Bearing fault diagnosis method and system based on multivariate symplectic sparse unified decomposition

Abstract

The invention belongs to but not limited to the technical field of fault diagnosis, and particularly relates to a bearing fault diagnosis method and system based on multivariate symplectic sparse unified decomposition, and the method comprises the steps: firstly, achieving the pre-noise reduction of symplectic geometric atoms through constructing a sparse filter; then, a CAP method is adopted to realize unified characterization of multi-channel signals; and finally, optimizing the parameters of the constructed sparse filter by taking a regularized singular local linear operator as an optimization target, thereby not only realizing modal alignment of a multi-channel signal decomposition result, but also constraining the multi-channel signal decomposition result as a local narrowband signal. The MSSUD method adopts a CAP method to process symplectic geometric atom reconstruction signals. According to the method, the projection vector can be adaptively acquired according to the characteristics of the multi-channel signal, the multi-channel signal is projected to the hyper-spherical surface to obtain the unified representation of the multi-channel signal, and the adaptive frequency band unified segmentation of the multi-channel signal can be realized by combining the sparse filter.

Description

Technical Field

[0001] The present invention belongs to but is not limited to the field of fault diagnosis technology, and in particular relates to a bearing fault diagnosis method and system based on multivariate sparse unified decomposition. Background Art

[0002] Due to the severity of rolling bearing faults, signal transmission paths, and interference from other components, the single-channel signal collected by the sensor often cannot accurately and comprehensively describe the fault characteristic information of the bearing. However, most existing fault diagnosis methods process single-channel signals of a single sensor and fail to effectively utilize multi-channel signals. Compared with single-channel signals, multi-channel signals can reduce the uncertainty of collected signals to a certain extent and can more accurately and comprehensively characterize the characteristic information of the equipment.

[0003] Thanks to the continuous efforts of researchers, signal processing methods in the field of fault diagnosis have flourished and achieved fruitful research results. Classic adaptive signal decomposition methods have their own shortcomings. EMD is simple and efficient, but it is prone to modal aliasing and endpoint effects. EEMD adds multiple groups of noise to the original signal, and reduces the impact of modal aliasing by ensemble averaging the intrinsic mode functions of different noisy signals, but it introduces residual noise. ITD borrows and modifies the extraction method of the mean curve in EMD, and uses linear transformation instead of cubic spline interpolation to further improve the decomposition efficiency, but the decomposition result is prone to burrs. VMD constructs a variational optimization problem in the frequency domain, constraining the intrinsic mode function to be an amplitude-frequency modulated component with different center frequencies and limited bandwidths. However, it is sensitive to parameter settings, especially the number of modes, which significantly reduces the adaptability of VMD.

[0004] Matrix decomposition is applied to signal processing, providing a new way to analyze signals. At first, singular value decomposition and singular spectrum analysis were used as a means of signal denoising, but their denoising effect is greatly affected by the reconstruction order and is sensitive to the dimension of the constructed matrix. A large matrix will increase the burden of the subsequent reconstruction link, while a small matrix will lead to incomplete signal-noise separation. Li et al. proposed the relative change rate of the singular envelope spectrum kurtosis to determine the reconstruction order of singular value decomposition, and combined the filtered signal with the envelope power spectrum to extract the fault characteristic frequency of the bearing. It is generally believed that after matrix decomposition, the characteristic information related to the fault in the signal will be distributed in the obtained eigenvectors, and how to determine it / them is the key to diagnosing the fault. Symplectic geometric mode decomposition believes that the characteristic information is concentrated in the eigenvectors corresponding to the first few eigenvalues, converts the individual eigenvectors into initial single components, merges the initial single components with similar cycles based on the cycle similarity metric, and sets a threshold for the normalized mean square error (NMSE) ratio to terminate the merger. This approach not only fuses the characteristic information scattered in different eigenvectors together, but also takes into account the additional burden of processing all eigenvectors.

[0005] However, the above methods are only applicable to single-channel signal processing, not to multi-channel signals. Although the above methods can also process the signals of multiple channels one by one, the one-by-one processing fails to take into account the correlation between the signals of each channel. Therefore, the results obtained by using the above methods for multi-channel signal processing are often difficult to fuse information. In view of the problem that the EMD method cannot process multi-channel signals, MEMD projects the multi-channel signals onto a hypersphere to obtain high-dimensional direction vectors uniformly distributed in space, and then calculates the local mean of the high-dimensional signal envelope to achieve a unified representation of the multivariate signal and ensure the consistency of the signal components of each channel in terms of quantity and frequency scale. Although the multivariate extension method of EMD inherits the original characteristics of EMD and overcomes the problem that the basic function cannot be adaptively selected, it still has disadvantages such as modal aliasing and sensitivity to noise. The MVMD method defines the multivariate signal by constructing variational optimization and constraining the joint frequency components of each channel to ensure that all channel signals have components with common frequencies, that is, the mode alignment property. However, like the VMD method, MVMD still needs to pre-set the number of components and penalty parameters.

[0006] In view of the above analysis, the technical problems that need to be urgently solved in the prior art are: the existing methods are only applicable to single-channel signal processing, and are not applicable to multi-channel signal processing. Although the existing methods can also process the signals of multiple channels one by one, the one-by-one processing fails to take into account the correlation between the signals of each channel. Summary of the invention

[0007] In view of the problems existing in the prior art, the present invention provides a bearing fault diagnosis method and system based on multi-symplectic sparse unified decomposition.

