:

[0050]

[0051] where the reconstructed signal and of the j-th column of the z-th channel are the j-th columns of the dictionary D z and the sparse coefficient matrix Φ z respectively, and σ represents the initial limit coefficient, which is used to limit the maximum value of the iteration step size. Subsequently, let the current iteration step size L = L a , and update the candidate set Θ z (t) with the following formula:

[0052]

[0053] where D z and They are the dictionary corresponding to the z-th channel signal after preprocessing and the residual of the t-th iteration. |<·>| represents the operation of taking the inner product, and MAX(| < D z ·r z |, L a ) means screening L z ·r z | from the inner products, extracting the corresponding atomic indices in D a , and then screening the k-th column atoms in D z from the candidate set. z The atoms in the updated dictionary corresponding to the z-th channel are obtained as follows: Update the atoms in the k-th column of D The formula is as follows:

[0054]

[0055] Step 33: Use each updated sub-dictionary to solve the updated sparse coefficient matrix corresponding to channel z The formula is as follows:

[0056]

[0057] In the formula, Φ z represents the sparse coefficient matrix before update corresponding to channel z.

[0058] Further update the set Λ z (t) of indices corresponding to channel z in this iteration, and screen the atoms with corresponding indices from Λ z (t) to form the new sub-dictionary for the (t + 1)-th iteration The formula is as follows:

[0059]

[0060] Then use the updated sub-dictionary to calculate the residual r n (t + 1) for the next iteration. The formula is as follows:

[0061]

[0062] Among them, r n (t + 1) is the sparse representation residual corresponding to the preprocessed multi-channel signal X generated in the (t + 1)-th iteration, f c (·) is the cross-correlation function, z1 and z2 are both channel indices, and Z c is the total number of signal channels. By calculating the residual r n (t + 1), the algorithm gradient is formed to achieve continuous iteration, and the signal X a is continuously estimated through the adaptive step size L zThe true sparsity. Using the residual r of each iteration n (t + 1) to determine whether the algorithm continues to iterate. When r n (t + 1) ≥ r n (t), then execute the following formula and return to step 32 to continue iterating: When r n (t + 1) < r n (t)

[0063]

[0064] When r n (t + 1) < r n (t), let t = t + 1 and return to step 32 to continue iterating until r n (t + 1) ≤ ε r , where ε r is the target residual, exit the iteration, and perform weighted fusion on the sparse coefficient matrices corresponding to all channels to obtain the fused joint sparse coefficient matrix The formula is as follows:

[0065]

[0066] Step 4: In order to avoid the reduction of detection efficiency in the calculation process of reconstructing the fused signal, the present invention proposes a weighted algorithm and an adaptive threshold based on the sparsity difference between the damage information and the noise interference for efficient and accurate damage detection. This algorithm calculates the autocorrelation coefficient S of the multi-channel AE signal X after WPT preprocessing, and constructs the weight ω by using the correlation difference between the autocorrelation coefficient and the joint sparse coefficient, and uses it to weight the joint sparse coefficient Finally, use the weighted joint sparse coefficient to solve the adaptive threshold curve for accurately detecting whether the damage information exists. The specific steps are as follows:

[0067] Step 41: For the multi-channel AE signal X after WPT preprocessing, calculate the autocorrelation coefficient S of each column in it j , the formula is as follows:

[0068]

[0069] Among them, f xcorr (·) is the autocorrelation coefficient function, represents the average value of the j-th column signal in the z-th channel of the preprocessed multi-channel AE signal X, represents the i-th element of the j-th column signal in the z-th channel of the preprocessed multi-channel AE signal X, and τ represents the number of delay points. Then all S j can form the autocorrelation vector S.

