A method for extracting abrasive grain features based on differential signal band selection adaptive filtering

Abstract

The present application belongs to the technical field of oil liquid abrasive particle monitoring, and particularly relates to a kind of abrasive particle feature extraction methods based on differential signal band selection adaptive filtering, including obtaining the differential signal to be detected by carrying out common mode rejection to oil liquid abrasive particle signal;Obtain multi-decomposition scale feature vector by wavelet packet decomposition to the differential signal to be detected through orthogonal wavelet base function;Calculate similarity index on each decomposition scale, extract target scale feature vector;Obtain filter vector by processing target scale feature vector using improved least mean square root adaptive filter;Carry out wavelet reconstruction to zero vector and filter vector to obtain noise reduction signal;Divide noise reduction signal into multiple segments, calculate composite recognition index of each segment;According to composite recognition index, calculate the weight of each segment, and obtain oil liquid abrasive particle feature signal extraction result by weighting all segments;The present application improves the signal-to-noise ratio of abrasive particle signal, has stronger adaptive ability, and helps to improve the accurate detection of oil liquid abrasive particle feature.

Description

Technical Field

[0001] This invention belongs to the field of oil abrasive monitoring technology, specifically relating to a method for abrasive feature extraction based on differential signal band selection adaptive filtering. Background Technology

[0002] When mechanical equipment is in operation, changes in load and working environment can alter the frictional characteristics between contacting components of the transmission device, accelerating wear and causing particulate matter shedding. As the wear process continues, the degree of wear between components gradually increases from slight to severe, leading to an increase in abrasive particle generation. When the contact surface is poorly clean or has strong adhesion, some abrasive particles will remain on the component surface, further aggravating wear and inducing lubrication failure in subsequent contacts, severely impacting the performance and service life of the mechanical equipment. Data shows that wear is the primary cause of 80% of mechanical equipment failures. Oil abrasive detection uses non-destructive testing and analysis to extract rich information on wear particles from the lubricating oil system, promptly identifying potential abnormal wear conditions and taking corresponding measures to reduce maintenance costs, extend the service life of mechanical equipment, and resolve potential operational problems.

[0003] Inductive abrasive sensors achieve accurate abrasive particle detection by sensing and extracting the induced voltage signal characteristics—the change in magnetic flux—induced when different material particles pass through the sensor's magnetic field region. Due to their convenience, timeliness, and interpretable mapping capabilities of abrasive particle physical properties, they are widely used in aerospace, marine transportation, and energy industries. However, abrasive sensors typically operate in extremely harsh environments. In practical applications, the output signal of inductive sensors is inevitably affected by various interferences and noises, making it impossible to directly and accurately extract the abrasive particle signal. Especially when machinery is subjected to vibration, impact, or strong electromagnetic interference, a large number of low-frequency, high-energy pulse signals will appear in the output signal, introducing significant errors in signal parameter estimation. This makes it difficult for abrasive particle signal identification algorithms to achieve a balance between protecting the integrity of abrasive particle features and eliminating interference components, seriously misleading the accurate identification of abrasive particle signals. Currently, single-coil-based inductive sensors can improve the signal-to-noise ratio through structural optimization and algorithm design, but the extraction of abrasive particle induced voltage characteristics under strong pulse interference still faces fundamental limitations. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a method for abrasive particle feature extraction based on differential signal band selection and adaptive filtering. Its working principle is based on the high temporal similarity of the output signals from the cross-reference induction coils of differential sensors. Considering the frequency band energy distribution characteristics of the abrasive particle signal, wavelet packet decomposition and correlation measurement are used to complete band selection. An improved adaptive filtering algorithm with variable step size is combined to suppress in-band noise. Finally, abrasive particle feature signal extraction is achieved through wavelet reconstruction and composite identification indices.

[0005] The specific plan includes the following steps:

[0006] S1. A lubricating oil wear monitoring system is constructed using a two-phase differential inductive sensor to collect differential oil wear signals p and q in real time;

[0007] S2. Perform low-pass filtering and periodic harmonic elimination on the oil abrasive signals p and q to obtain the differential signals p0 and q0 to be detected;

[0008] S3. Calculate the optimal decomposition scale J based on the broadband characteristics of the oil abrasive signal spectrum, and obtain the multi-decomposition scale feature vector by performing wavelet packet decomposition on each differential signal to be detected through orthogonal wavelet basis functions.

