A multi-sensor correlation joint sparse representation method for rail structure health monitoring

Abstract

The application discloses a multi-sensor related joint sparse expression rail structure health monitoring method, first, signal is preprocessed by multi-layer wavelet packet transformation, then, a new JSR method is proposed by using the correlation difference between multi-channel data to realize data fusion and damage information enhancement. In order to improve the fusion efficiency and accuracy, a joint sparse adaptive matching pursuit algorithm (SAMP-AS) with an adaptive step is proposed, and a joint sparse coefficient weighting algorithm and an adaptive threshold are designed in combination with the sparse difference to enhance the real-time damage detection capability. The method breaks through the limitation of the sensor monitoring range by installing multiple vehicle-mounted sensors on the detection wheel, and further combines the joint sparse expression algorithm with the adaptive step to accurately fuse and denoise the multi-sensor data, and finally realizes high-precision large-range rail SHM based on the AE technology.

Description

TECHNICAL FIELD

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

[0002] As a key component of rail transit systems, rails will develop fatigue, cracks and fractures over time due to frequent contact with train wheels, thereby affecting safety and efficiency. In order to ensure the safety of rail transit and timely maintenance, large-scale SHM of rails is imperative. At present, AE-based health monitoring technology is favored for its non-invasiveness, high sensitivity and simple equipment. However, complex wheel-rail rolling noise (WRRN) is generated during the contact between the wheel and the rail, and the frequency band of the WRRN partially overlaps with the damage signal, which is difficult to eliminate by simple filtering methods, thereby reducing the accuracy of damage detection. Therefore, it is an urgent task for rail SHM to eliminate WRRN from the collected AE signals and avoid noise from drowning out effective damage information. On the other hand, the traditional single-sensor signal denoising method is severely dependent on the signal quality of the sensor and cannot cope with sensor failure and other situations, 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 the AE signal, the installation position has a significant impact on the final damage detection accuracy. SUMMARY

[0003] In view of the problem that the existing rail SHM method relies on a single sensor with limited monitoring range and cannot effectively eliminate WRRN, causing false detection, the present application combines multiple vehicle-mounted AE sensors, breaks through the detection range limitation, and provides a multi-sensor related joint sparse representation rail structural health monitoring method. The method installs multiple vehicle-mounted sensors on the detection wheel, breaks through the sensor monitoring range limitation through mobile detection, and further combines a joint sparse representation algorithm with an adaptive step for accurate fusion and denoising of multi-sensor data, and finally realizes high-precision large-scale rail SHM based on AE technology.

[0004] The purpose of the present application is realized by the following technical solutions:

[0005] A multi-sensor correlation joint sparse representation method for rail structure health monitoring is proposed. First, the signals are preprocessed using multi-level wavelet packet transform (WPT). Then, utilizing the correlation differences between multi-channel data, a novel JSR method is proposed to achieve data fusion and damage information enhancement. To improve fusion efficiency and accuracy, a joint sparse adaptive matching pursuit algorithm with adaptive step size (SAMP-AS) is proposed. Furthermore, a joint sparse coefficient weighting algorithm and adaptive threshold are designed based on sparsity differences to enhance real-time damage detection capabilities. The specific steps include the following:

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

[0007] Step 2: In order to fuse redundant damage information in multi-channel signals and eliminate residual WRRN, an improved JSR algorithm with correlation constraints is proposed. In this process, the K-order singular value decomposition algorithm (KSVD) is used to train the multi-channel sub-dictionary, and a correlation constraint term is added in the dictionary atom solution process, thereby retaining the damaged atoms and eliminating the invalid information atoms.

[0008] Step 3: From an energy perspective, a SAMP-AS algorithm is proposed. This algorithm continuously adjusts the iteration step size by using the short-time energy (STE) of the signal segment. The step size is shortened in the damaged signal part and increased in the noise part. Finally, the true sparsity of the signal is estimated by using this adaptive step size, thereby eliminating WRRN and solving the joint sparsity coefficient.