[0070] Step 42: In fact, since the joint sparse coefficient is the mapping of the original signal in the sparse domain, the relevant characteristics can still be maintained after JSR reconstruction. By solving the difference C = [c j |j = 1, 2,..., N] between the autocorrelation coefficient of the joint sparse coefficient and S, the characteristics of the damage information can be effectively enhanced. The formula is as follows:

[0071]

[0072] N or (x) = [x - min(x)] / [max(x) - min(x)]

[0073]

[0074] where max(·) and min(·) represent the maximum value and the minimum value respectively, is the j-th column in the joint sparse coefficient matrix, ρ = 0.1 is the penalty factor, and both δ1 = 0.45 and δ2 = 0.2 are constants. δ1 is used to calculate the peak value of the autocorrelation difference, while δ2 is used for the range of variance change. When the variance is too large, it indicates that the sparsity of the corresponding signal has changed drastically, suggesting that the signal is interference information. Otherwise, this segment of the signal is considered damage information, and c j is used to weight it to obtain

[0075] Step 43: For the weighted joint sparse coefficient Since the correlation of the damage signal is much higher than that of the noise, only by finding the correct peak value can the damage be identified. Therefore, the formula for constructing the adaptive threshold T is as follows:

[0076]

[0077] where b = 100 represents the total number of segments included in each column of the signal after being divided by the detection window, represents the i-th element in the j-th column weighted sparse coefficient vector, and η = 1.5 is a constant. The total number of segments b determines the detection resolution. The larger b is, the stronger the anti-interference ability is, and the smaller b is, the higher the detection sensitivity is. By detecting the occurrence time of the damaged signal through the adaptive threshold, efficient and accurate large-range rail SHM can be achieved.

[0078] Example:

[0079] To simulate the environment of wheel-rail rolling contact, a wheel-rail rolling experimental platform was established in this example, as Figure 2As shown. The platform includes an actual train wheel 1 (in-service wheel), an experimental rail 2 cut from an in-service rail (made of U75V steel), AE sensor 3 (model: RIC-900) and AE sensor 4 (model: RIC-900) fixed on the wheel rim by a magnetic fixture for collecting signals, AE sensor 5 (model: 1045s) fixed on the rail waist by a magnetic fixture for sending pre-stored standard damage signals, and a pull rod for pulling the rail. As Figure 2 shown on the right, the platform includes a laptop computer 6 (recording the waveform stream information of the signal), an AE signal acquisition system 7 (model: Vallen AMSY-6), an oscilloscope 8 (monitoring the simulated damage signal), an arbitrary waveform generator 9 (model: Tektronix AFG3101) for generating simulated signals, and a magnetic fixture, a gate signal generator 10 (model: Agilent 33220A) for controlling the signal transmission interval, a high-voltage amplifier 11 (model: Ritec GA-2500A), a 50-ohm high-power terminal impedance 12, and a 6 dB fixed attenuation 13. To verify the effectiveness of the method proposed in the present invention, an on-vehicle multi-sensor wheel-rail signal acquisition experiment was carried out, and multiple sensor angles were used in the experiment. The installation positions of the on-vehicle multi-sensors and the connection method of the AE signal acquisition experimental equipment are as Figure 3 shown.

[0080] In this experiment, two RIC-900 AE sensors were fixed on the wheel rim at a 30-degree angle by a magnetic fixture. The two sensors and the laptop computer were connected to the Vallen AMSY-6 AE signal acquisition system through shielded cables to collect and record signals. The 1045S AE sensor was connected to the high-voltage amplifier through a magnetic clamp at the rail waist and a shielded wire passing through a 6 dB fixed attenuation and a 50-ohm safety load. In addition, the high-voltage amplifier, the arbitrary waveform generator, and the gate generator were connected in series and connected to the oscilloscope to monitor the output waveform. Subsequently, the pre-acquired simulated damage signal was input into the arbitrary waveform generator and periodically transmitted to the rail at an interval of 1 s.

[0081] The standard damage signal comes from a standard tensile test, which has been proven in previous work to effectively simulate real rail damage signals. Then, the rail was pulled by the pull rod to make the wheel roll on the rail, thereby generating wheel-rail rolling noise. The AE sensors on the wheel captured the noise after being modulated by the wheel-rail contact surface and the simulated damage signal. The sampling frequency was set to 5 MHz. The captured signals were recorded in the form of multi-channel data collected at the current sensor angle. Then, the sensors were re-arranged at angles of 60, 90, 120, 150, and 180 degrees, and the above experimental steps were repeated. The experiment was repeated 10 times at each angle, and a total of 60 groups of multi-channel data were obtained for further analysis.

