Rolling Bearing Compound Fault Diagnosis Method Based on Improved Symplectic Geometric Mode Decomposition

Abstract

The present invention discloses a rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition, belonging to the technical field of fault diagnosis. This method constructs an objective function of weighted unbiased autocorrelation kurtosis, and determines the optimal inverse filter coefficients of minimum entropy deconvolution through this objective function, which can enhance the weak periodic components related to faults in the filtered signal. The method of the present invention also proposes an adaptive periodic symplectic geometric mode decomposition method, adaptively selects the symplectic geometric components related to the bearing by using the cosine difference factor and the kurtosis criterion, and proposes a heuristic criterion for screening singular values to denoise the fault signal and eliminate interference components, thereby enhancing the fault periodic components, and finally separating them through hierarchical clustering to identify the compound fault types.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical fault diagnosis, and more specifically, to a rolling bearing compound fault diagnosis method based on improved symplectic geometric modal decomposition. Background Art

[0002] Bearings, especially rolling bearings, as key basic components of major equipment, their healthy service is an important guarantee for the safe operation of the whole equipment. Under extreme service conditions and environments, bearing failures caused by rolling element slip, fatigue spalling, and friction and wear often occur, directly leading to a reduction in equipment operation accuracy and increased vibration, and in severe cases, huge economic losses can be caused.

[0003] Due to the complexity of the internal composition of the equipment and the harshness of the working environment, the picked-up vibration signals are often composed of the vibration modes of multiple components and noise coupling. At the same time, most traditional signal processing methods and pattern recognition methods have disadvantages such as instability and lack of robustness, and it is difficult to effectively decompose, denoise, and discriminate complex signals.

[0004] The existing compound fault diagnosis and recognition methods have the following defects: First, various periodic components related to faults are coupled. If there are obvious differences between stronger and weaker fault information, it is very difficult to extract relatively weaker fault components, and it is difficult to fully identify faults, resulting in missed diagnoses. Second, for the symplectic geometric modal decomposition method, the symplectic geometric components obtained by decomposition contain residuals and noise, and these components are not completely independent.

[0005] Therefore, how to improve the accuracy of fault diagnosis under the conditions of strong background noise, bearing compound fault coupling and difficult identification is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a rolling bearing compound fault diagnosis method based on improved symplectic geometric modal decomposition.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] Step 1, obtain compound fault signals of different types of rolling bearings.

[0009] Among them, the compound fault signals of different types of rolling bearings include inner ring - outer ring compound faults, inner ring - ball compound faults, outer ring - ball compound faults, and inner ring - outer ring - ball compound faults.

[0010] Step 2, perform noise reduction processing on the compound fault signal by using an autoregressive model to obtain a noise-reduced signal;

[0011] Step 3: Calculate the weighted unbiased autocorrelation kurtosis of the noise-reduced signal, and use the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution to filter the noise-reduced signal to obtain the filtered signal.

[0012] Step 3 specifically includes the following steps:

[0013] Step 3.1: Perform an unbiased autocorrelation transformation on the noise-reduced signal to obtain the signal obtained by the unbiased autocorrelation transformation. The calculation formula is as follows:

[0014]

[0015] In the formula: R xx is the signal obtained by performing an unbiased autocorrelation transformation on the noise-reduced signal x; τ = q / f s is the delay coefficient; N is the data length of the noise-reduced signal; t i is the time; q = 0, 1, … N-1; f s is the signal sampling frequency;

[0016] Step 3.2: According to the signal R xx obtained by the unbiased autocorrelation transformation of the noise-reduced signal, obtain the signal processed by the weighted unbiased autocorrelation transformation The calculation formula is as follows:

[0017]

[0018] In the formula: w is the weighting coefficient of the unbiased autocorrelation;

[0019] Step 3.3: Construct the kurtosis function WUAK(n) of the signal processed by the weighted unbiased autocorrelation transformation and calculate the kurtosis of the transformed signal. The kurtosis function WUAK(n) formula is as follows:

[0020]

[0021] In the formula: is the mean value of;

[0022] Step 3.4: Update the filter coefficients, and the filter corresponding to when the kurtosis function WUAK(n) reaches the maximum is used as the optimal inverse filter f

[0023]

[0024] Step 3.5: Use the inverse filter to filter the input signal y(n) to obtain the filtered signal x(n), and the formula is as follows:

[0025] x(n) = f(n) * y(n).

[0026] Step 4: Decompose the filtered signal using the symplectic geometric modal decomposition method to obtain the symplectic geometric components of the filtered signal.

[0027] Step 4 specifically includes the following steps:

[0028] Step 4.1: Based on the filtered signal x = (x1, x2,... x n ), where n represents the length of the filtered signal, construct the reconstructed phase space matrix X:

[0029]

[0030] where d represents the embedding dimension, τ′ is the delay time in the reconstruction space process, τ′ = 1, and m = n - (d - 1)τ′;

[0031] Step 4.2: Obtain the covariance matrix A = X T X;

[0032] Step 4.3: Calculate the eigenvalues of the covariance matrix A and the eigenvectors Q i (i = 1, 2,... d);

[0033] Step 4.4: Calculate the transformation coefficient matrix S according to the reconstructed phase space matrix X and the eigenvector Q i and obtain the corresponding reconstructed matrix Z = Z1 + Z2 +... + Z i by the single-component matrix formula Z i = Q i S i d ;

[0034] Step 4.5: Convert Z i to a time series Y i of length n through diagonal averaging transformation, n = y1, y2,... y n (i = 1, 2,..., d), thus obtaining d time series of length n, that is, d symplectic geometric components SGC of the filtered signal i .

[0035] Step 5: Preliminarily screen the symplectic geometric components of the filtered signal using the cosine difference factor.