[0009] S4. Calculate the similarity index of the two multi-scale feature vectors at each scale, and extract the zero-set vector and the target scale feature vector p based on the similarity index. b and target scale feature vector q b The zeroing vector includes a first zeroing vector and a second zeroing vector.

[0010] S5. Based on the target scale feature vector p b and q b The filter vector is obtained by using an improved minimum root mean square adaptive filter with variable step size to suppress in-band noise.

[0011] S6. Perform wavelet reconstruction on the zeroing vector and the filter vector to obtain the denoised signal.

[0012] S7. Reduce noise signal Divide into multiple segments of equal length and calculate the composite identification index for each segment;

[0013] S8. The weight of each segment is obtained by weight binarization based on the composite identification index, and all segments are weighted to obtain the final result of oil abrasive feature signal extraction.

[0014] The beneficial effects of this invention are:

[0015] The algorithm proposed in this invention can effectively avoid misidentification caused by low-frequency high-energy pulse signals while suppressing background noise, and achieve accurate identification of abrasive induced voltage signals while fully protecting the integrity of abrasive features. Currently, traditional algorithms in this field inevitably lead to distortion of the target signal features. The most prominent problem is that they change the amplitude of the abrasive voltage signal, thus affecting the judgment of mechanical health status and failing to provide a reliable basis for subsequent wear evolution analysis. The abrasive feature extraction method based on differential signal band selection adaptive filtering proposed in this invention can quickly and accurately perform output signal noise reduction and abrasive feature identification based on a dual-channel differential inductive abrasive sensor, without damaging the abrasive features and preserving the original signal features to the maximum extent. At the same time, it avoids the excessive reliance on prior conditions in threshold selection of complex traditional feature extraction algorithms and reduces the requirements for users' expertise in signal processing. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention;

[0017] Figure 2 This refers to the two-phase differential signal to be detected after preprocessing according to the present invention.

[0018] Figure 3 The present invention selects two-phase differential signals after adaptive filtering;

[0019] Figure 4 This invention provides a composite identification index and adaptive threshold based on energy estimation and Euclidean distance metric.

[0020] Figure 5 This is the final abrasive particle identification result of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention provides a method for extracting abrasive grain features based on differential signal band selection adaptive filtering, such as... Figure 1 As shown, it includes the following steps:

[0023] S1. A lubricating oil wear monitoring system is constructed using a two-phase differential inductive sensor to collect differential oil wear signals p = [p(0), p(1), ..., p(N-1)] and q = [q(0), q(1), ..., q(N-1)] in real time; p(n) and q(n) are the n = 0, 1, ..., N-1 elements in the differential oil wear signals p and q, respectively.

[0024] Specifically, the process of acquiring raw signals by the lubricating oil wear particle monitoring system includes:

[0025] In the lubricating oil wear particle monitoring system, the data acquisition card model is NI-9219, and the sampling frequency is set to f. s =5000, sampling time is 4s, number of sampling points is N=20000. The inductive abrasive particle detection sensor (two-phase differential inductive sensor) uses DC excitation, drive current I=0.5A, preamplifier amplification factor is 2000, and peristaltic pump flow rate is set to 510ml / min. Abrasive particles (equivalent diameter of spheres) pass through the inductive abrasive particle detection sensor in sequence at 170mm and 130mm, and the inductive abrasive particle detection sensor will generate two corresponding induced voltage signals similar to a single-cycle sine wave.

[0026] Specifically, the output signal model of the two coils of the two-phase differential inductive sensor is as follows:

[0027]

[0028] q(n) = r2(n)

[0029] Where r1(n) and r2(n) are the interference signals output by the two coils, u(n) represents the abrasive characteristic signal, ε represents the width of the abrasive signal, and τ represents the center position of the abrasive signal.

[0030] S2. Perform low-pass filtering and periodic harmonic elimination on the oil abrasive signals p and q to obtain the differential signals p0 and q0 to be detected.