[0082] Step 1: Based on the above experimental steps, the present invention obtains the complete multi-channel data for each detection wheel rolling period. Among the collected multi-channel data, the signal spectra collected by the two sensors at a sensor angle of 120 degrees are as Figure 4 shown. Comparing Figure 4 (a) and (b), the signal collected by Sensor 2 contains more noise signals because Sensor 2 is closer to the track during the wheel pair process. Comparing Figure 4 (c) and (d), the signal frequencies are mainly distributed in the frequency band range of 0 - 0.5 MHz. In the part where the frequency exceeds 0.5 MHz, there are also a small number of frequency bands distributed, mainly caused by high-frequency damage signals and harmonics generated by WRRN during the modulation process. Compared with the stationary state, the noise during the rolling process increases sharply, drowning out the damage signals and hindering damage detection based on the time-domain waveform.

[0083] To remove the random noise in the signal, the present invention integrates the AE signals collected by the two sensors into a multi-channel signal in columns, and then performs 4-layer WPT decomposition based on the Biorthogonal wavelet basis, and screens the wavelet coefficient nodes to be retained (the second node) through weighting. Since the characteristic differences between the damage signal and the noise are mainly distributed in the high-frequency band, while the main energy of the random noise signal is distributed in the low-frequency band. Therefore, performing the inverse WPT operation based on the wavelet coefficients of this frequency band node can reconstruct the preprocessed multi-channel AE signal to eliminate random noise. The multi-channel signal after 4-layer WPT preprocessing by the two sensors at 120 degrees is as Figure 5 shown.

[0084] For the signal of Sensor 1, the random noise in the multi-channel AE signal after WPT preprocessing is basically eliminated between 2.5 - 4 s. For the signal of Sensor 2, the same denoising effect is also achieved. Most of the damage signals can be found through the time-domain waveform. Since there is partial overlap between WRRN and the damage spectrum, there are still some high-amplitude noise signals that cannot be eliminated by WPT preprocessing. In addition, comparing Figure 5 (a) and (b), the waveforms of the preprocessed signals are significantly different in the noise part. By fusing the data of the two sensor channels and conducting a more comprehensive analysis of the signal characteristics, it helps to further denoise and detect damage. Therefore, the present invention proposes a JSR algorithm with correlation constraints to fuse multi-channel signals, eliminate WRRN, and uses the SAMP-AS algorithm with an adaptive step size to improve the accuracy and speed of the fusion result.

[0085] Step 2: Organize the data of each sensor into a signal matrix with 2048 sampling points in each column, which serves as the input of JSR. Finally, a sparse coefficient matrix is obtained, fusing the data of the two sensors. To clearly show the relationship between the sparse coefficient matrix and the original multi-channel data, the autocorrelation coefficients of the original AE signal and the sparse coefficient vector collected by Sensor 1 are as Figure 6 shown.

[0086] The blue line and the red line respectively represent the autocorrelation of the original signal of Sensor 1 and the autocorrelation of the sparse coefficient matrix over time. In addition, there are periodic amplitude spikes indicating damaged signals, with each interval being 1 second. Compared with the original signal, the autocorrelation coefficient of the sparse coefficient contains fewer noise spikes. The spikes at the positions of the noise signals change more than those at the positions of the damaged signals. In the multi-channel signal, JSR eliminates the noise components at the positions of the damaged signals, making the damage information more prominent. The correlation of the noise signal changes violently, while the correlation of the damaged signal changes less. For example, the spike signals at 2.47 seconds and 3.45 seconds change by 50% and 87.5% respectively compared with those before fusion using the JSR algorithm with correlation constraints, indicating that the spike signals at these two positions are noise. In contrast, the change rate at other spike positions does not exceed 40%.