[0036] Step 5 specifically includes the following steps:

[0037] Step 5.1: Calculate the sum of the first k groups of components based on the symplectic geometric components of the filtered signal obtained in Step 4 to obtain the superimposed component S k :

[0038]

[0039] Among them, k is the serial number of the symplectic geometric component; d is the total number of groups of symplectic geometric components;

[0040] Step 5.2: Calculate the cosine value d between adjacent superimposed components cl , and the calculation formula is as follows:

[0041]

[0042] Step 5.3: Construct a cosine difference factor based on the cosine value between adjacent superimposed components. When the cosine difference factor approaches stability and is less than the set threshold, select the first c groups of symplectic geometric components as effective components.

[0043] Step 6: Further screen the symplectic geometric components initially screened using the kurtosis criterion to obtain the symplectic geometric components related to the rolling bearing fault.

[0044] Step 6 specifically includes the following steps:

[0045] Select the components with kurtosis values greater than 3.5 from the first c groups of symplectic geometric components according to the kurtosis criterion as the symplectic geometric components related to the rolling bearing fault.

[0046] Step 7: Reconstruct the symplectic geometric components related to the rolling bearing fault using the heuristic criterion to obtain the reconstructed symplectic geometric components.

[0047] Step 7 specifically includes:

[0048] Step 7.1: Denote the symplectic geometric components related to the rolling bearing fault as d i (t), i = 1, 2,..., h, where h is the total number of symplectic geometric components related to the rolling bearing fault;

[0049] Step 7.2: Perform singular value decomposition on the row vector matrix composed of d i (t) to obtain the corresponding eigenvalues;

[0050] Step 7.3: Select the number of eigenvalues that satisfy the following inequality condition. The inequality is:

[0051]

[0052] In the formula: e is the number of eigenvalues that satisfy the inequality, and o is the total number of eigenvalues;

[0053] Step 7.4: Identify the eigenvalue pairs obtained in Step 7.3 using the heuristic criterion. The heuristic criterion specifically includes:

[0054] If the following conditions are satisfied simultaneously, then select the eigenvalues and use them as the period pairs without noise:

[0055]

[0056]

[0057] Wherein: λ i and λ j are eigenvalues, and p m and p n refer to the highest values obtained from the Fourier transform of the eigenvectors, and i, j are less than e.

[0058] Step 8: Classify the reconstructed symplectic geometric components using Spearman similarity to obtain the fault categories of the rolling bearing.

[0059] Specifically, it includes: taking each reconstructed symplectic geometric component as a clustering center, calculating the Spearman similarity between every two clustering centers, and the Spearman similarity is calculated by the following formula:

[0060]

[0061] Wherein, 1 ≤ i ≤ N, and N is the data length.

[0062] In another improved embodiment, the above method further includes:

[0063] Step 9: Perform envelope demodulation on the fault categories obtained in Step 8 to obtain the corresponding envelope spectrogram.

[0064] From the above technical solutions, it can be seen that compared with the prior art, the present invention discloses a rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition, which has the following beneficial effects:

[0065] The present invention proposes a rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition. This method constructs an objective function of weighted unbiased autocorrelation kurtosis and determines the optimal inverse filter coefficients of minimum entropy deconvolution through this objective function. The method of the present invention also proposes an adaptive periodic symplectic geometric mode decomposition method, adaptively selects symplectic geometric components related to the bearing using the cosine difference factor and kurtosis criterion, and proposes a heuristic criterion for screening singular values to denoise the fault signal and eliminate interference components, thereby enhancing the fault periodic components, and finally separating and identifying the compound fault types through hierarchical clustering.

[0066] In the construction of the weighted unbiased autocorrelation kurtosis objective function of the method of the present invention, it is possible to enhance the weak periodic components related to faults after filtering the signal. Using the cosine difference factor and the kurtosis criterion can reduce the calculation cost, adaptively determine the termination condition of component decomposition, retain the components related to faults to the greatest extent, use the heuristic criterion to exclude interference noise signals and enhance the fault periodic components, separate different types of faults from the rolling bearing compound fault signal through hierarchical clustering, accurately separate three different types of fault periods, prevent the missed diagnosis and misdiagnosis of the rolling bearing compound fault signal, and replace the faulty components in time. Description of the Drawings

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0068] Figure 1 It is a schematic diagram of the overall flow of the method provided by the embodiment of the present invention.

[0069] Figure 2 is a time-domain waveform diagram and an envelope spectrum diagram of the original signal collected in the embodiment of the present invention. Among them, Figure 2(a) is a time-domain waveform diagram and an envelope spectrum diagram of the inner race - outer race compound fault signal collected in Embodiment 1, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 2(b) is a time-domain waveform diagram and an envelope spectrum diagram of the inner race - ball compound fault signal collected in Embodiment 2, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 2(c) is a time-domain waveform diagram and an envelope spectrum diagram of the outer race - ball compound fault signal collected in Embodiment 3, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 2(d) is a time-domain waveform diagram and an envelope spectrum diagram of the inner race - outer race - ball compound fault signal collected in Embodiment 4, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram.

[0070] Figure 3 is the time-domain waveform diagram and envelope spectrum diagram of the filtered signal processed by using enhanced minimum entropy deconvolution according to the embodiments of the present invention. Among them, Figure 3(a) is the time-domain waveform diagram and envelope spectrum diagram of the filtered signal after the inner-outer race composite fault processed in Embodiment 1, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 3(b) is the time-domain waveform diagram and envelope spectrum diagram of the filtered signal after the inner-race-ball composite fault processed in Embodiment 2, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 3(c) is the time-domain waveform diagram and envelope spectrum diagram of the filtered signal after the outer-race-ball composite fault processed in Embodiment 3, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 3(d) is the time-domain waveform diagram and envelope spectrum diagram of the filtered signal after the inner-outer race-ball composite fault processed in Embodiment 4, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram.