[0031] S3. Calculate the optimal decomposition scale J based on the broadband characteristics of the oil abrasive signal spectrum, and obtain the multi-decomposition scale feature vector by performing wavelet packet decomposition on each differential signal to be detected through orthogonal wavelet basis functions.

[0032] Specifically, the optimal decomposition scale J mentioned in step S3 is calculated by the following formula:

[0033]

[0034] Among them, L c v represents the axial width of the induction coil in a two-phase differential inductive sensor. dγ represents the estimated flow velocity; γ represents the bandwidth expansion index, which is generally taken as 2.5-3.5.

[0035] S4. Calculate the similarity index of the two multi-scale feature vectors at each scale, and extract the zero-set vector and the target scale feature vector p based on the similarity index. b and target scale feature vector q b The zeroing vector includes a first zeroing vector and a second zeroing vector.

[0036] Specifically, step S4 includes:

[0037] S41. The multi-scale eigenvector obtained by wavelet packet decomposition of each differential signal to be detected using orthogonal wavelet basis functions (Haar, DB, etc.) is expressed as follows:

[0038] X1 = {p1, p2, ..., p} M},p m ∈R 1×(N / M)

[0039] X2={q1,q2,...,q M},q m ∈R 1×(N / M)

[0040] Where X1 represents the multi-decomposition scale feature vector of the differential signal p0 to be detected, p m X1 represents the feature vector at the m-th decomposition scale of the differential signal p0 to be detected; X2 represents the feature vector at multiple decomposition scales of the differential signal q0 to be detected, q m R represents the feature vector at the m-th decomposition scale of the differential signal q0 to be detected; 1×(N / M) This represents a real matrix, where the length of each decomposed wavelet coefficient is equal to the number of sampling points N, and M = 2. J Indicates the number of decomposition scales;

[0041] S42. Due to the high similarity between the non-abrasive components in the two differential signals to be detected, the energy containing abrasive feature components will be significantly greater than the energy containing only interference signal components. Based on the frequency band concentration of abrasive signals, a composite similarity index combining Euclidean distance (ED) and similarity measurement is used to calculate the correlation between the decomposition scales of the differential signals to be detected. The formula for calculating the composite similarity index of two multi-decomposition scale feature vectors at each decomposition scale is expressed as follows:

[0042]

[0043] Where, k m Let represent the composite similarity index at the m-th decomposition scale, <·> represent the vector dot product, and ||·||2 represent the L-2 norm;

[0044] S43. Define a band selection vector statistical feature condition based on statistical characteristics, and select the frequency band scale using the band selection vector statistical feature condition. Specifically, for each composite similarity index, if it satisfies the band selection vector statistical feature condition, then the decomposition scale corresponding to the composite similarity index is marked as the band selection scale; the band selection vector statistical feature condition is expressed as follows:

[0045]

[0046] Where b represents the selected band scale;

[0047] S44. Extract all feature vectors corresponding to the selected scales from the multi-scale feature vector X1 to form the target scale feature vector p. b Simultaneously, extract all feature vectors corresponding to non-selective scales from the multi-scale feature vector X1 and set them to zero to obtain the first zeroed vector; extract all feature vectors corresponding to selected scales from the multi-scale feature vector X2 to form the target scale feature vector q. b Meanwhile, the second zeroing vector is obtained by extracting all feature vectors corresponding to the non-selective scale from the multi-decomposition scale feature vector X2 and setting them to zero.

[0048] Specifically, setting non-domain vectors (feature vectors corresponding to non-selective scales) directly to zero can eliminate out-of-band noise.

[0049] S5. Based on the target scale feature vector p b and q b The filter vector is obtained by using an improved minimum root mean square adaptive filter with variable step size to suppress in-band noise.

[0050] Specifically, step S5 includes:

[0051] S51. Construct an adaptive filtering framework based on the least mean square root.

[0052] z(n) = p b (n)-w(n)q b (n)

[0053] w(n+1)=w(n)+2μz(n)q b (n)

[0054] Where z(n) represents the filtering result, p b (n) represents the eigenvector p b The nth element in the filter, w(n), represents the nth order coefficient of the filter, q b (n) represents the eigenvector q b The nth element in the filter is w(n+1), which represents the (n+1)th order coefficient of the filter, and μ represents the update step size.