[0087] It should be noted that different angles between the two sensors will seriously affect the effect of JSR. A slight sensor angle will result in a large amount of duplicate information between the multi-channel data, making the JSR process require more sufficient damage information and reducing the quality of the fused sparse coefficients. On the contrary, although a too large sensor angle can ensure the complementarity between the multi-channel data, it will cause the sensor to be far away from the rail. The limitation of the receiving range will reduce the quality of the received signal and affect the subsequent damage detection. Therefore, it is necessary to find the optimal angle between the sensors. To clearly show the effectiveness of JSR at different sensor angles, the fused signal is reconstructed based on the obtained joint sparse coefficients, and the formula is as follows:

[0088]

[0089] Furthermore, the Peak Signal-to-Noise Ratio (PSNR) is used as an evaluation index. The higher the PSNR value, the better the quality of the sparse coefficient matrix after JSR. The calculation method of PSNR is as follows:

[0090]

[0091] where represents the mean square error value of the signal , is The j-th column in. In addition, the average kurtosis KURT is introduced to quantify the enhancement of damage information in the JSR results of each sensor installation angle. The formula is as follows:

[0092]

[0093] where E a [·] represents the fused signal of the expectation, μ and σ represent respectively the mean and variance of.

[0094] The PSNR and KURT of the reconstructed fused signal at each sensor installation angle are as Figure 7 shown. In terms of PSNR, the maximum value of the fused signal at 120 degrees is 11.87, which is 1.626 dB higher than that at 90 degrees. Similarly, the KURT of the fused signal also performs well at 120 degrees, reaching 8.33, which is 2.11 dB higher than the second place. From 30 degrees to 120 degrees, the PSNR and KURT gradually increase and then continue to decline. The reason for the increase in PSNR between 30 and 120 degrees is that as the angle between sensors increases, the energy of the damaged signal is more concentrated and the penetration power is greater than that of the noise. When the sensor angle continuously increases starting from 120 degrees, due to the propagation distance, the sensor cannot effectively receive the damaged signal, resulting in a decrease in the denoising effect. The above results show that the optimal installation angle of the vehicle-mounted multi-sensor based on AE technology is 120 degrees.

[0095] Execute Step 3: The SAMP-AS algorithm adjusts the iteration step size through the STE feature to improve the calculation speed and accuracy. To illustrate the advantage of the SAMP-AS algorithm in terms of calculation speed, a random signal with a length of 2048 is constructed. The improved SAMP algorithm and the traditional SAMP algorithm are respectively used to reconstruct the random signal. The restriction factor is set to 5. Since the traditional SAMP algorithm has the highest iteration accuracy when the step size is small, 1 is used as the initial step size, and the results are as Figure 8 shown. In Figure 8 SAMP-AS only needs 34 iterations to reach a signal sparsity of 54, and the calculation time is reduced by 74.18%. The results show that the SAMP-AS algorithm can perform faster JSR operations on the signal while ensuring accuracy by adaptively adjusting the iteration step size.

[0096] Execute Step 4: The present invention uses a penalty factor to weight the autocorrelation difference of the sparse coefficients to eliminate the interference of WRRN. To illustrate the effectiveness of the proposed method, based on the sparse coefficients generated by 120-degree multi-channel data fusion, the penalty factor is used to weight the autocorrelation difference. The weighted joint sparse coefficients are as Figure 9As shown, all high-amplitude WRRNs are eliminated. All damaged signals become obvious in the weighted autocorrelation difference and have an amplitude higher than other noises or interferences.

[0097] Finally, the adaptive threshold proposed in the present invention is used for damage detection based on the weighted joint sparse coefficients. The detection results at six different installation angles of in-vehicle AE sensors are as Figure 10 shown. In the detection results, the interval of all damaged signals is 1 second, which is consistent with the transmission interval of the simulated damaged signals in the experiment. With the arrival of interference noises, the threshold will adaptively increase to minimize the occurrence of false detections. Then, the threshold will return to a lower level to maintain the sensitivity of damage detection. In addition, in Figure 10 (c) and (d), although all damages can be detected, there is still some noise close to the adaptive threshold. These high-amplitude interferences are caused by the extrusion of iron filings or dust on the rail surface, which may generate AE signals, resulting in greater noise than that collected at other sensor angles. Among a total of 60 groups of data, all damage signals are detected by the adaptive threshold without false detections. The above results show that the method proposed in the present invention can quickly and accurately fuse multi-channel data. By weighting the fused sparse coefficients, the high-amplitude WRRN interference is successfully eliminated. Finally, an adaptive threshold is constructed to detect damage signals in the data at all sensor angles, providing a theoretical guidance for the practical application of large-scale in-vehicle multi-sensor rail SHM based on AE technology.