[0071] Figure 4 is a schematic diagram showing the change of the cosine difference factor according to the embodiments of the present invention. Among them, Figure 4(a) is a schematic diagram showing the change of the cosine difference factor of the inner-outer race composite fault provided in Embodiment 1; Figure 4(b) is a schematic diagram showing the change of the cosine difference factor of the inner-race-ball composite fault provided in Embodiment 2; Figure 4(c) is a schematic diagram showing the change of the cosine difference factor of the outer-race-ball composite fault provided in Embodiment 3; Figure 4(d) is the inner-outer race-ball composite fault provided in Embodiment 4.

[0072] Figure 5 is a schematic diagram of the kurtosis curve of the symplectic geometric component provided by the embodiment of the present invention. Among them, Figure 5 (a) is a schematic diagram of the kurtosis curve of the symplectic geometric component of the inner-outer race composite fault provided in Embodiment 1; Figure 5 (b) is a schematic diagram of the kurtosis curve of the symplectic geometric component of the inner-race-ball composite fault provided in Embodiment 2; Figure 5 (c) is a schematic diagram of the kurtosis curve of the symplectic geometric component of the outer-race-ball composite fault provided in Embodiment 3; Figure 5 (d) is a schematic diagram of the kurtosis curve of the symplectic geometric component of the inner-outer race-ball composite fault provided in Embodiment 4.

[0073] Figure 6 is a schematic diagram of the hierarchical clustering result provided by the embodiment of the present invention. Among them, Figure 6(a) is a schematic diagram of the hierarchical clustering result of the inner-outer race composite fault provided in Embodiment 1; Figure 6(b) is a schematic diagram of the hierarchical clustering result of the inner-race-ball composite fault provided in Embodiment 2; Figure 6(c) is a schematic diagram of the hierarchical clustering result of the outer-race-ball composite fault provided in Embodiment 3; Figure 6(d) is a schematic diagram of the hierarchical clustering result of the inner-outer race-ball composite fault provided in Embodiment 4.

[0074] Figure 7 Time-domain waveform diagram and envelope spectrum diagram of the inner-outer race composite fault separation result provided by Embodiment 1 of the present invention. Among them, Figure 7(a) is the time-domain waveform diagram and envelope spectrum diagram of the inner-race fault in the inner-outer race composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 7(b) is the time-domain waveform diagram and envelope spectrum diagram of the outer-race fault in the inner-outer race composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram.

[0075] Figure 8 Time-domain waveform diagram and envelope spectrum diagram of the inner-race-ball composite fault separation result provided by Embodiment 2 of the present invention. Among them, Figure 8(a) is the time-domain waveform diagram and envelope spectrum diagram of the inner-race fault in the inner-race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 8(b) is the time-domain waveform diagram and envelope spectrum diagram of the ball fault in the inner-race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram.

[0076] Figure 9 Time-domain waveform diagram and envelope spectrum diagram of the outer-race-ball composite fault separation result provided by Embodiment 3 of the present invention. Among them, Figure 9(a) is the time-domain waveform diagram and envelope spectrum diagram of the outer-race fault in the outer-race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 9(b) is the time-domain waveform diagram and envelope spectrum diagram of the ball fault in the outer-race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram.

[0077] Figure 10 Time-domain waveform diagram and envelope spectrum diagram of the inner-outer race-ball composite fault separation result provided by Embodiment 4 of the present invention. Among them, Figure 10(a) is the time-domain waveform diagram and envelope spectrum diagram of the inner-race fault in the inner-outer race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 10(b) is the time-domain waveform diagram and envelope spectrum diagram of the outer-race fault in the inner-outer race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram; Figure 10(c) is the time-domain waveform diagram and envelope spectrum diagram of the ball fault in the inner-outer race-ball composite fault separation, and (1) is the time-domain waveform diagram, and (2) is the envelope spectrum diagram. Detailed implementation manners

[0078] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0079] An improved symplectic geometric mode decomposition-based rolling bearing composite fault diagnosis method of the present invention, as Figure 1 shown, is specifically implemented according to the following steps:

[0080] Step 1: Obtain compound fault signals of different types of rolling bearings.

[0081] In specific practice, compound fault signals of different types of rolling bearings can be collected on a mechanical fault comprehensive simulation test bench. Specific compound fault signal types can include inner ring - outer ring compound faults, inner ring - ball compound faults, outer ring - ball compound faults, inner ring - outer ring - ball compound faults, and other compound fault types.

[0082] Step 2: Use an autoregressive model to denoise the obtained compound fault signals and obtain denoised signals.

[0083] This process can be carried out by using an existing autoregressive model to process the compound fault signals, and this embodiment of the present invention will not be further elaborated.

[0084] Step 3: Calculate the weighted unbiased autocorrelation kurtosis of the denoised signal, and use the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution to filter the denoised signal to obtain a filtered signal.

[0085] The specific steps are as follows:

[0086] Step 3.1: Perform an unbiased autocorrelation transformation on the denoised signal to obtain the signal obtained by the unbiased autocorrelation transformation. The calculation formula is Equation (1):

[0087]

[0088] In Equation (1): R xx is the signal obtained by performing an unbiased autocorrelation transformation on the denoised signal x; τ = q / f s is the delay coefficient; N is the data length of the denoised signal; t i is the time; q = 0, 1, … N - 1; f s is the signal sampling frequency; x(t i ) can be understood as the observed denoised signal.

[0089] Step 3.2: According to the signal R obtained by the unbiased autocorrelation transformation of the denoised signal xx obtain the signal processed by the weighted unbiased autocorrelation transformation The calculation formula is Equation (2):

[0090]

[0091] In Equation (2): w is the weighting coefficient of the unbiased autocorrelation kurtosis. w is related to the amplitude change between the original vibration signal and the denoised signal. The specific weighting coefficient can be obtained through the following formula:

[0092] w = p × L max , p ∈ N+ , specifically, in this embodiment, p is a positive integer between 1 and 5. Among them, L max is the maximum number of sampling points of different types of faults in a cycle of the composite fault;

[0093] In the above steps for obtaining the weighting coefficient, the maximum number of sampling points L of different types of faults in a cycle of the composite fault max is calculated as follows:

[0094] L max = [L1, L2, …, L j max

[0095] where: j ∈ N + is the number of different types of faults, L j = f s / f j is the number of sampling points of different types of faults in a cycle, f s is the sampling frequency, f j is the characteristic frequency of different types of faults in the fault signal time series.