[0008] The present invention is implemented as follows: a bearing fault diagnosis method based on multivariate sparse unified decomposition, comprising:

[0009] Firstly, a symplectic geometric atom library of the vibration signals of each channel is constructed. Then, effective atoms are selected and merged through the regularized smoothing operator to obtain the smoothed vibration signals, thereby realizing the pre-denoising of the signals of each channel. Then, the advantage of CAP that can adaptively obtain the projection vector according to the characteristics of multi-channel signals is utilized to project the multi-channel signals onto the hypersphere to obtain a unified representation of the multi-channel signals. Finally, taking the regularized local narrowband operator as the optimization target, the constructed sparse filter parameters are optimized to achieve the unified segmentation of the frequency bands of multi-channel signals while making the decomposition results constrained to local narrowband signals have better physical meaning.

[0010] Furthermore, the bearing fault diagnosis method based on multivariate sparse unified decomposition specifically includes:

[0011] Step 1: Symplectic geometry pre-denoising;

[0012] Step 2: Multi-channel signal projection;

[0013] Step 3: Frequency band uniform division.

[0014] Further, step 1 specifically includes:

[0015] S101, for a multivariate signal S(n)=[s1(n),s2(n),…,s l (n)], respectively for each s i (n) performs pre-noise reduction, let r1(n) = s i (n), construct the phase space trajectory matrix X.

[0016]

[0017] n is the data length, d is the embedding dimension, which is usually set to n / 3, τ is the delay length, m = n-(d-1)τ, and the embedding dimension d and delay length τ are determined by PSD to obtain the reconstruction matrix X, and the symplectic geometric atomic library Y = [y1(n), y2(n),…,y k (n),…].

[0018] S102, calculating the singular local linear operator of each initial single component.

[0019]

[0020] in, For evaluating symplectic geometry atoms, The larger the symplectic geometry, the greater the energy of the atom, and the smaller the decomposition residue. k The regularized smoothness operators of (n) are sorted from large to small as follows:

[0021] Y'=[y1'(n),y2'(n),…,y k '(n),…]

[0022] S103, construct u=smooth(y k '(n)) / smooth(r1(n)) is used as the reconstruction threshold index, and the symplectic geometric atoms with u>0.001 are selected for reconstruction to obtain the partial symplectic geometric atomic matrix Y"=[y1'(n),y2'(n),…,y m '(n)], the remaining large number of weak invalid components do not participate in the reconstruction process, thereby reducing the amount of calculation and improving the decomposition speed.

[0023] S104, merge y1'(n) with other symplectic geometry atoms in turn, recalculate the singular local linear operator value, and merge if it decreases, to obtain the components s after symplectic geometry pre-denoising i '(n), and construct the noise reduction multi-channel signal matrix S'(n).

[0024] Further, step 2 specifically includes:

[0025] S201, let R(n) = S'(n), and use the CAP projection strategy to obtain J projection vectors according to the characteristics of R(t) itself Then, calculate R(n)=[r1(n),r2(n),…,r M (n)]

[0026] S202, averaging the J projection signals to obtain a unified representation signal m(n) of the multi-channel signal.

[0027]

[0028] Further, step 3 specifically includes:

[0029] S301, construct filter X(k|λ), λ=[ω,ω b ,ω c ]:

[0030] By solving the following optimization problem P1, the optimal filtering parameter λ1=[ω,ω b ,ω c ]:

[0031]

[0032] in For As a singular local linear operator, the optimization problem is solved by minimizing The unified representation signal of the filtered multi-channel signal is constrained to be a local narrowband signal, thereby achieving the purpose of adaptive frequency band segmentation. Used to regularize the optimization objective function, D' is a differential operation used to regularize The λ weight can usually be set to

[0033] S303, order Repeat S302 to construct the optimal filter parameter matrix F = [λ1, λ2, ..., λ i ,…] until Finally, the filter bank constructed in F is used to filter the channel signals after symplectic geometry denoising in Y” to achieve unified segmentation of multi-channel signal bands and obtain the multivariate symplectic sparsest mode component (MSSMC) of each channel.

[0034] Another object of the present invention is to provide a bearing fault diagnosis system based on multivariate sparse unified decomposition to implement the bearing fault diagnosis method based on multivariate sparse unified decomposition, comprising:

[0035] Pre-denoising module: used for symplectic geometry pre-denoising;

[0036] Signal projection module: used for multi-channel signal projection;

[0037] Consent segmentation module: used to perform uniform frequency band segmentation.

[0038] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the bearing fault diagnosis method based on multi-symplectic sparse unified decomposition.

[0039] Another object of the present invention is to provide a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the bearing fault diagnosis method based on multi-symplectic sparse unified decomposition.

[0040] Another object of the present invention is to provide an information data processing terminal, which includes the bearing fault diagnosis system based on multi-symplectic sparse unified decomposition.