Claims

1. A multi-sensor correlation joint sparse expression rail structure health monitoring method, characterized in that The method comprises the following steps: Step 1: Decompose the AE signal in each channel through the WPT operation, and reconstruct the preprocessed AE signal through the weighted filtered wavelet coefficients to eliminate random noise; Step 2: In order to fuse the redundant damage information in the multi-channel signal and eliminate the residual WRRN, an improved JSR algorithm with correlation constraints is proposed. In this process, the KSVD algorithm is used to train the multi-channel sub-dictionary, and the correlation constraint term is added in the dictionary atom solution process, so as to retain the damage atoms and eliminate the invalid information atoms. Step 3: From the energy perspective, a joint sparse adaptive matching pursuit algorithm with adaptive step size is proposed. The algorithm continuously adjusts the iteration step size according to the short-term energy of the signal segment, shortens the step size in the damaged signal part, and increases the step size in the noise part. Finally, the real sparsity of the signal is estimated through the adaptive step size, thereby residually eliminating WRRN and solving the joint sparse coefficient. Step 4: According to the sparsity difference between the damage information and the noise, a weighted algorithm based on sparsity difference and an adaptive threshold are proposed for efficient and accurate damage detection. The algorithm calculates the autocorrelation coefficient S of the multi-channel AE signal X after WPT preprocessing, and uses the correlation difference between the autocorrelation coefficient and the joint sparse coefficient to construct the weight ω, which is used to weight the joint sparse coefficient. Finally, the weighted joint sparse coefficient is used Solve the adaptive threshold curve to accurately detect whether damage information exists.

2. The multi-sensor correlation joint sparse expression rail structure health monitoring method according to claim 1 is characterized in that The specific steps of step 1 are as follows: Step 1.1: For a multi-channel AE signal in, Indicates the signal corresponding to the zth channel, z represents the channel number of the signal, Z c is the total number of channels, M is the number of elements in each column, N is the number of columns, i and j are the row and column numbers in the entire matrix respectively, and the multi-layer WPT process is formulated as follows: in, represents the wavelet space corresponding to the vth scale coefficient, t rans represents the translation variable, ψ v for The parent function of represents the domain of positive integers; Step 1.2: In order to eliminate the low-frequency part in WRRN, the change trend between noise and effective information is tracked based on the gradient change of wavelet coefficient energy ratio, and whether the wavelet coefficient of the corresponding node should be retained is determined by the following formula: In the formula, For the The weight of the wavelet coefficients at each scale, τ c is the number of layers decomposed by WPT, a total of wavelet nodes; Step 1.3: Obtain the wavelet coefficient weights The wavelet coefficient nodes used to reconstruct the signal are selected, and then the preprocessed multi-channel acoustic emission signal X is reconstructed using the inverse WPT operation for subsequent fusion and analysis. The formula is as follows: In the formula, is the inverse wavelet packet transform, Ψ WPT represents the wavelet basis function, X z It represents the AE signal after WPT preprocessing of the zth channel.

3. The multi-sensor correlation joint sparse expression rail structure health monitoring method according to claim 1 is characterized in that The specific steps of step 2 are as follows: Step 21: For a z-th channel WPT preprocessed AE signal X z , there exists a dictionary and a sparse coefficient matrix in, Indicates D z The kth column of dictionary atoms in , K is the total number of dictionary atoms, Represents Φ z The j-th column sparse coefficient vector in , then the input signal is represented as follows: Among them, ε is the regularization coefficient; Step 22: As a supplementary information constraint, the cross-correlation between multi-channel data is added as a constraint term to the SR process, and the formula is as follows: Where C(·) represents the cross-correlation function, j1 and j2 are different sparse vector column numbers, and are different sparse vectors, ε1 and ε2 are different constants.