[0096] Next, the calculation methods for the fault characteristic frequencies of types such as the inner ring of the bearing, the outer ring of the bearing, and the ball in the composite fault in this embodiment are introduced.

[0097] Among them, the fault characteristic frequency f of the inner ring of the bearing i is calculated as follows:

[0098]

[0099] where: f i is the inner ring fault characteristic frequency, d is the ball diameter, Z is the number of balls, α is the contact angle (0°), f r is the spindle rotation frequency;

[0100] The outer ring fault characteristic frequency f o is calculated as follows:

[0101]

[0102] where: f o is the outer ring fault characteristic frequency, d is the ball diameter, Z is the number of balls, α is the contact angle (0°), f r is the spindle rotation frequency;

[0103] The ball fault characteristic frequency f b is calculated as follows:

[0104]

[0105] where: f​b is the ball fault characteristic frequency, d is the ball diameter, Z is the number of balls, α is the contact angle (0°), f r The main axis rotation frequency;

[0106] In actual calculation, f i 、f o 、f b Replace the calculation formula L of the number of sampling points in a cycle respectively j =f s / f j f j .

[0107] Step 3.3: Construct the signal processed by weighted unbiased autocorrelation transform The kurtosis function WUAK(n) is used to calculate the kurtosis of the transformed signal. The signal processed by the weighted unbiased autocorrelation transform The calculation formula of the kurtosis function WUAK(n) is as follows:

[0108]

[0109] In formula (3): for The mean of , n represents the signal sequence.

[0110] Step 3.4: Further update the filter coefficients and weight the unbiased autocorrelation transform processed signal When the kurtosis function WUAK(n) reaches the maximum, the corresponding filter is used as the optimal inverse filter f.

[0111] First, the norm of the weighted unbiased autocorrelation kurtosis objective function WUAK(n) obtained after deconvolution is calculated, which is defined as:

[0112]

[0113] Where: is the norm of WUAK(n).

[0114] The target norm function Taking the derivative and setting it equal to 0, we get:

[0115]

[0116] because Therefore, we can get:

[0117]

[0118] Write the above formula in matrix form:

[0119] B=A*F

[0120] where: B, i.e., on the left side of the equal sign is the cross-correlation matrix of the input and output; A, i.e., on the right side of the equal sign is the L×L autocorrelation matrix of the input signal y(n).

[0121] The matrix expression of the inverse filter f obtained by iterative calculation is:

[0122]

[0123] Therefore, by using the inverse filter f, the output filtered signal x(n) is restored to the input signal y(n) to the greatest extent, that is, the filtered signal x is expressed by the following formula:

[0124] x(n) = f(n) * y(n)

[0125] where: y(n) is the input signal; x(n) is the output filtered signal.

[0126] Step 4: Decompose the filtered signal by using the symplectic geometric mode decomposition method to obtain the symplectic geometric components of the filtered signal.

[0127] This step specifically includes:

[0128] Step 4.1: The filtered signal obtained in Step 3 is x = (x1, x2,... x n ), n represents the length of the filtered signal, then the reconstructed phase space matrix X is:

[0129]

[0130] where, d represents the embedding dimension, τ′ is the delay time in the reconstructed space process, τ′ = 1, m = n - (d - 1)τ.

[0131] The embedding dimension d is selected according to the power spectral density (PSD) of the original vibration signal x. Define the frequency of the highest peak in the power spectral density PSD as F max , when the normalized frequency F max / F s is less than 0.001, the embedding dimension d = N / 3; otherwise k = 1.2×(F s / F max ).

[0132] Step 4.2: Obtain the covariance matrix A = X T X;

[0133] Step 4.3: Calculate the eigenvalues of the covariance matrix A and the eigenvectors Q corresponding to the eigenvalues i(i = 1, 2, … d), in this step, the Hamiltonian matrix can be obtained according to the covariance matrix A:

[0134]

[0135] Let F = M 2 , then the following expression can be obtained by using the symplectic orthogonal matrix Q:

[0136]

[0137] where B is an upper triangular matrix, and its element b ij = 0 (i > j + 1). Through singular value decomposition, the eigenvalues of the upper triangular matrix B can be obtained as λ1, λ2, … λ d ; therefore, the eigenvalues of the covariance matrix A are and the eigenvectors are Q i (i = 1, 2, … d).

[0138] Step 4.4, calculate the transformation coefficient matrix S according to the reconstructed phase space matrix X and the eigenvector Q i , i Through the single-component matrix formula Z i = Q i S i , the corresponding reconstructed matrix Z = Z1 + Z2 + … + Z d is obtained.

[0139] Step 4.5, convert Z i to a time series Y of length n through diagonal averaging transformation i = y1, y2, … y n (i = 1, 2, …, d), and thus d time series of length n are obtained, that is, the symplectic geometric components SGC of d filtered signals i .

[0140] In the above steps, the reconstructed trajectory matrix Z is constructed by a series of single-component matrices Z i (i = 1, 2, … d), that is: Z = Z1 + Z2 + … + Z d , where

[0141] In the single-component matrix Z i , z ij (1 ≤ i ≤ d, 1 ≤ j ≤ m) are the elements of the matrix. If m < d, then otherwise The diagonal averaging formula of the single-component matrix is:

[0142]

[0143] ​where: d* = min(m, d); m* = max(m, d) and n = m + (d - 1)τ. Diagonal averaging is performed on each reconstructed matrix in turn to convert Z i into a time series Y of length n i = y1, y2, … y n (i = 1, 2, …, d), and the sum of d components can be obtained, that is, the symplectic geometric component SGC of d filtered signals i as shown in Equation (4).