[0009] Step 4: Based on the sparsity difference between damage information and noise, a weighted algorithm based on sparsity difference and an adaptive threshold are proposed 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 using the correlation difference between the autocorrelation coefficient and the joint sparsity coefficient, which is then used to weight the joint sparsity coefficient. Finally, the weighted joint sparsity coefficient is used. Solve for the adaptive threshold curve to accurately detect the presence of 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, which uses correlation differences to filter out irrelevant dictionary atoms, enhances the damage information, and eliminates WRRN in the signal.

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

[0013] 3) By utilizing the sparsity difference, a unique sparse coefficient weighting algorithm and adaptive threshold were designed, which bypassed the reconstruction process of the traditional JSR algorithm and improved the accuracy and efficiency of damage detection.

[0014] 4) Through the analysis of experimental data, the optimal installation angle of the vehicle-mounted sensor was determined, providing theoretical support for the design of mobile rail inspection vehicles and guidance for large-scale rail safety monitoring. Attached Figure Description

[0015] Figure 1 A conceptual diagram illustrating a multi-sensor correlation joint sparse representation method for monitoring the health of rail structures.

[0016] Figure 2 For the wheel-rail rolling test platform, (a) the detection wheel and the on-board AE sensor, and (b) the AE data acquisition system.

[0017] Figure 3 This diagram shows the installation locations of the vehicle-mounted multi-sensor and the connection to the AE signal acquisition experimental equipment.

[0018] Figure 4 The time-domain waveforms and spectra of multi-channel AE data acquired at a 120-degree angle are shown below: (a) Time-domain waveform of sensor 1 signal, (b) Spectrum of sensor 1 signal, (c) Time-domain waveform of sensor 2 signal, and (d) Spectrum of sensor 2 signal.

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

[0020] Figure 6 The autocorrelation coefficient is the original AE signal and sparse coefficient vector acquired by sensor 1 (angle between the two sensors: 120 degrees).

[0021] Figure 7 PSNR and KURT of the fused signal reconstructed at each sensor mounting angle.

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

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

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

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0026] This invention provides a multi-sensor correlation joint sparse representation method for rail structure health monitoring. First, multi-channel AE signals are preprocessed using a multi-layer WPT to eliminate additive random noise. To enhance damage information and eliminate WRRN (Warning-Related Noise Reduction), an improved JSR algorithm with correlation constraints is proposed for multi-channel data fusion and denoising. Subsequently, to improve the computational efficiency of the sparse process and the accuracy of sparse coefficient calculation, a novel SAMP-AS algorithm is proposed. Prior information on sparsity is accurately estimated through an automatic conditional iteration step. To further improve the detection accuracy and real-time performance of the SHM (Surplus Damage Monitoring) system, an innovative weighted algorithm based on sparsity differences and an adaptive threshold are proposed for accurate and efficient detection of damage signals. Furthermore, data analysis provides the optimal installation angle between multiple vehicle-mounted AE sensors, supporting the design of subsequent mobile rail damage detection vehicles and guiding the practical application of large-scale rail SHM. Figure 1 As shown, the specific steps are as follows:

[0027] Step 1: For rail structure health monitoring based on onboard multi-sensor systems, the frequency distribution of the AE (Advanced Effect) signal is between 0.1 and 900 kHz. In these data, the damage signal is superimposed with the modulation effect generated by the WRRN (Wheel-Rail Rolling Contact) during wheel-rail rolling contact. In the WRRN, noise distributed in the low-frequency portion and following a Gaussian distribution is called random noise, while another portion is distributed in the high-frequency portion, overlapping with the effective damage information in frequency band. This invention first decomposes the AE signal in each channel using WPT (Wheel-Pulse Test) and then reconstructs the preprocessed AE signal using weighted and filtered wavelet coefficients to eliminate random noise. The specific steps are as follows:

[0028] Step 1.1: For a multi-channel AE signal in, This represents the signal corresponding to the z-th channel, where z represents the channel number of the signal. c Let M be the total number of channels, N be the number of elements in each column, and i and j be the row and column indices in the entire matrix, respectively. The multi-level WPT process can be formulated as follows:

[0029]

[0030] in, Let t represent the wavelet space corresponding to the v-th scaling coefficient. rans ψ represents the translation variable. v for The parent function, Represents a positive integer field.