[0055] S52. Calculate the estimated fragment feature width Select the width closest to the fragment feature. The average molecular segment length N s ;where f s L represents the sampling frequency. c v represents the axial width of the induction coil in a two-phase differential inductive sensor. d This indicates an estimated flow rate.

[0056] S53. Based on the average segment length N s The partitioning yields G = N / N s For each sub-segment, the correlation coefficient ρ is calculated using the cosine similarity function. g Let g = 1, 2, ..., G. Because noise in long-term signals is highly correlated, the correlation coefficient drops sharply when fragmentation occurs. For noisy correlated sequences, directly eliminating any one value has almost no impact on the average of the sequence. Therefore, to avoid the influence of fragmentation, the average of all correlation coefficients except the maximum correlation coefficient is calculated as the initial weight ω0.

[0057] S54. A fixed step size may cause excessive fluctuations in filter weights during the final convergence phase, thereby reducing fitting performance. Therefore, this invention constructs an adaptive step size μ. s (n) replaces the fixed update step size μ, resulting in an improved minimum root mean square adaptive filter with a variable step size, denoted as:

[0058] w(n+1)=w(n)+2μ s (n)z(n)q b (n)

[0059]

[0060] Where w(0)=ω0.

[0061] S55. An improved least mean square root adaptive filter is used to optimize the target-scale eigenvector p. b q b In-band noise suppression is performed to obtain the filter vector.

[0062] S6. Perform wavelet reconstruction on the zeroing vector and the filter vector to obtain the denoised signal.

[0063] Specifically, step S6 includes:

[0064] S61. Combine the first zeroing vector and the filtering vector into a vector. Wavelet reconstruction is performed to obtain the denoised signal. Restruct(·) represents wavelet reconstruction processing. Representing vectors The eigenvectors at the m-th decomposition scale;

[0065] S62. Combine the second zeroing vector and the filtering vector into a vector. Wavelet reconstruction is performed to obtain the denoised signal. Representing vectors The eigenvectors at the m-th decomposition scale.

[0066] Specifically, by performing wavelet reconstruction on the zeroing vector and the filtered vector, the reconstructed vector can also be expressed as:

[0067]

[0068] Where LMS(·) represents the adaptive filtering operator, and zeros(·) represents the vector zeroing operator.

[0069] S7. Based on the stability of the morphological characteristics of abrasive grain signals before and after filtering and the decay characteristics of interference components, a composite identification index based on energy estimation and Euclidean distance metric is established. Specifically, a sliding window is set to filter the denoised signal. Divide the data into multiple segments of equal length and calculate the composite identification index for each segment.

[0070] Specifically, step S7, which calculates the composite identification index based on the noise-reduced signal, includes:

[0071] S71. In adaptive filtering, due to the high similarity of signal components at the same moment, the energy of segments containing wear-particle characteristics will differ significantly from the residual noise. The energy characteristic index is calculated as follows:

[0072]

[0073] Where, λ l Indicates noise reduction signal The energy characteristic index of the l-th segment, η p,l ∈R 1×S Indicates noise reduction signal The l-th segment, S represents the segment length, R 1×S Represents a real matrix. It represents the square of the L-2 norm; by introducing a logarithmic-based metric, we can highlight the energy characteristics and reduce the impact of differences in peak signal values ​​of different abrasive particles on the identification results.

[0074] S72. The electromagnetic induction caused by abrasive particles passing outside the closed magnetic field of the coil is negligible. The formula for calculating the time stamp matching degree index is defined as follows:

[0075]

[0076] Where, φ l η represents the time-stamp matching index of the l-th segment. q,l Indicates noise reduction signal The lth segment;

[0077] S73. Calculate composite identification index

[0078] ζ l =λ l ×φ l

[0079] Where, ζ l This represents the composite identification index of the l-th segment.

[0080] S8. The weight of each segment is obtained by weight binarization based on the composite identification index, and all segments are weighted to obtain the final result of oil abrasive feature signal extraction.