[0144]

[0145] In Equation (4): i = 1, 2, … d, and d is the embedding dimension.

[0146] Step 5. Calculate the cosine difference factor of the continuous symplectic geometric superposition components, and use the cosine difference factor to preliminarily screen the symplectic geometric components of the filtered signals. The specific steps are as follows:

[0147] Step 5.1. Calculate the sum of the first k groups of components based on the symplectic geometric components of the filtered signals obtained in Step 4 to obtain the superposition component S k :

[0148]

[0149] where: k is the serial number of the symplectic geometric component, k ∈ N + ;

[0150] Step 5.2. Calculate the cosine value d cl between adjacent superposition components. The calculation formula is as follows:

[0151]

[0152] In Equation (5): S k and S k+1 are the vector representations of two adjacent superposition components. Equation (5) is obtained by respectively substituting the adjacent superposition components Sk and Sk+1 into the vectors a and e in the following formula: where a j and e j are the components of a and e, j ∈ N + .

[0153] Step 5.3. Construct the cosine difference factor based on the cosine value between adjacent superposition components. When the cosine difference factor is close to stable and less than the set threshold, select the first c groups of symplectic geometric components as effective components.

[0154] The cosine difference factor CD l and the threshold expression are shown in Equation (6).

[0155]

[0156] When the CD l is close to stable and lower than the threshold ε f , the first c groups of components are fault components, and the components after the c-th one are noise. Therefore, the signal can be decomposed as:

[0157]

[0158] Step 6: Further screen the symplectic geometric components preliminarily selected by using the kurtosis criterion to obtain the symplectic geometric components related to the rolling bearing fault. The specific steps are as follows:

[0159] Calculate the kurtosis values of the first c groups of symplectic geometric components by using the kurtosis formula; select the components with kurtosis values greater than 3.5 from the first c groups of symplectic geometric components according to the kurtosis criterion as the symplectic geometric components related to the rolling bearing fault. Then the signal can be decomposed as:

[0160]

[0161] In the formula: the first u symplectic geometric components are selected by the kurtosis criterion, u ∈ N + .

[0162] Step 7: Reconstruct the symplectic geometric components related to the rolling bearing fault by using the heuristic criterion to obtain the reconstructed symplectic geometric components.

[0163] The essence of this step is to use the rejection criterion to screen the singular value sub-pairs corresponding to the periodic components in each symplectic geometric mode component obtained in Step 6, and then perform signal noise reduction and interference component elimination processing. The specific steps are as follows:

[0164] Step 7.1: Denote the symplectic geometric components related to the bearing fault as d i (t), i = 1, 2,..., h, where h is the total number of symplectic geometric components related to the bearing fault.

[0165] Step 7.2: Perform singular value decomposition on the row vector matrix composed of d i (t) to obtain the corresponding eigenvalues.

[0166] Step 7.3: Select the number of eigenvalues that satisfy the following inequality condition. The inequality is:

[0167]

[0168] In the formula: e is the number of eigenvalues that satisfy the inequality, and o is the total number of eigenvalues; if the inequality is not satisfied, the corresponding eigenvalue pairs are ignored.

[0169] Step 7.4: To obtain only the periodic components, use a heuristic criterion to identify the eigenvalue pairs obtained in Step 7.3. The specific heuristic criterion includes:

[0170] If the following conditions are satisfied simultaneously, select the eigenvalue and use it as a periodic pair without noise:

[0171]

[0172]

[0173] In the formula: λ i , λ j are eigenvalues, and p m , p n refer to the highest values obtained from the Fourier transform of the eigenvector, where i, j are less than e.

[0174] Step 8: Classify the reconstructed symplectic geometric components using Spearman similarity to obtain the fault categories of the bearing.

[0175] In this step, use the symplectic geometric components obtained in Step 7 as the clustering centers, calculate the Spearman similarity between each clustering center, and reconstruct and classify the components with similar periodicity. The specific steps are as follows:

[0176] In Step 8, regard each symplectic geometric component as a clustering center. Calculate the Spearman similarity of each clustering center pair (x i , y i ) in set T. The Spearman similarity is calculated by formula (12).

[0177]

[0178] In formula (12), 1 ≤ i ≤ N, where N is the data length.

[0179] Classify the symplectic geometric components with similar periodicity obtained from formula (12) into c types of faults, i.e., T = (x1, x2…x c )

[0180] Step 9: Perform envelope demodulation on the c types of faults obtained in Step 8, calculate the theoretical fault characteristic frequencies, and identify different types of compound faults of the rolling bearing from the envelope spectrum diagram.

[0181] Next, use 4 examples to verify the effectiveness of this method.

[0182] Example 1

[0183] As Figure 1As shown, an improved symplectic geometric mode decomposition-based rolling bearing compound fault diagnosis method of the present invention is applied to a mechanical fault comprehensive simulation test bench produced by Spectrum Quest Incorporated (SQI) to test rolling bearings with compound faults. The ER-16k deep groove ball bearing is selected as the experimental object, and the specific steps are as follows:

[0184] Step 1: Collect the vibration signals of different types of compound faults of the rolling bearing. In this embodiment, the compound fault type collected is the inner race - outer race compound fault. The time-domain waveform diagram and envelope spectrum diagram of its original signal are shown in Figure 2(a), and the defect widths are 1.2 mm and 1.2 mm respectively. The relevant parameters of the faulty bearing are: the inner raceway diameter is D i = 30.585 mm, the outer raceway diameter is D o = 46.47 mm, the ball diameter is d = 7.92 mm, the number of balls Z = 9, and the contact angle α = 0. The inner race of the bearing rotates on the main shaft, the outer race is fixed, and the rotational speed is 1500 r / min, that is, the rotational frequency f r is 25 Hz;

[0185] Step 2: Filter the compound fault signal using an autoregressive model.