[0031] Step 1.2: To eliminate the low-frequency components in WRRN, the gradient change of the wavelet coefficient energy ratio is used to track the changing trend between noise and effective information, and to determine whether the wavelet coefficients of the corresponding nodes should be retained. The formula is as follows:

[0032]

[0033] In the formula, For the first The weights of the wavelet coefficients at each scale, τ c The number of levels in the WPT decomposition, generating a total of Wavelet nodes.

[0034] Step 1.3: Weighting the obtained wavelet coefficients Wavelet coefficient nodes can be selected for signal reconstruction, and then the preprocessed multi-channel acoustic emission signal X can be reconstructed using inverse WPT operation for subsequent fusion and analysis. The formula is as follows:

[0035]

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

[0037] In the formula, For wavelet packet inverse transform, Ψ WPT Let X represent the wavelet basis function. z Let X represent the AE signal after WPT preprocessing of the z-th channel. Based on the weighted selection of wavelet coefficient nodes, random noise in the multi-channel AE signal X can be eliminated after WPT preprocessing.

[0038] Step 2: To fuse redundant impairment information in multi-channel signals and eliminate residual WRRNs, this 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 during the dictionary atom solving process, thereby retaining the damaged atoms and eliminating invalid information atoms. The specific steps are as follows:

[0039] Step 21: 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 smallest error. For an AE signal X after WPT preprocessing in the z-th channel... z There exists a dictionary and a sparse coefficient matrix in, D represents z The dictionary atom in the k-th column, where K is the total number of dictionary atoms, φ j z Φ z Given the j-th column of the sparse coefficient vector in the matrix, 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, which means that the reconstructed signal obtained by multiplying the dictionary and the sparse coefficient matrix should be as close as possible to the original signal, and the second term is the sparsity constraint term, which means that the sparse coefficients should have fewer non-zero elements to eliminate redundant information in the signal.

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

[0043]

[0044] Where C(·) represents the cross-correlation function, and j1 and j2 are the different sparse vector column indices, and Let ε1 and ε2 be different sparse vectors, and let ε1 and ε2 be different constants. The third term in the above equation indicates that the algorithm searches for the global optimal solution in the direction of higher relevance during the solution process.

[0045] Step 3: Addressing the issue that traditional SR algorithms require pre-setting parameters based on prior information about signal sparsity, resulting in speed and accuracy limitations for large-scale rail SHM systems, this invention proposes a SAMP-AS algorithm from an energy perspective. This algorithm continuously adjusts the iteration step size through the STE of signal segments. In damaged signal sections, the step size is shortened to improve the detail resolution of the SR process; in noisy sections, the step size is increased to improve computational efficiency and avoid interference. Finally, this adaptive step size efficiently and accurately estimates the true sparsity of the signal, thereby eliminating residual interference (WRRN) and solving for the joint sparsity coefficients. The specific steps are as follows:

[0046] Step 31: For an AE signal X preprocessed by WPT in the z-th channel... z Set initial residual in, and The residual matrix and the signal matrix X are respectively. z The Nth column in the dataset is used to construct the candidate set. Let the number of iterations be t = 1.

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

[0048]

[0049] in, X represents the signal after preprocessing of the z-th channel. z In the j-th column, Γ represents the window function of the Hamming window. Then, the adaptive step size L is calculated. a The formula is as follows:

[0050]

[0051] Among them, the reconstructed signal of the z-th channel and the j-th column and D, respectively z and sparse coefficient matrix Φ z In the j-th column of the diagram, σ represents the initial constraint coefficient, which is used to limit the maximum value of the iteration step size. Then, the current iteration step size is set to L = L... a Update the candidate set Θ for the t-th iteration. z The formula for (t) is as follows:

[0052]