4. The multi-sensor correlation joint sparse expression rail structure health monitoring method according to claim 1 is characterized in that The specific steps of step 3 are as follows: Step 31: For a z-th channel WPT preprocessed AE signal X z , set the initial residual in, and are the residual matrix and signal matrix X respectively z The Nth column in the Let the number of iterations t = 1; Step 32: Calculate the short-time energy f for each column of signal in each channel in X E , the formula is as follows: Among them, x j z Represents the signal X after preprocessing of the zth channel z In the j-th column, Γ represents the window function of the Hamming window; Calculate the adaptive step size L a , the formula is as follows: Among them, the reconstructed signal of the jth column of the zth channel is and D z and the sparse coefficient matrix Φ z In the jth column of , σ represents the initial restriction coefficient; Let the current iteration step length L = L a , update the candidate set Θ of the tth iteration z (t) The formula is as follows: Among them, D z and are the dictionary corresponding to the z-th channel signal after preprocessing and the residual of the t-th iteration, respectively. |〈·>| represents the inner product operation. MAX(| <D z ·r z 〉|,L a ) means from |〈D z ·r z 〉|Screen L in the inner product a The largest value is extracted from D z The corresponding atomic number in; Select D from the candidate set z The k-th column of atoms in Update and get the dictionary corresponding to the zth channel after the update The formula is as follows: Step 33: Use each updated sub-dictionary separately Solve the updated sparse coefficient matrix corresponding to channel z The formula is as follows: In the formula, Φ z Represents the sparse coefficient matrix before update corresponding to channel z; Further update the sequence number set Λ corresponding to the channel z of this iteration z (t), and from Λ z The atoms with corresponding serial numbers in (t) are selected to form a new sub-dictionary for the t+1th iteration. The formula is as follows: Use the updated sub-dictionary to calculate the residual r of the next iteration n (t+1), the formula is as follows: Among them, r n (t+1) is the sparse expression residual corresponding to the preprocessed multi-channel signal X generated by the t+1th iteration, f c (·) is the cross-correlation function, z1 and z2 are channel numbers, Z c is the total number of signal channels; By calculating the residual r n (t+1) forms the algorithm gradient, realizes continuous iteration, and continuously passes the adaptive step size L a Estimated signal X z The true sparsity of Using the residual r of each iteration n (t+1) to decide whether the algorithm continues to iterate. n (t+1)≥r n (t), then execute the following formula and return to step 32 to continue iteration: n (t+1)<r n (t) When n (t+1)<r n (t), set t = t + 1 and return to step 32 to continue iterating until r n (t+1)≤ε r , where ε r is the target residual, exits the iteration, and performs weighted fusion on the sparse coefficient matrices corresponding to all channels to obtain the fused joint sparse coefficient matrix The formula is as follows:

5. The multi-sensor correlation joint sparse expression rail structure health monitoring method according to claim 1 is characterized in that The specific steps of step 4 are as follows: Step 41: For the multi-channel AE signal X after WPT preprocessing, calculate the autocorrelation coefficient S of each column j , the formula is as follows: Among them, f xcorr (·) is the autocorrelation coefficient function, represents the average value of the jth column signal in the zth channel of the preprocessed multi-channel AE signal X, represents the i-th element of the j-th column signal in the z-th channel of the preprocessed multi-channel AE signal X, τ represents the number of delay points, and all S j Construct the autocorrelation vector S; Step 42: By solving the difference between the autocorrelation coefficient of the joint sparse coefficient and S, C = [c j |j=1,2,...,N] enhances the damage information characteristics, the formula is as follows: N or (x)=[x-min(x)] / [max(x)-min(x)] Among them, max(·) and min(·) respectively represent the maximum value and the minimum value. is the jth column in the joint sparse coefficient matrix, ρ is the penalty factor, δ1 and δ2 are both constants; Step 43: The formula for constructing the adaptive threshold T is as follows: Where b represents the total number of fragments contained in each column of the signal after being divided by the detection window. It represents the i-th element in the j-th column of the weighted sparse coefficient vector, η is a constant, and the occurrence moment of the damage signal is detected by adaptive threshold to achieve large-scale rail SHM.

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