[0041] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0042] First, the present invention uses symplectic geometry mode decomposition (SGMD) to decompose the time series into several symplectic geometry mode components with independent modes. It has the advantages of not requiring subjective custom parameters and being able to effectively reconstruct existing modes and eliminate noise. On its theoretical basis, the MSSUD method is proposed. MSSUD first constructs a symplectic geometry atom library, and selects effective atoms through regularized complex-valued differential operators for merging, thereby achieving pre-noise reduction of each channel signal. Then, the advantage of CAP that can adaptively obtain projection vectors according to the characteristics of multi-channel signals is used to project multi-channel signals onto a hypersphere to obtain projection signals, thereby achieving unified representation of multi-channel signals. Finally, taking the regularized singular local linear operator as the optimization target, the parameters of the constructed sparse filter are optimized, and the decomposition results are constrained to local narrowband signals while achieving unified segmentation of multi-channel signal bands, so that the decomposition results have physical meaning. The simulation and experimental analysis results show that the MSSUD method not only has the ability to align the modes of different channel components, but also outperforms the compared MEMD and MVMD methods in terms of decomposition accuracy and noise resistance. The innovations are as follows:

[0043] 1. Aiming at the problem that the modes of decomposition results are difficult to align when the SGMD method processes multi-channel vibration signals, the fully adaptive projection method (CAP) is used to achieve unified representation of multi-channel signals, and then a series of sparse filter groups are constructed to achieve unified segmentation of multi-channel signals in the frequency domain.

[0044] 2. In order to solve the problem that the SGMD method lacks physical meaning, the parameters of the constructed sparse filter are optimized by using the complex-valued differential operator as the optimization objective function, so that the decomposed components are constrained to be local narrow-band signals, making the decomposition results have physical meaning. On this basis, the MSSUD method is proposed.

[0045] 3. The comparative analysis with MVMD and MEMD methods shows that the MSSUD method not only has the modal alignment property, but also has better decomposition accuracy and anti-noise ability.

[0046] Second, as auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0047] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0048] (2) The technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0049] As a relatively novel adaptive signal decomposition method, SGMD has received extensive attention and continuous research from many scholars. At present, several improved versions have been extended, all of which have achieved good results. However, these algorithms still focus on single-channel signals and have poor adaptability to multi-channel signals. Judging from the current development trend, multi-channel signals can characterize the state of the device under test more comprehensively and meticulously from multiple dimensions, avoiding the randomness and contingency of the measurement to a certain extent, and will have a wider range of applications in the future. The technology of the present invention expands the original SGMD method technology based on this, so that it has the ability to process multi-channel signals. At the same time, compared with the existing popular multi-channel signal processing technology methods MEMD and MVMD, it has better decomposition effect. Specifically manifested in:

[0050] 1. Using fully adaptive projection technology, the processing core of the multi-channel signal decomposition algorithm is realized: mode alignment. The same mode of signals from different channels is linked to each other, and the state information of each channel is intuitively obtained, which facilitates the implementation of subsequent processing technology.

[0051] 2. The signal decomposition process is constrained by the set singular local linear operator to ensure that each component exhibits amplitude and frequency modulation characteristics in the time domain. Compared with the components obtained by MEMD and MVMD decomposition, they have clear physical meanings.

[0052] 3. Design sparse filters and optimize filter parameters through advanced optimization algorithms to avoid falling into local optimal solutions. Divide the signal into different frequency bands in the frequency domain, and adjust the center frequency and bandwidth to avoid overlapping of different signal components in the frequency domain, thereby effectively preventing the occurrence of modal aliasing.

[0053] Third, the technical solution of the present invention solves the following key problems in the prior art through a bearing fault diagnosis method based on multivariate sparse unified decomposition, and has achieved significant technical progress:

[0054] 1. Technical problems of existing technologies

[0055] Large noise interference and inaccurate signal extraction: In traditional bearing fault diagnosis methods, due to factors such as external environmental noise and equipment resonance, the signal preprocessing effect is not ideal in multi-channel signals, and it is difficult to accurately extract the characteristic signals of bearing faults.

[0056] Complex multi-channel signal processing: The amount of multi-channel vibration signal data is large, and existing methods cannot effectively integrate the information of each channel for unified analysis, resulting in the inability to fully reflect the fault characteristics, which increases the complexity and inaccuracy of fault identification.

[0057] Frequency band segmentation is not suitable for fault feature extraction: In the existing technology, frequency band segmentation technology generally has the problem of too coarse segmentation granularity, which cannot adapt to the local frequency characteristics of bearing faults, thus affecting the diagnosis accuracy.

[0058] Poor sparse decomposition effect: Existing sparse decomposition methods usually have problems of over-decomposition or large decomposition residues when processing multi-modal signals in bearing fault diagnosis, resulting in the inability to effectively extract fault modes, affecting the efficiency and accuracy of fault diagnosis.

[0059] 2. Significant technical advancement of the present invention

[0060] The pre-noise reduction method based on symplectic geometry improves signal quality: The present invention constructs a symplectic geometry atomic library and combines it with a regularized smoothing operator for effective noise reduction, which significantly improves the signal-to-noise ratio of multi-channel vibration signals, makes the characteristic signals of bearing faults clearer, and solves the problem of inaccurate signal extraction caused by noise interference.

[0061] The unified representation of multi-channel signals improves the fault diagnosis accuracy: the CAP projection strategy is used to project multi-channel vibration signals onto a hypersphere to generate a unified signal representation, which overcomes the defect that multi-channel signals are difficult to comprehensively process in the existing technology, and can better extract the global characteristics of bearing faults, greatly improving the diagnosis accuracy.