[0053] Among them, D z and Let be 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 ) indicates from | <D z ·r z Filter L from the inner product of >| a Find the largest value and extract it in D. z The corresponding atomic number is then used to select D from the candidate set. z The kth column of atoms Perform an update to obtain the dictionary corresponding to the z-th channel after the update. The formula is as follows:

[0054]

[0055] Step 33: Utilize each updated sub-dictionary separately. Solve for the updated sparse coefficient matrix for the corresponding channel z. The formula is as follows:

[0056]

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

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

[0059]

[0060] Then, the residual r for the next iteration is calculated using the updated sub-dictionary. n (t+1), the formula is as follows:

[0061]

[0062] Where, r n (t+1) represents the sparse representation residual of the preprocessed multi-channel signal X generated in the (t+1)th iteration, f c (·) represents the cross-correlation function, where z1 and z2 are channel indices. c This represents the total number of signal channels. The residual r is calculated. n (t+1) forms the algorithm gradient, enabling continuous iteration, and continuously adjusting the adaptive step size L. a Estimated signal X zThe true sparsity. Utilizing the residual r from each iteration. n (t+1) is used 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 When (t), let t = t + 1 and return to step 32 to continue iterating until r. n (t+1)≤ε r , where ε r To obtain the target residual, exit the iteration and perform a weighted fusion of 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: To avoid reducing detection efficiency during the reconstruction and fusion signal calculation process, this invention proposes a weighted algorithm based on the sparsity difference between damage information and noise interference, along with an adaptive threshold, for efficient and accurate damage detection. This algorithm calculates the autocorrelation coefficient S on the multi-channel AE signal X after WPT preprocessing, and constructs a weight ω using the correlation difference between the autocorrelation coefficient and the joint sparse coefficient, which is then used to weight the joint sparse coefficient. Finally, the weighted joint sparsity coefficient is used. The adaptive threshold curve is calculated to accurately detect the presence of damage information. 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. j The formula is as follows:

[0068]

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

[0070] Step 42: In fact, since the joint sparse coefficients are a mapping of the original signal in the sparse domain, they can still retain correlation characteristics after JSR reconstruction. This is achieved by solving for the difference C = [c...] between the autocorrelation coefficient of the joint sparse coefficients and S. j |j=1,2,...,N] can effectively enhance the characteristics of damage information, as shown in the following formula:

[0071]

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

[0073]

[0074] Where max(·) and min(·) represent the maximum and minimum values, respectively. The j-th column of the joint sparse coefficient matrix is ​​represented by ρ = 0.1, which is a penalty factor. δ1 = 0.45 and δ2 = 0.2 are both constants. δ1 is used to calculate the peak value of the autocorrelation difference, while δ2 is used to determine the range of variance. When the variance is too large, it indicates a drastic change in the sparsity of the corresponding signal, suggesting that the signal is interference information. Otherwise, the signal segment is considered damaged information, and c is used to... j Weighted acquisition

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

[0076]

[0077] Where b = 100 represents the total number of segments contained in each column of signal after being divided by the detection window. Let represent the i-th element in the j-th column of the weighted sparse coefficient vector, where η = 1.5 is a constant. The total number of segments, b, determines the detection resolution. A larger b results in stronger anti-interference capability, while a smaller b results in higher detection sensitivity. By using adaptive thresholding to detect the occurrence time of damage signals, efficient and accurate large-scale rail SHM can be achieved.

[0078] Example:

[0079] To simulate the environment of wheel-rail rolling contact, this embodiment establishes a wheel-rail rolling experimental platform, such as... Figure 2As shown. The platform includes an actual train wheel 1 (current service wheel), an experimental rail 2 (made of U75V steel) cut from a current service rail, AE sensor 3 (model: RIC-900, 3) and AE sensor 4 (model: RIC-900) fixed to the wheel flange by magnetic clamps for signal collection, AE sensor 5 (model: 1045s) fixed to the rail web by magnetic clamps for transmitting pre-stored standard damage signals, and a lever for pulling the rail. Figure 2 As shown on the right, the platform includes a laptop computer 6 (for recording waveform information), an AE signal acquisition system 7 (model: VallenAMSY-6), an oscilloscope 8 (for monitoring simulated damage signals), an arbitrary waveform generator 9 (model: TektronixAFG3101) for generating analog signals, a magnetic clamp, a gate signal generator 10 (model: Agilent33220A) for controlling the signal transmission interval, a high-voltage amplifier 11 (model: Ritec GA-2500A), a 50-ohm high-power terminating impedance 12, and a 6dB fixed attenuation 13. To verify the effectiveness of the proposed method, a vehicle-mounted multi-sensor wheel-rail signal acquisition experiment was conducted, using multiple sensor angles. The installation positions of the vehicle-mounted multi-sensor and the connection method of the AE signal acquisition experimental equipment are as follows. Figure 3 As shown.

[0080] In this experiment, two RIC-900AE sensors were fixed to the wheel rim at a 30-degree angle using magnetic clamps. The two sensors and a laptop computer were connected to a VallenAMSY-6AE signal acquisition system via shielded cables to acquire and record signals. A 1045S AE sensor was connected to a high-voltage amplifier via a magnetic clamp at the rail web and a shielded wire with 6dB fixed attenuation and a 50-ohm safe load. Furthermore, the high-voltage amplifier, an arbitrary waveform generator, and a gate generator were connected in series and linked to an oscilloscope to monitor the output waveform. Subsequently, a pre-acquired simulated damage signal was input to the arbitrary waveform generator and periodically transmitted to the guide rail at 1-second intervals.

[0081] The standard damage signal was derived from a standard tensile test, which has been proven in previous work to effectively simulate real rail damage signals. The rail was then pulled by a tie rod, causing the wheel to roll on it, thus generating wheel-rail rolling noise. An AE sensor on the wheel captured this noise after modulation with the simulated damage signal at the wheel-rail contact surface. The sampling frequency was set to 5 MHz. The captured signal was recorded as multi-channel data acquired at the current sensor angle. The sensor was then rearranged 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, yielding a total of 60 sets of multi-channel data for further analysis.

[0082] Step 1: Based on the above experimental steps, this invention obtained complete multi-channel data for each detection wheel's rolling cycle. In the collected multi-channel data, the signal spectra collected by the two sensors at a 120-degree sensor angle are as follows... Figure 4 As shown. Comparison Figure 4 In (a) and (b), the signal collected by sensor two contains more noise because sensor two is closer to the track during wheelset movement. (Comparison) Figure 4 In (c) and (d), the signal frequency is mainly distributed in the 0–0.5 MHz frequency range. A small portion of the frequency band also exists above 0.5 MHz, primarily caused by high-frequency damage signals and harmonics generated by WRRN during modulation. Compared to the static state, the noise during rolling increases dramatically, overwhelming the damage signal and hindering time-domain waveform-based damage detection.

[0083] To remove random noise from the signal, this invention integrates the AE signals acquired by the two sensors into a single multi-channel signal, column by column. Then, it performs a 4-level WPT decomposition based on the Biorthogonal wavelet basis, and weighted selection of wavelet coefficient nodes (the second node) to be retained. Since the characteristic differences between damaged signals and noise are mainly distributed in the high-frequency band, while the main energy of random noise signals is distributed in the low-frequency band, inverse WPT operations based on the wavelet coefficients of these frequency band nodes can reconstruct the preprocessed multi-channel AE signal, thus eliminating random noise. The multi-channel signal preprocessed by the two sensors at 120 degrees using a 4-level WPT is shown below. Figure 5 As shown.