[0186] Step 3: Construct the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution according to equations (1)-(3), and then process the filtered signal to obtain the time-domain waveform diagram and envelope spectrum diagram of the filtered signal as shown in Figure 3(a).

[0187] Comparing Figure 2(a) and Figure 3(a), it can be seen from the time-domain waveform diagram (1) that the periodic components are significantly enhanced. From the envelope spectrum diagram (2), it can be seen that after being processed by this method, the sideband frequency 2f i ±2f r of the inner race can be observed, while it was not observed in the envelope spectrum of the original signal. Therefore, the proposed method enhances the inner race fault, making it easy to identify, and also reduces the interference of noise.

[0188] Step 3: Suppress the interference components through equations (4) to (7). The variation of the cosine difference factor is shown in Figure 4(a). After the number of iterations N it = 18, the change of the symplectic geometric component similarity tends to be stable, the cosine difference factor tends to be stable, and ε f is 0.05%.

[0189] Step 4: Select the symplectic geometric components related to the bearing fault according to equation (8). The variation of the kurtosis is as shown in Figure 5 (a). The components with kurtosis greater than 3.5 are regarded as useful components. It can be seen from the figure that all components are greater than 3.5.

[0190] Step 5: Periodically enhance the symplectic geometric components obtained in Step 4 to form components, select singular value sub-pairs using Eqs. (9)-(11), and reconstruct the components corresponding to the singular value sub-pairs to obtain reconstructed symplectic geometric components.

[0191] Step 6: Take each reconstructed symplectic geometric component as a clustering center, calculate the Spearman similarity values in each pair of clusters according to Eq. (12), and reconstruct the components with large similarities together. As shown in Fig. 6(a), the inner race fault is reconstructed from components 1 to 12, and the outer race fault is reconstructed from components 13 to 18.

[0192] Step 7: Conduct envelope spectrum analysis on the reconstructed components. The analysis results are shown in Fig. 7. From Fig. 7, the inner-outer race compound fault can be accurately separated. Specifically, from Fig. 7(a), it can be seen that there are rotational frequency f r , bearing inner race fault characteristic frequency f i , harmonic frequency 2f i , 3f i , sideband frequency f i ± f r , f i ± 2f r , 2f i ± f r , 2f i ± 2f r , 3f i ± f r , 3f i ± 2f r , and it can be identified that this fault is an inner race fault. From Fig. 7(b), it can be seen that there are outer race fault characteristic frequency f o , harmonic frequency 2f o , 3f o , 4f o , 5f o , and it can be identified that this fault is an outer race fault. Therefore, the inner race and outer race faults are accurately separated and identified.

[0193] Example 2

[0194] The type of compound fault collected in this example is an inner race - ball compound fault. The time - domain waveform diagram and envelope spectrum diagram of its original signal are shown in Fig. 2(b) respectively, and the defect widths are 1.2 mm and 1.2 mm respectively; use the autoregressive model to filter the compound fault signal; construct the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution according to Eqs. (1)-(3), and then process the filtered signal to obtain the time - domain waveform diagram and envelope spectrum diagram of the filtered signal as shown in Fig. 3(b); comparing Fig. 2(b) and Fig. 3(b), it can be seen from the time - domain waveform diagram that the periodic components are significantly enhanced, and from the envelope spectrum diagram, it can be seen that after being processed by the proposed method, the rotational frequency fr , the sideband frequency f of the inner ring i ±2f r , 2f i ±2f r , 2f i +f r , 3f i ±f r , 3f i ±2f r , and the characteristic frequency f of the ball b can be observed, but not in the envelope spectrum of the original signal. Therefore, the proposed method enhances the inner ring fault and the ball fault, making them easy to identify, and also reduces the interference of noise.

[0195] Suppress the interference components through equations (4) to (7). The variation of the cosine difference factor is shown in Figure 4(b). After the number of iterations N it = 5, the cosine difference factor tends to be stable, and ε f is 0.09%. Select the symplectic geometric components related to the bearing fault according to equation (8). The variation of kurtosis is as Figure 5 (b). The components with kurtosis greater than 3.5 are regarded as useful components. It can be seen from the figure that all components are greater than 3.5; Enhance the obtained symplectic geometric components into periodic components, select the singular value sub-pairs using equations (9) to (11), and reconstruct the components corresponding to the singular value sub-pairs to obtain the reconstructed symplectic geometric components.

[0196] Take each reconstructed symplectic geometric component as the clustering center, calculate the Spearman similarity value in each pair of clusters according to equation (12), and reconstruct the components with large similarity together. As shown in Figure 6(b), the inner ring fault is reconstructed by components 1 to 3, and the ball fault is reconstructed by components 4 and 5; Perform envelope spectrum analysis on the reconstructed components. As shown in Figure 8, the inner ring and ball compound faults can be accurately separated from Figure 8. Specifically, it can be seen from Figure 8(a) that there are f r , f i , the harmonic frequency 2f r , 2f i , 3f i , the sideband frequency 2f i +f r , 3f i +f r , and it can be identified that the fault is an inner ring fault. It can be seen from Figure 8(b) that there are f r , f o , the harmonic frequency 2f r , 2f b , 3f b , 4f b , 5f b , 6fb , 7f b , sideband frequency f b ±f r , 3f b -f r , 5f b ±f r , it can be recognized that this fault is a ball fault. Therefore, the inner ring and ball faults are accurately separated and identified.