[0062] Adaptive frequency band segmentation enhances the sensitivity of fault feature extraction: by optimizing the filter parameters and combining the regularized local narrowband operator, the present invention realizes the adaptive frequency band unified segmentation of multi-channel signals, which can accurately extract the local narrowband features of bearing faults, improve the precision of feature extraction, and thus achieve more sensitive fault detection.

[0063] Efficient sparse decomposition reduces the amount of calculation: The present invention avoids unnecessary decomposition calculations and significantly reduces the amount of calculation by optimizing the sparse filter parameters and selecting effective symplectic geometric atoms for reconstruction. At the same time, the decomposition results have better physical meaning, making the modal characteristics of the bearing fault more prominent, thereby improving the efficiency and accuracy of fault diagnosis.

[0064] The present invention has made significant technical progress in the preprocessing, characterization, frequency band segmentation and sparse decomposition of multi-channel signals through the multi-symplectic sparse unified decomposition method, and solved many bottleneck problems in the prior art. This method not only improves the extraction quality of bearing fault signals, but also significantly enhances the accuracy and efficiency of diagnosis, and has broad industrial application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a schematic diagram of a CAP projection strategy provided by an embodiment of the present invention;

[0066] Figure 2 is a flow chart of the MSSUD method provided by an embodiment of the present invention;

[0067] Figure 3 is a schematic diagram of a filter χ(k|λ) provided in an embodiment of the present invention;

[0068] Figure 4 is a schematic diagram of MSSMC components obtained by decomposing MSSUD according to an embodiment of the present invention;

[0069] Figure 5 is a schematic diagram of SSMC components obtained by SGMD decomposition according to an embodiment of the present invention;

[0070] Figure 6 Schematic diagram of Gaussian white noise with a standard deviation of 0.01 added to the three channel simulation signals provided by an embodiment of the present invention; wherein (a) is the noise n1(t) added to S1(t); (b) is the noise n2(t) added to S2(t); c) is the noise n3(t) added to S3(t);

[0071] Figure 7 is a schematic diagram of MSSMC components obtained by decomposing MSSUD according to an embodiment of the present invention;

[0072] Figure 8 is a schematic diagram of MIMF components obtained by MVMD decomposition according to an embodiment of the present invention;

[0073] Fig. 9 is a schematic diagram of MIMF components obtained by MEMD decomposition according to an embodiment of the present invention;

[0074] Fig.10 Schematic diagram of Gaussian white noise with a standard deviation of 1 added to the three channel simulation signals provided by an embodiment of the present invention; wherein (a) is the noise n1(t) added to S1(t); (b) is the noise n2(t) added to S2(t); c) is the noise n3(t) added to S3(t);

[0075] Fig.11 is a schematic diagram of MSSMC components obtained by decomposing MSSUD according to an embodiment of the present invention;

[0076] Fig.12 is a schematic diagram of MIMF components obtained by MVMD decomposition according to an embodiment of the present invention;

[0077] Fig.13is a schematic diagram of MIMF components obtained by MEMD decomposition according to an embodiment of the present invention;

[0078] Fig.14 Time domain diagram of multi-channel bearing fault simulation signal;

[0079] Fig.15 Schematic diagram of the envelope spectrum of multi-channel bearing fault simulation signal; (a) is the envelope spectrum corresponding to S1(t); (b) is the envelope spectrum corresponding to S2(t); (c) is the envelope spectrum corresponding to S3(t);

[0080] Fig.16 The component graph obtained by decomposing the multi-channel bearing fault simulation signal and fusing it is obtained by using the MSSUD method;

[0081] Fig.17 The component graph obtained by fusion after decomposing the multi-channel bearing fault simulation signal by MVMD method;

[0082] Fig.18 The component graph obtained by fusion after decomposing the multi-channel bearing fault simulation signal using MEMD method;

[0083] Fig.19 Envelope spectrum of multi-channel bearing fault simulation signal components; (a) MSSUD method; (b) MVMD method; (c) MEMD method;

[0084] Fig. 20 is a schematic diagram of a bearing fault test bench provided by an embodiment of the present invention;

[0085] Fig.21 is a schematic diagram of an experimental bearing provided by an embodiment of the present invention;

[0086] Fig. 22 is a time domain diagram of a three-channel bearing inner ring fault vibration signal provided by an embodiment of the present invention;

[0087] Fig.23 : is an envelope spectrum of a three-channel bearing inner ring fault vibration signal provided by an embodiment of the present invention; wherein, (a) S1; (b) S2; (c) S3;

[0088] Fig.24 is a schematic diagram of fused fault vibration signal components obtained by using MSSUD decomposition according to an embodiment of the present invention;

[0089] Fig.25 is a schematic diagram of fused fault vibration signal components obtained by using MVMD decomposition according to an embodiment of the present invention;

[0090] Fig.26 is a schematic diagram of fused fault vibration signal components obtained by using MEMD decomposition according to an embodiment of the present invention;

[0091] Fig. 27 Schematic diagram of envelope spectrum of corresponding components obtained by using MSSUD method provided by an embodiment of the present invention; wherein, (a) MSSMC1; (b) MSSMC2; (c) MSSMC3; (d) MSSMC4;