[0084] For the signal from sensor one, the multi-channel AE signal after WPT preprocessing essentially eliminated random noise between 2.5 and 4 seconds. The same denoising effect was achieved for the signal from sensor two. Most of the damaged signals could be detected through the time-domain waveform. However, due to partial overlap between WRRN and the damaged spectrum, some high-amplitude noise signals remained, which WPT preprocessing could not eliminate. Furthermore, compared... Figure 5 In (a) and (b), the waveforms of the preprocessed signals show significant differences in the noise portion. By fusing data from two sensor channels, a more comprehensive analysis of the signal characteristics is possible, which aids in further denoising and damage detection. Therefore, this invention proposes a JSR algorithm with correlation constraints to fuse multi-channel signals, eliminate WRRN, and utilizes a SAMP-AS algorithm with adaptive step size to improve the accuracy and speed of the fusion results.

[0085] Step 2: The data from each sensor is used to form a signal matrix with 2048 sampling points, which serves as the input to the JSR. Finally, a sparse coefficient matrix is ​​obtained, which fuses the data from the two sensors. To clearly illustrate the relationship between the sparse coefficient matrix and the original multi-channel data, the autocorrelation coefficients of the original AE signal acquired by sensor one and the sparse coefficient vector are shown below. Figure 6 As shown.

[0086] The blue and red lines represent the autocorrelation of the original sensor signal and the autocorrelation of the sparse coefficient matrix over time, respectively. Additionally, there are periodic amplitude spikes representing the damaged signal, each at 1-second intervals. Compared to the original signal, the autocorrelation coefficients of the sparse coefficients contain fewer noise spikes. Spikes at noise signal locations vary more significantly than spikes at damaged signal locations. In the multi-channel signal, JSR eliminates noise components at damaged signal locations, making the damage information more prominent. The correlation of the noise signal changes drastically, while the correlation of the damaged signal changes less. For example, the spikes at 2.47 seconds and 3.45 seconds have changed by 50% and 87.5% respectively compared to before fusion using the JSR algorithm with correlation constraints, indicating that the spikes at these two locations are noise. In contrast, the change rate at other spike locations does not exceed 40%.

[0087] It is worth noting that different angles between the two sensors significantly affect the performance of JSR. Slight sensor angles lead to significant redundancy in the multi-channel data, requiring more substantial damage information for the JSR process and reducing the quality of the fused sparsity coefficients. Conversely, excessively large sensor angles, while ensuring complementarity between the multi-channel data, cause the sensors to be too far from the rail. This limitation in receiving range reduces the quality of the received signal, impacting subsequent damage detection. Therefore, it is necessary to find the optimal angle between the sensors. To clearly demonstrate the effectiveness of JSR at different sensor angles, the fused signal is reconstructed based on the obtained joint sparsity coefficients, as shown in the following formula:

[0088]

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

[0090]

[0091] in Indicates signal The mean square error value, for The j-th column in the table. Furthermore, the mean kurtosis (KURT) is introduced to quantify the enhancement of damage information in the JSR results for each sensor mounting angle, as shown in the following formula:

[0092]

[0093] Where E a [·] indicates the fusion signal The expected value, μ and σ represent respectively The mean and variance of.

[0094] The PSNR and KURT of the reconstructed fused signal at each sensor mounting angle are as follows: Figure 7 As shown, regarding PSNR, the fused signal has a maximum value of 11.87 at 120 degrees, which is 1.626 dB higher than 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-best. From 30 degrees to 120 degrees, both PSNR and KURT gradually increase and then continuously decrease. The reason for the increase in PSNR between 30 and 120 degrees is that as the angle between the sensors increases, the energy of the destructive signal becomes more concentrated, and its penetration is greater than that of noise. When the sensor angle continues to increase from 120 degrees, due to the propagation distance, the sensor cannot effectively receive the destructive signal, resulting in a decrease in the denoising effect. The above results indicate that the optimal installation angle for multi-sensor vehicles based on AE technology is 120 degrees.

[0095] Step 3: The SAMP-AS algorithm adjusts the iteration step size using STE features to improve computational speed and accuracy. To illustrate the speed advantage of the SAMP-AS algorithm, a random signal of length 2048 is constructed. The random signal is reconstructed using both the improved SAMP algorithm and the traditional SAMP algorithm. The constraint factor is set to 5. Since the traditional SAMP algorithm achieves the highest iteration accuracy with a smaller step size, an initial step size of 1 is used. The results are as follows. Figure 8 As shown. In Figure 8 In this study, SAMP-AS achieves a signal sparsity of 54 in just 34 iterations, reducing computation time by 74.18%. The results demonstrate that the SAMP-AS algorithm, by adaptively adjusting the iteration step size, can perform JSR operations on signals faster while maintaining accuracy.