[0197] Embodiment 3

[0198] The composite fault type collected in this embodiment is an outer ring - ball composite fault. The time - domain waveform diagram and envelope spectrum diagram of its original signal are shown in Figure 2(c) respectively, and the defect widths are 1.2 mm and 1.2 mm respectively; the autoregressive model is used to filter the composite fault signal; according to equations (1) to (3), the weighted unbiased autocorrelation kurtosis is constructed as the objective function of minimum entropy deconvolution, and then the filtered signal is processed to obtain the time - domain waveform diagram and envelope spectrum diagram of the filtered signal as shown in Figure 3(c); comparing Figure 2(c) and Figure 3(c), it can be seen from the time - domain waveform diagram that the periodic components are significantly enhanced, and from the envelope spectrum diagram, it can be seen that after being processed by the proposed method, the rotation frequency f r , harmonic frequency 2f r , 2f b , 3f b , 4f b , 5f b can be observed, but it is not recognized in the envelope spectrum of the original signal, which indicates that the proposed method enhances the ball fault, making it easy to be recognized, and also reduces the interference of noise.

[0199] Suppress the interference components through equations (4) to (7). The variation of the cosine difference factor is shown in Figure 4(c). After the number of iterations N it = 264, the cosine difference factor tends to be stable, and ε f is 0.05%. Select the symplectic geometric components related to bearing faults according to equation (8). The variation of kurtosis is as shown in Figure 5 (c). Take the components with kurtosis greater than 3.5 as useful components. It can be seen from the figure that all components are greater than 3.5; enhance the obtained symplectic geometric components into periodic components, select the singular value sub - pairs by using equations (9) to (11), and reconstruct the components corresponding to the singular value sub - pairs to obtain the reconstructed symplectic geometric components.

[0200] Taking each reconstructed symplectic geometry component as the clustering center, calculate the Spearman similarity value in each pair of clusters according to Equation (12), and reconstruct the components with large similarity together. As shown in Figure 6(c), the outer race fault is reconstructed from components 1 to 12, 15, 19, 27, and the ball fault is reconstructed from components 14, 16, 17, 18, 20, 21, 24, 28, 26, 22, 23, 25, 29, 30, 31; perform envelope spectrum analysis on the reconstructed components. As shown in Figure 9, the outer race and ball compound fault can be accurately separated from Figure 9.

[0201] Example 4

[0202] The compound fault type collected in this example is inner race - outer race - ball compound fault. The time - domain waveform diagram and envelope spectrum diagram of its original signal are shown in Figure 2(d) respectively, and the defect widths are 1.2 mm, 1.2 mm, 1.2 mm respectively; use the autoregressive model to filter the compound fault signal; construct the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution according to Equations (1) to (3), and then process the filtered signal to obtain the time - domain waveform diagram and envelope spectrum diagram of the filtered signal as shown in Figure 3(d); comparing Figure 2(d) and Figure 3(d), it can be seen from the time - domain waveform diagram that the periodic components are significantly enhanced, and from the envelope spectrum diagram, it can be seen that after being processed by the proposed method, the harmonic frequencies 2f r , 2f i , 3f i , 4f o , 5f o , the side - band frequency f i + f r , 2f i - 2f r , and the characteristic frequency f b of the ball can be observed, but not observed in the envelope spectrum of the original signal. Therefore, the proposed method enhances the inner race fault and outer race fault, making them easy to be identified, and also reduces the interference of noise.

[0203] Suppress the interference components through Equations (4) to (7). The change of the cosine difference factor is shown in Figure 4(d). After N it = 21, the cosine difference factor tends to be stable, and ε f is 0.0007%. Select the symplectic geometry components related to bearing faults according to Equation (8). The change of kurtosis is as shown in Figure 5 (d). Take the components with kurtosis greater than 3.5 as useful components; enhance the periodic components of the obtained symplectic geometry components, select the singular value sub - pairs by using Equations (9) to (11), and reconstruct the components corresponding to the singular value sub - pairs to obtain the reconstructed symplectic geometry components;

[0204] Taking each reconstructed symplectic geometry component as the clustering center, calculate the Spearman similarity values in each pair of clusters according to Equation (12), and reconstruct the components with large similarities together. As shown in Figure 6(d), the outer race fault is reconstructed from components 1 to 11, the inner race fault is reconstructed from components 12 to 16, and the ball fault is reconstructed from components 17 to 21. Perform envelope spectrum analysis on the reconstructed components. As shown in Figure 10, the inner race, outer race, and ball compound faults can be accurately separated from Figure 10. Specifically, as can be seen from Figure 10(a), there are rotational frequency f r , inner race fault characteristic frequency f i , harmonic frequency 2f r , 2f i , 3f i , sideband frequency f i ±f r , f i ±2f r , 2f i -f r , and it can be recognized that this fault is an inner race fault. As can be seen from Figure 10(b), there are f o , harmonic frequency 2f o , 3f o , 4f o , 5f o , and it can be recognized that this fault is an outer race fault. As can be seen from Figure 10(c), there are rotational frequency f r , outer race fault characteristic frequency f o , harmonic frequency 2f r , 2f b , 3f b , 4f b , 5f b , 6f b , 8f b , sideband frequency 3f b +f r , 5f b -f r , 8f b -f r , and it can be recognized that this fault is a ball fault. Therefore, the inner race, outer race, and ball faults are accurately separated and recognized.

[0205] In summary, it can be seen that this method can effectively separate and identify fault information from the compound fault signal under noise interference, realize the determination of bearing fault types, thus verifying the effectiveness of this method.

[0206] In the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts among the various embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description in the method section.