[0092] Fig.28 Schematic diagram of envelope spectra of corresponding components obtained by using the MVMD method provided in an embodiment of the present invention; wherein, (a) MIMF1; (b) MIMF2; (c) MIMF3; (d) MIMF4;

[0093] Fig.29 Schematic diagram of envelope spectra of corresponding components obtained using the MEMD method provided in an embodiment of the present invention; wherein, (a) MIMF1; (b) MIMF2; (c) MIMF3; (d) MIMF4. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0095] The bearing fault diagnosis method based on multivariate sparse unified decomposition provided by the present invention can be applied in the following two industrial embodiments:

[0096] Example 1: Bearing Fault Diagnosis of Wind Turbine Generator Set

[0097] In a wind turbine generator set, the bearing is one of the key mechanical components, and its operating status directly affects the performance and reliability of the generator. Through this method, multi-channel vibration signal collection and analysis of the bearing of the wind turbine generator set can be performed. The specific implementation steps are as follows:

[0098] 1. Pre-noise reduction: The vibration signal of the wind turbine is interfered by environmental noise and other mechanical vibrations. Through symplectic geometry atom library screening and preprocessing, the interference noise can be effectively removed to obtain a clear bearing vibration signal.

[0099] 2. Multi-channel signal projection: Combining the multi-channel vibration signals of the wind turbine, the CAP projection strategy is used for unified characterization to generate signal features representing the bearing fault status.

[0100] 3. Frequency band segmentation and fault identification: By optimizing the filter group to achieve unified frequency band segmentation of the bearing vibration signal, the characteristic frequency of the bearing fault can be better decomposed and early faults such as wear and fatigue cracks can be identified.

[0101] Example 2: Bearing Fault Monitoring for Railway Locomotives

[0102] In railway locomotives, bearings bear the mechanical load between wheels and tracks, and bearing failures can lead to serious safety hazards. This method can be used to monitor locomotive bearings online, and the specific steps include:

[0103] 1. Pre-noise reduction: The vibration signal of a railway locomotive is complex during operation. By constructing a symplectic geometry atom library of vibration signals and using pre-noise reduction technology to remove invalid vibration components, the clarity of the signal can be improved.

[0104] 2. Multi-channel signal projection: For the multi-channel sensor data of different parts of the locomotive, the overall signal representation is obtained through multi-channel unified projection, so as to extract the fault characteristic signal.

[0105] 3. Frequency band segmentation and fault analysis: By optimizing the frequency band segmentation through the filter group, specific fault frequencies can be identified, such as rolling element wear, inner and outer ring peeling, etc., thereby realizing real-time health monitoring of locomotive bearings.

[0106] These two embodiments demonstrate the application potential of this method in the fields of wind power generation and railway transportation, and can effectively improve the fault diagnosis accuracy and early fault identification capabilities of mechanical equipment.

[0107] 1. Relevant theories applied in the embodiments of the present invention

[0108] 1.1 Fully Adaptive Projection

[0109] The Completely Adaptive Projection (CAP) method can effectively solve the problem of lack of adaptability of projection vectors generated by traditional hypersphere uniform sampling methods such as uniform angle sampling method and Hammersley uniform sampling method. The basic process of the CAP method is as follows:

[0110] Assume that the multi-channel signal to be decomposed can be expressed as a set {y1(t),y2(t),…,y d (t),…,y D (t)} (t=1,2,…,T',D is the number of channels). Then, the multi-channel signal is represented by a multivariate signal Y(t), Y(t)=[y1(t),y2(t),…,y d (t),…,y D (t)].

[0111] (1) Using the Hamersley uniform sampling method, uniform sampling is performed on the (D-1)-dimensional sphere to obtain a series of projection vectors (I is the number of projections, Construct the covariance matrix E{Y(t) TY(t)} (E is the statistical expectation operator, T is the transpose of the matrix), for the covariance matrix E{Y(t) T Y(t)} is subjected to eigenvalue decomposition. Define E{Y(t) T The eigenvector corresponding to the largest eigenvalue of Y(t)} is the principal direction vector, is the main reverse direction vector. Calculate each uniform projection vector P i To the main direction vector The Euclidean distance will be close to the main direction vector Half uniform projection vector Formula (1) is used for relocation.

[0112]

[0113] (2) Close to the main reverse vector Half uniform projection vector Formula (2) is used for relocation.

[0114]

[0115] In formula (1) and formula (2), and is the uniform projection vector is the aggregation direction, and c is the aggregation degree. The aggregation degree is related to the power imbalance between multi-channel signals.

[0116] (3) The power of multi-channel signals can be expressed by calculating the square of the power of each channel of the multivariate signal, and the Gini index can well reflect the imbalance of the data. Therefore, the degree of aggregation a can be determined by calculating the Gini index of the square of the power vector of each channel of the multivariate signal. a can be expressed by formula (3).

[0117]

[0118] Through the above steps, a fully adaptive projection vector suitable for the multivariate signal itself can be obtained:

[0119]

[0120] The projection strategy of CAP is as follows Figure 1 shown.

[0121] Figure 1 The blue and red points in the figure represent the principal component direction vector and its reverse direction vector, respectively. When a=0, the projection vectors are evenly distributed, and the projection degenerates into Hammersley uniform projection. When a=1, the projection vectors gather toward the principal component direction vector and its reverse direction vector, respectively. CAP can adaptively obtain a according to the characteristics of the signal itself.