[0096] Step 4: This 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, the autocorrelation difference is weighted using a penalty factor based on the sparse coefficients generated by 120-degree multi-channel data fusion. The weighted joint sparse coefficients are as follows: Figure 9As shown, all high-amplitude WRRNs were eliminated. All corrupted signals became apparent in the weighted autocorrelation difference, with amplitudes higher than other noise or interference.

[0097] Finally, based on the adaptive threshold proposed in this invention, damage detection based on weighted joint sparsity coefficients is performed. The detection results under six different mounting angles of the vehicle-mounted AE sensor are as follows: Figure 10 As shown. In the detection results, all damaged signals are spaced 1 second apart, consistent with the transmission interval of simulated damaged signals in the experiment. With the arrival of interference noise, the threshold adaptively increases to minimize false detections. Afterward, the threshold returns to a lower level to maintain the sensitivity of damage detection. Furthermore, in Figure 10 In (c) and (d), although all damage was detected, some noise remained close to the adaptive threshold. This high-amplitude interference is due to the potential for AE signals generated by the compression of metal filings or dust on the track surface, resulting in noise levels higher than those collected at other sensor angles. In a total of 60 data sets, all damage signals were detected by the adaptive threshold without false detections. These results demonstrate that the proposed method can rapidly and accurately fuse multi-channel data. By weighting the fused sparse coefficients, high-amplitude WRRN interference was successfully eliminated. Finally, an adaptive threshold was constructed that can detect damage signals in the data at all sensor angles, providing theoretical guidance for the practical application of large-scale onboard multi-sensor rail SHM based on AE technology.

Claims

1. A method for monitoring the health of rail structures using multi-sensor correlation joint sparse representation, characterized in that... The method includes the following steps: Step 1: Decompose the AE signal in each channel using WPT operation, and reconstruct the preprocessed AE signal using weighted wavelet coefficients to eliminate random noise; Step 2: In order to fuse redundant impairment information in multi-channel signals and eliminate 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 a correlation constraint term is added in the dictionary atom solution process, thereby retaining the impairment atom and eliminating the invalid information atom. Step 3: From an energy perspective, a joint sparse adaptive matching pursuit algorithm with an adaptive step size is proposed. This algorithm continuously adjusts the iteration step size based on the short-time energy of the signal segment, shortening the step size in the damaged signal part and increasing the step size in the noisy part. Finally, the true sparsity of the signal is estimated through this adaptive step size, thereby eliminating WRRN and solving for the joint sparsity coefficients. The specific steps are as follows: Step 31: For a first AE signal after WPT preprocessing in one channel Set initial residual ,in, and The residual matrix and the signal matrix are respectively. The first in Columns, and then construct a candidate set. Let the number of iterations be... ; Step 32: [Regarding...] Short-time energy is calculated for each signal in each channel. ; Calculate the adaptive step size Let the current iteration step size be... Update # Candidate set of the next iteration ; Screening from the candidate set The first in column atoms Perform an update and obtain the updated version. Dictionary of each channel ; Step 33: Utilize each updated sub-dictionary separately. Solve for the corresponding channel Updated sparse coefficient matrix Further updates to the channels in this iteration. The corresponding set of serial numbers and from The atoms with corresponding serial numbers are selected to form a new first sequence. Sub-dictionary of the next iteration ; Calculate the residual for the next iteration using the updated sub-dictionary. By calculating the residuals This generates an algorithm gradient, enabling continuous iteration and constantly adjusting the step size. Estimated signal The true sparsity; utilizing the residuals of each iteration. To determine whether the algorithm continues to iterate, when Then execute the following formula and return to step 32 to continue iteration: when when season Then return to step 32 and continue iterating until... ,in To obtain the target residual, exit the iteration and perform a weighted fusion of the sparse coefficient matrices corresponding to all channels to obtain the fused joint sparse coefficient matrix. ; Step 4: Based on the sparsity difference between damage information and noise, a weighted algorithm based on sparsity difference and an adaptive threshold are proposed for efficient and accurate damage detection. This algorithm utilizes the multi-channel AE signal preprocessed by WPT. Calculate the autocorrelation coefficient The weights are constructed by utilizing the correlation difference between the autocorrelation coefficient and the joint sparsity coefficient. And used for weighted joint sparsity coefficients. Finally, the weighted joint sparsity coefficients are used. Solve for the adaptive threshold curve to accurately detect the presence of damage information.