[0081] Specifically, the weight of each segment is obtained by weight binarization of each composite identification index, and is represented as follows:

[0082]

[0083] in, This represents the weight of the segment l = 1, 2, ..., L, where L represents the number of segments. Let ζ represent a binary weight vector, N represent the number of signal sampling points, mean(·) represent the mean function, and ζ = (ζ1, ζ2, ..., ζ2) L ) represents a composite index vector. This represents the signal segment width coefficient.

[0084] The weighted operation is represented as:

[0085]

[0086] Where ξ represents the final result of oil abrasive feature signal extraction, and Hadamard(·) represents the Hadamard product operator. This represents the binary weight vector after zero padding.

[0087] In one embodiment, differential oil abrasive signals are acquired using a two-phase differential inductive sensor, and common-mode suppression is used for signal preprocessing to obtain the following result: Figure 2 The signal to be detected is shown. The optimal decomposition scale J = 3 is calculated. Wavelet packet decomposition of the signal to be detected is performed using orthogonal wavelet basis functions to obtain the wavelet packet tree with M = 2. J=8 multi-scale feature vectors. The correlation between features at each layer of the signal to be detected is calculated using a composite similarity index to obtain the selected scale. Here, the composite similarity index for each decomposition scale is 0.0029, 0.0015, 0.0004, 0.0008, 0.0001, 9.2528e-05, 2.2610e-05, and 3.4523e-06, respectively. Based on the statistical characteristics of the selected vectors, an adaptive threshold method is set to extract the target scale feature vector, where the adaptive threshold... Non-domain vectors are directly zeroed to eliminate out-of-band noise; for the difference vectors corresponding to the indices, an improved least mean square adaptive filter with a variable step size is used to suppress in-band noise. Wavelet reconstruction is performed on the filtered vector and the zeroed vector to obtain the denoised signal, such as... Figure 3 As shown. Based on the stability of the abrasive particle signal morphology characteristics and the decay characteristics of interference components before and after filtering, a composite identification index based on energy estimation and Euclidean distance metric is established, and a sliding window is set for weight calculation. The identification feature domain and adaptive identification threshold are as follows: Figure 4 As shown in the figure. Finally, an adaptive threshold is used for weighted binarization, and further signal weighting is used to identify abrasive grain features. The identified abrasive grain feature signals are as follows: Figure 5 As shown.

[0088] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "setting," "connection," "fixing," "rotation," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components or the interaction between two components. Unless otherwise explicitly limited, those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0089] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for extracting abrasive grain features based on differential signal band-selective adaptive filtering, characterized in that, Includes the following steps: S1. A lubricating oil wear monitoring system is constructed using a two-phase differential inductive sensor to collect differential oil wear signals p and q in real time; S2. Perform low-pass filtering and periodic harmonic elimination on the oil abrasive signals p and q to obtain the differential signals p0 and q0 to be detected; S3. Calculate the optimal decomposition scale J based on the broadband characteristics of the oil abrasive signal spectrum, and obtain the multi-decomposition scale feature vector by performing wavelet packet decomposition on each differential signal to be detected through orthogonal wavelet basis functions. S4. Calculate the composite similarity index of the two multi-scale feature vectors at each scale, and extract the zero-set vector and the target scale feature vector p based on the composite similarity index. b and target scale feature vector q b The zeroing vector includes a first zeroing vector and a second zeroing vector. S5. Based on the target scale feature vector p b and q b The filter vector is obtained by using an improved minimum root mean square adaptive filter with variable step size to suppress in-band noise. Step S5 specifically includes: S51. Construct an adaptive filtering framework based on the least mean square root. Where z(n) represents the filtering result, p b (n) represents the eigenvector p b The nth element in the filter, w(n), represents the nth order coefficient of the filter, q b (n) represents the eigenvector q b The nth element in the filter, w(n+1) represents the (n+1)th order coefficient of the filter, and μ represents the update step size; S52. Calculate fragment feature width Based on fragment feature width Determine the average molecular segment length N s ;where f s L represents the sampling frequency. c v represents the axial width of the induction coil in a two-phase differential inductive sensor. d Indicates the estimated flow rate; S53. Based on the average segment length N s The partitioning yields G = N / N s For each sub-segment, calculate the correlation coefficient ρ of each sub-segment. g , g=1,2,…,G; calculate the average of all correlation coefficients except the maximum correlation coefficient as the initial weight ω0; S54. Constructing an adaptive step size μ s (n) replaces the fixed update step size μ, resulting in an improved minimum root mean square adaptive filter with a variable step size, denoted as: ； S55. An improved least mean square root adaptive filter is used to optimize the target-scale eigenvector p. b q b The filter vector is obtained by performing in-band noise suppression. S6. Perform wavelet reconstruction on the zeroing vector and the filter vector to obtain the denoised signal. ; S7. Reduce noise signal Divide into multiple segments of equal length and calculate the composite identification index for each segment; Step S7 calculates the composite identification index based on the noise-reduced signal, including: S71. Calculate energy performance indicators Where, λ l Indicates noise reduction signal The energy characteristic index of the l-th segment Indicates noise reduction signal The lth segment, Denotes the square of the L-2 norm; S72. Calculate the timestamp matching index in, This represents the time-stamp matching index of the l-th segment. Indicates noise reduction signal The lth segment; S73. Calculate composite identification index in, The composite identification index represents the l-th segment; S8. The weight of each segment is obtained by weight binarization based on the composite identification index, and all segments are weighted to obtain the final result of oil abrasive feature signal extraction.