[0122] 1.2 Single-component AM-FM annihilation operator

[0123] The second-order differential operator can annihilate the AM-FM component in the signal, that is, the operator T1 satisfies The operator is shown in formula (5). The second and first differential operations on the AM-FM component are represented respectively.

[0124] T1=D”+P(t)*D'+Q(t) (5)

[0125] Furthermore, by solving the ordinary differential equation formed by the above equation, the parameters P(t) and Q(t) in the operator T1 can be determined. The specific result is shown in equation (6). Therefore, the single-component AM-FM component annihilation operator T2 is also determined.

[0126]

[0127] Among them, A(t) and are the amplitude and phase of the AM-FM signal, is the angular frequency.

[0128] 1.3 Principle of the Multivariate Symplectic Sparse Unified Decomposition Method

[0129] The multivariate sparse unified decomposition (MSSUD) method first constructs a symplectic geometric atom library for the vibration signals of each channel, selects valid atoms through the regularized smoothing operator for merging, and obtains the smoothed vibration signal, thereby realizing the pre-noise reduction of each channel signal. Then, the advantage of CAP's ability to adaptively obtain the projection vector according to the characteristics of the multi-channel signal is used to project the multi-channel signal onto the hypersphere to obtain a unified representation of the multi-channel signal. Finally, taking the regularized local narrowband operator as the optimization target, the constructed sparse filter parameters are optimized to achieve unified segmentation of the multi-channel signal band while making the decomposition results constrained to the local narrowband signal have better physical meaning. The MSSUD method is divided into three main steps: symplectic geometric pre-noise reduction, multi-channel signal projection, and unified band segmentation. The algorithm flow is as follows: Figure 2 As shown, the iterative process is as follows:

[0130] Step 1: Symplectic geometry pre-denoising

[0131] (1) For a multivariate signal S(n) = [s1(n), s2(n), …, s l (n)], respectively for each s i (n) performs pre-noise reduction, let r1(n) = s i (n), construct the phase space trajectory matrix X.

[0132]

[0133] n is the data length, d is the embedding dimension, which is usually set to n / 3, τ is the delay length, m = n-(d-1)τ, and the embedding dimension d and delay length τ are determined by PSD to obtain the reconstruction matrix X, and the symplectic geometric atomic library Y = [y1(n), y2(n),…,y k (n),…].

[0134] (2) Calculate the singular local linear operator of each initial single component.

[0135]

[0136] in, For evaluating symplectic geometry atoms, The larger the symplectic geometry, the greater the energy of the atom, and the smaller the decomposition residue. k The regularized smoothness operators of (n) are sorted from large to small as follows:

[0137] Y'=[y1'(n),y2'(n),…,y k '(n),…] (9)

[0138] (3) Construct u = smooth (y k '(n)) / smooth(r1(n)) is used as the reconstruction threshold index, and the symplectic geometric atoms with u>0.001 are selected for reconstruction to obtain the partial symplectic geometric atomic matrix Y"=[y1'(n),y2'(n),…,y m '(n)], the remaining large number of weak invalid components do not participate in the reconstruction process, thereby reducing the amount of calculation and improving the decomposition speed.

[0139] (4) Merge y1'(n) with other symplectic geometry atoms in turn, recalculate the singular local linear operator value, and merge if it decreases, to obtain the components s after symplectic geometry pre-denoising i '(n), and construct the noise reduction multi-channel signal matrix S'(n).

[0140] Step 2: Multi-channel signal projection

[0141] (1) Let R(n) = S'(n), and use the CAP projection strategy to obtain j projection vectors according to the characteristics of R(t) Then, calculate R(n)=[r1(n),r2(n),…,r M (n)]

[0142] (2) Calculate the average of the J projection signals to obtain a unified representation signal m(n) of the multi-channel signal.

[0143]

[0144] Step 3: Band uniform division

[0145] (1) Construct the filter χ(k|λ) in equation (11), λ=[ω,ω b ,ω c ],χ(k|λ) Figure 3 Displayed in.

[0146]

[0147] (2) By solving the following optimization problem P1, the optimal filtering parameter λ1 = [ω, ω b ,ω c ]:

[0148]

[0149] in For As a singular local linear operator, the optimization problem is solved by minimizing The unified representation signal of the filtered multi-channel signal is constrained to be a local narrowband signal, thereby achieving the purpose of adaptive frequency band segmentation. Used to regularize the optimization objective function, D' is a differential operation used to regularize The λ weight can usually be set to

[0150] (3) Order Repeat step (2) to construct the optimal filter parameter matrix F = [λ1,λ2,…,λ i ,…] until Finally, the filter bank constructed in F is used to filter the channel signals after symplectic geometry denoising in Y” to achieve unified segmentation of multi-channel signal bands and obtain the multivariate symplectic sparsest mode component (MSSMC) of each channel.

[0151] 2. Simulation signal analysis

[0152] 2.1 Comparison between MSSUD and SGMD

[0153] To prove that the multivariate signal processing method MSSUD has the property of modal alignment when processing multi-channel signals. The multivariate simulation signal shown in equation (13) is constructed and decomposed by MSSUD and SGMD methods respectively. It is worth noting that the signals S1(t), S2(t) and S3(t) of different channels are decomposed separately by SGMD method in turn. The sampling rate and sampling time are set to 3000Hz and 1s. The decomposition results of the two methods are shown as follows: Figure 4 and Figure 5 shown.