2. The multi-sensor correlation joint sparse expression rail structure health monitoring method according to claim 1, characterized in that... The specific steps of step 1 are as follows: Step 1.1: For a multi-channel AE signal , ,in, Indicates the first The signal corresponding to each channel Indicates the channel number of the signal. The total number of channels. The number of elements in each column. For column numbers, and Here, the row and column indices are respectively the row and column numbers in the entire matrix. The multi-level WPT process is formulated as follows: in, Indicates the first Wavelet space corresponding to each scaling factor Indicates the translation variable. for The parent function, Represents a field of positive integers; Step 1.2: To eliminate the low-frequency components in WRRN, the gradient change of the wavelet coefficient energy ratio is used to track the changing trend between noise and effective information, and to determine whether the wavelet coefficients of the corresponding nodes should be retained. The formula is as follows: In the formula, For the first Weights of wavelet coefficients at each scale The number of levels in the WPT decomposition, generating a total of Wavelet nodes; Step 1.3: Weighting the obtained wavelet coefficients Wavelet coefficient nodes for signal reconstruction are selected, and then the preprocessed multi-channel acoustic emission signal is reconstructed using inverse WPT operation. This is used for subsequent fusion and analysis, and the formula is as follows: In the formula, This is the inverse wavelet packet transform. Describe the wavelet basis functions. Indicates the first The AE signal after WPT preprocessing in one channel.

3. The multi-sensor correlation joint sparse expression method for monitoring the health of rail structures according to claim 1, characterized in that... The specific steps of step 2 are as follows: Step 21: For a first AE signal after WPT preprocessing in one channel There exists a dictionary and a sparse coefficient matrix ,in, express The first in List dictionary atoms, The total number of atoms in the dictionary. express The first in Given a sparse coefficient vector, the input signal is represented as follows: in, The regularization coefficient is used. Step 22: As a supplementary information constraint, the cross-correlation between multi-channel data is added as a constraint term to the SR process, as shown in the following formula: in, Represents the cross-correlation function. and These are the different sparse vector column indices. and These are different sparse vectors. and These are different constants.

4. The multi-sensor correlation joint sparse expression method for monitoring the health of rail structures according to claim 1, characterized in that... The specific steps of step 4 are as follows: Step 41: For the multi-channel AE signal after WPT preprocessing Calculate the autocorrelation coefficient of each column. The formula is as follows: in, This is the autocorrelation coefficient function. This indicates the preprocessed multi-channel AE signal. The Middle The first channel The average value of the column signal, This indicates the preprocessed multi-channel AE signal. The Middle The first channel The first of the series signals One element, Indicates the delay points, all of them. Constructing the autocorrelation vector ; Step 42: Solve for the autocorrelation coefficient of the joint sparse coefficients and Differences between The formula to enhance damage information characteristics is as follows: in, and The formulas represent the maximum and minimum values, respectively. The first sparse coefficient in the joint sparse coefficient matrix List, As a penalty factor, and All are constants; Step 43: Construct an adaptive threshold The formula is as follows: in, This indicates the total number of segments contained in each column of signal after being divided by the detection window. Indicates the first The first column in the weighted sparse coefficient vector One element, The value is constant, and the occurrence time of the damage signal is detected by adaptive threshold to achieve large-scale rail SHM.

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