2. The method for extracting abrasive grain features based on differential signal band selection adaptive filtering according to claim 1, characterized in that, Step S4 specifically includes: S41. The multi-scale eigenvector obtained by wavelet packet decomposition of each differential signal to be detected using orthogonal wavelet basis functions is expressed as follows: Where X1 represents the multi-decomposition scale feature vector of the differential signal p0 to be detected, p m X1 represents the feature vector at the m-th decomposition scale of the differential signal p0 to be detected; X2 represents the feature vector at multiple decomposition scales of the differential signal q0 to be detected, q m R represents the feature vector at the m-th decomposition scale of the differential signal q0 to be detected; 1×(N / M) Let M represent a real number matrix, N represent the number of sampling points, and M=2. J Indicates the number of decomposition scales; S42. Calculate the composite similarity index of two multi-scale feature vectors at each scale, denoted as: Where, k m Let represent the composite similarity index at the m-th decomposition scale, <·> represent the vector dot product, and ||·||2 represent the L-2 norm; S43. For each composite similarity index, if it satisfies the selected-band vector statistical feature condition, then the decomposition scale corresponding to the composite similarity index is marked as the selected-band scale; the selected-band vector statistical feature condition is expressed as follows: Where b represents the selected band scale; S44. Extract all feature vectors corresponding to the selected scales from the multi-scale feature vector X1 to form the target scale feature vector p. b Simultaneously, extract all feature vectors corresponding to non-selective scales from the multi-scale feature vector X1 and set them to zero to obtain the first zeroed vector; extract all feature vectors corresponding to selected scales from the multi-scale feature vector X2 to form the target scale feature vector q. b Meanwhile, the second zeroing vector is obtained by extracting all feature vectors corresponding to the non-selective scale from the multi-decomposition scale feature vector X2 and setting them to zero.

3. The method for extracting abrasive grain features based on differential signal band selection adaptive filtering according to claim 1, characterized in that, Step S6 specifically includes: S61. Combine the first zeroing vector and the filtering vector into a vector. Wavelet reconstruction is performed to obtain the denoised signal. Restruct(·) represents wavelet reconstruction processing. Representing vectors The eigenvectors at the m-th decomposition scale; S62. Combine the second zeroing vector and the filtering vector into a vector. Wavelet reconstruction is performed to obtain the denoised signal. , Representing vectors The eigenvectors at the m-th decomposition scale.

4. The method for extracting abrasive grain features based on differential signal band selection adaptive filtering according to claim 1, characterized in that, Weight binarization is performed on each composite identification index to obtain the weight of each segment, denoted as: Where φ(l) represents the weight of the l-th segment, N represents the number of signal sampling points, and mean(·) represents the mean function. Represents a composite index vector. This represents the composite identification index of the l-th segment, where L represents the number of segments. This represents the signal segment width coefficient.

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