[0207] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Thus, the invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition, characterized in that, It includes the following steps: Step 1, obtain compound fault signals of different types of rolling bearings; Step 2, perform noise reduction processing on the compound fault signals by using an autoregressive model to obtain noise-reduced signals; Step 3, calculate the weighted unbiased autocorrelation kurtosis of the noise-reduced signals, and use the weighted unbiased autocorrelation kurtosis as the objective function of minimum entropy deconvolution to filter the noise-reduced signals to obtain filtered signals; Step 3 specifically includes the following steps: Step 3.1, perform an unbiased autocorrelation transformation on the noise-reduced signals to obtain the signals obtained by the unbiased autocorrelation transformation, and the calculation formula is as follows: Where: R xx is the signal obtained by performing an unbiased autocorrelation transformation on the noise-reduced signal x; c = q / f s is the delay coefficient; N is the data length of the noise-reduced signal; t i is the time; q = 0, 1, … N-1; f s is the signal sampling frequency; Step 3.2, the signal R obtained from the unbiased autocorrelation transformation of the noise-reduced signal xx Obtain the signal processed by weighted unbiased autocorrelation transformation The calculation formula is as follows: In the formula: w is the weighted coefficient of the unbiased autocorrelation; The weighted coefficient w is obtained through the following formula: w = p × L max , p ∈ N + , where p is a positive integer between 1 and 5, and L max is the maximum number of sampling points of different types of faults in a cycle in the composite fault; The maximum number of sampling points L max has the following calculation formula: L max = [L1, L2, …, L j max ​ where: j ∈ N + is the number of different types of faults, L j = f s / f j is the number of sampling points of different types of faults in one cycle, f s is the sampling frequency, f j is the characteristic frequency of different types of faults in the fault signal time series; Step 3.3, construct a signal processed by weighted unbiased autocorrelation transformation and calculate the kurtosis of the transformed signal. The formula for the kurtosis function WUAK(n) is as follows: In the formula: is the mean value of; Step 3.4, update the filter coefficients, and the filter corresponding to when the kurtosis function WUAK(n) reaches the maximum is used as the optimal inverse filter f Step 3.5, filter the input signal y(n) by using the inverse filter to obtain a filtered signal x(n), and the formula is as follows: x(n) = f(n) * y(n); Step 4, decompose the filtered signal by using the symplectic geometric mode decomposition method to obtain the symplectic geometric components of the filtered signal; Step 5, preliminarily screen the symplectic geometric components of the filtered signal by using the cosine difference factor; specifically including: Step 5.1, calculate the sum of the first k groups of components according to the symplectic geometric components of the filtered signal to obtain a superimposed component; Step 5.2, calculate the cosine value d between adjacent superimposed components cl ; Step 5.3, construct a cosine difference factor according to the cosine values between adjacent superimposed components, and select the first c groups of symplectic geometric components as effective components. Specifically, Cosine difference factor CD l and the threshold expression is as follows: When CD l is close to being stable and lower than the threshold ε f the first c groups of components are fault components, and the components after the c-th one are noise; Step 6, further screen the symplectic geometric components preliminarily screened by using the kurtosis criterion to obtain the symplectic geometric components related to the rolling bearing faults; Step 7, reconstruct the symplectic geometric components related to the rolling bearing faults by using a heuristic criterion to obtain the reconstructed symplectic geometric components; Step 8, classify the reconstructed symplectic geometric components by using the Spearman similarity to obtain the fault categories of the rolling bearings.

2. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 1, characterized in that It also includes: Step 9, perform envelope demodulation on the fault categories obtained in Step 8 to obtain the corresponding envelope spectrogram.

3. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 1, wherein The compound fault signals of different types in Step 1 include inner ring - outer ring compound faults, inner ring - ball compound faults, outer ring - ball compound faults, and inner ring - outer ring - ball compound faults.

4. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 1, wherein Step 4 specifically includes the following steps: Step 4.

1. Based on the filtered signal \(x=(x_1,x_2,\cdots,x\) n ), where \(n\) represents the length of the filtered signal, construct the reconstructed phase space matrix \(X\): Where, d represents the embedding dimension, τ′ is the delay time in the reconstruction space process, τ′ = 1, m = n - (d - 1)τ′; Step 4.

2. Obtain the covariance matrix A = X according to the reconstructed phase space matrix X T X; Step 4.3: Calculate the eigenvalues of the covariance matrix A and the corresponding eigenvectors Q i (i = 1, 2,... d); Step 4.

4. Calculate the transformation coefficient matrix S according to the reconstructed phase space matrix X and the eigenvector Q i where S i = Q i i T X T (i = 1, 2, 3,..., d). Through the single-component matrix formula Z i = Q i S i , the corresponding reconstructed matrix Z = Z1 + Z2 + … + Z d is obtained;​ Step 4.

5. Convert Z through diagonal averaging transformation i to a time series Y of length n i = y1, y2, … y n (i = 1, 2, …, d), thereby obtaining d time series of length n, that is, the symplectic geometric components SGC of d filtered signals i .

5. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 1, characterized in that Step 6 specifically includes the following steps: Select the components with a kurtosis value greater than 3.5 from the first c groups of symplectic geometric components according to the kurtosis criterion as the symplectic geometric components related to the bearing faults.

6. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 5, wherein Step 7 specifically includes the following steps: Step 7.1: Denote the symplectic geometric components related to the rolling bearing fault as d i (t), i = 1, 2,..., h, where h is the total number of symplectic geometric components related to the rolling bearing fault; Step 7.

2. Perform singular value decomposition on the row vector matrix composed of d i (t) to obtain the corresponding eigenvalues; Step 7.3, select the number of eigenvalues that satisfy the following inequality condition, and the inequality is: In the formula: e is the number of eigenvalues that satisfy the inequality, and o is the total number of eigenvalues; Step 7.4, identify the eigenvalue pairs obtained in Step 7.3 by using a heuristic criterion.

7. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 6, wherein The heuristic criterion in Step 7.4 specifically includes: If the following conditions are satisfied simultaneously, then select the eigenvalues and use them as the period pairs without noise: where: λ i , λ j are eigenvalues, p m , p n refer to the highest values obtained from the Fourier transform of the eigenvectors, and i, j are less than e.

8. The rolling bearing compound fault diagnosis method based on improved symplectic geometric mode decomposition according to claim 1, characterized in that, Step 8 specifically includes: Taking each reconstructed symplectic geometry component as a clustering center, calculate the Spearman similarity between every two clustering centers, and the Spearman similarity is calculated by the following formula: In the formula, 1 ≤ i ≤ N, where N is the data length.

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