[0154]

[0155] contrast Figure 4 and Figure 5 It is known that in Figure 4 Components at the same sorting position in have similar oscillation patterns, while Figure 5 The components in the same sorting position do not have similar oscillation modes. This shows that the MSSUD method can link the same signal components from different channels in the multivariate signal with each other and has the property of modal alignment. However, the SSMD method does not have this modal alignment property.

[0156] 2.2 Comparison of decomposition performance

[0157] In order to illustrate the superiority of the MSSUD method over other multivariate signal analysis methods, a multivariate simulation signal consisting of an amplitude modulated signal, a sine signal, a cosine signal and intermittent Gaussian white noise is defined as shown in Equation 14, and is decomposed using MSSUD, MVMD and MEMD, respectively, and the decomposition results are compared.

[0158]

[0159] n(t) is an intermittent Gaussian white noise with a standard deviation of 0.01, such as Figure 6 The sampling frequency is 3000Hz and the sampling time is 1s. The decomposition results are as follows: Figure 7-9 shown.

[0160] Depend on Figure 7 and Figure 8 It can be seen that the components at the same sorting position have similar oscillation modes, which once again proves that MSSUD and MVMD also have the property of modal alignment. In addition, MSSUD separates the added noise and has a higher decomposition accuracy than MVMD. Fig. 9 In the example, although MEMD also has the property of modal alignment, the noise causes the generated components to undergo modal aliasing. To show the noise resistance of MSSUD, intermittent Gaussian white noise with a standard deviation of 1 is added to the multivariate simulation signal, as shown in Fig.10 As shown. And use the above three methods to decompose in turn, the results are as follows Figure 11-13 As shown in the figure. Although the noise enhancement further deteriorates the decomposition effect of MEMD, the components of different frequencies in MSSUD and MVMD still maintain modal alignment. In terms of decomposition accuracy, since MSSUD separates the noise in the simulation signal more thoroughly than MVMD, the components generated by MSSUD are closer to the original components and have higher decomposition accuracy.

[0161] 2.3 Simulation fault signal analysis

[0162] To illustrate the feasibility of MSSUD in rolling bearing fault diagnosis, further simulation analysis is performed as follows. The multi-channel signal collected by the sensor is often a mixture of multiple component signals with noise, and there are differences between the signals of different channels. To simulate the multi-channel rolling bearing fault signal collected under actual conditions, the following three original signals x1(t), x2(t) and x3(t) are defined.

[0163]

[0164] Where x3(t) is a simplified model representing the vibration signal of the bearing inner ring fault. r is the transfer frequency, f i is the characteristic frequency of the inner race fault. The frequencies of the three original signals are set as: f1 = 40 Hz, f2 = 150 Hz, f i =100Hz, f r =24Hz, sampling rate is 2000, sampling time is 1s.

[0165] Use a 3×3 matrix A for random mixing, which can be obtained by the random function:

[0166]

[0167] And add Gaussian white noise n with standard deviation 1 i , and obtain Fig.12 The simulated fault signals of the three channels are shown in the figure. The specific process is as follows:

[0168]

[0169] The envelope spectrum of channel signals S1(t), S2(t) and S3(t) is analyzed in turn. The envelope spectrum is as follows: Fig.13 As shown, Fig.13 The red dotted line is f r and its double frequency, the red dotted line is f i It can be observed from the envelope spectrum that both the rotation frequency and the fault characteristic frequency are masked by noise. It can be concluded that directly performing envelope spectrum analysis on the signal cannot directly extract the fault characteristic frequency and rotation frequency information of the simulated multi-channel bearing fault signal.

[0170] The three aforementioned multivariate signal decomposition methods are used to decompose the simulation signals of the three channels in turn. Because the three multivariate signal decomposition methods all have the property of modal alignment, the components with the same sequence number in the three channels are added together, and the components after fusion of each method are as follows Figure 14-16 Then, the component with the most fault information is selected for envelope spectrum analysis. The envelope spectra corresponding to the three methods are shown as follows: Fig.17 As shown in the figure. The envelope spectrum corresponding to MSSUD contains the rotation frequency and the double frequency of the rotation frequency. At the same time, the fault characteristic frequency and its double frequency are also relatively obvious, and the fault characteristic information in the simulated multi-channel bearing fault signal is extracted. Although the envelope spectrum corresponding to MVMD also contains the rotation frequency and its double frequency, the fault characteristic frequency is not as obvious as MSSUD, and the double frequency is difficult to observe. The envelope spectrum corresponding to MEMD only contains the more prominent rotation frequency, and the fault characteristic frequency is submerged in the interference of other spectral lines. Therefore, the MVMD and MEMD methods cannot extract the fault characteristic information in the simulated multi-channel bearing fault signal.

[0171] 3. Experiment

[0172] In order to study the effectiveness of this method in actual rolling bearing fault diagnosis, a Fig. 20 The bearing test bench shown in the figure is used for experimental verification. The test bench is generally composed of a servo motor, a test bearing, a support bearing, a coupling, an acceleration sensor and a B&K Pulse signal acquisition system.

[0173] The three acceleration sensors are fixed on the top and both sides of the experimental bearing seat by magnetic attraction. The sampling rate is set to 65536Hz. When the signal acquisition system works normally, the bearing vibration data of three channels from three sensors can be recorded simultaneously. The test bearing model is 6206, and the parameters are shown in Table 2. The inner ring fault is artificially set by electric spark cutting, and the cutting depth is 0.2mm. The faulty part is as follows Fig.21 shown.

[0174] Table 2 Experimental bearing specifications

[0175]

[0176] Table 3 Fault related frequencies

[0177]

[0178] The speed was set to 1182 rpm during the test. After the speed stabilized, 43 seconds of bearing inner race fault data were collected. The time domain signals of the three channels at the 15th to 16th seconds were intercepted. Fig. 22 As shown in the figure, the signal is used as the experimental signal for fault analysis. First, the envelope spectrum of the experimental signals of the three channels is analyzed. The envelope spectrum is shown in Fig.23 As shown, the red dotted line in the figure is the rotation frequency f r and its double frequency. The red dotted line is the characteristic frequency f of the inner ring fault. i The relevant frequencies of the fault signals and their double frequency are shown in Table 3. Due to the presence of environmental noise in the acquired data, the transfer frequency and fault characteristic frequency in the envelope spectrum are masked by noise interference. It can be seen that the direct use of the envelope spectrum analysis method cannot directly extract the fault characteristic frequency and transfer frequency information contained in the vibration signals of the three channels of the bearing.

[0179] Then, the vibration signals of the three channels of the faulty bearing are decomposed by using the MSSUD, MVMD, and MEMD methods. Since the multivariate signal decomposition methods all have the frequency alignment property, when actually applied to fault diagnosis, the components with the same serial number in each channel are directly added together and used as the fused components for subsequent analysis. The obtained signal components are as follows: Figure 24-26 The envelope spectrum of the fused signal components obtained by the three methods is analyzed respectively. The envelope spectrum of the signal components obtained by MSSUD, MVMD, and MEMD is shown in Figure 27-29 The envelope spectrum of the components obtained by MSSUD contains the first and second harmonics of the rotation frequency, and the fault characteristic frequency in the envelope spectrum is also prominent. Therefore, MSSUD can be used to diagnose the inner ring fault of the test bench motor bearing. Fig.26 The envelope spectrum of the components obtained by MVMD is used to extract the double frequency of the rotation frequency and the fault characteristic frequency, but the remaining frequency information is lost. Fig. 27 (b) The envelope spectrum of the components obtained by MEMD only extracts a weak rotation frequency, and the noise has a great impact on the accurate extraction of fault information. Therefore, it is difficult to accurately and effectively diagnose the inner ring bearing fault of the fault test bench using MEMD and MVMD. The above analysis results show that compared with the MEMD and MVMD methods, the MSSUD method can accurately extract the fault feature information in the vibration signal from the noise, and combined with the envelope spectrum, it can effectively realize the fault diagnosis of rolling bearings.

[0180] An application embodiment of the present invention provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor executes the steps of a bearing fault diagnosis method based on multi-symplectic sparse unified decomposition.

[0181] An application embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of a bearing fault diagnosis method based on multivariate symplectic sparse unified decomposition.

[0182] An application embodiment of the present invention provides an information data processing terminal, which includes a bearing fault diagnosis system based on multi-symplectic sparse unified decomposition.

[0183] 1. Specific application fields or related products of the present invention.

[0184] The technology of this invention can be applied to the fault diagnosis of key components (bearings, gears) of rotating machinery or other equipment. The specific application form is: by reasonably arranging multiple acceleration sensors at different positions of the components to be tested, cooperating with the data acquisition system (the acquisition system is generally composed of acquisition card hardware and software system) to collect the vibration signal generated when the equipment is running, and then storing the signal data and importing it into software analysis tools such as matlab or python, the multivariate sparse sparse decomposition algorithm program compiled according to the technology of this invention is used to analyze and process the signal data, classify the original signal into multiple signal components with different characteristics, and finally use the envelope spectrum algorithm program to extract and characterize the fault characteristics, so as to judge the health status of the sensor detection component and achieve the purpose of fault diagnosis.

[0185] 2. Relevant evidence of the technical effects obtained by the embodiments of the present invention.

[0186] To illustrate the practicality of the technology of the present invention, the technology has been successfully applied to a built bearing fault test bench. By analyzing and processing the multi-channel vibration signal data collected by the test bench, the health status of the bearing can be accurately determined. The details are as follows:

[0187] For the test bench shown in the figure below, the experimental bearing is set to the inner ring fault state. The specific parameters of the bearing are shown in Table 1. When the motor of the test bench is running at 1182rpm, the three sensors simultaneously collect signals from three channels. The original time domain diagram of the signal is shown in Figure 2 As shown in the figure, it can be seen from the time domain waveform that the collected signal is mixed with a lot of noise and does not show obvious fault characteristics, that is, periodic pulse shocks.

[0188] In order to diagnose the fault of the signal, the corresponding inner ring fault characteristic frequency is first calculated according to the empirical formula and bearing parameters, as shown in Table 2. Next, the envelope spectrum analysis is directly performed on the signal of each channel. The envelope spectrum is shown in Figure 3 As shown, it is difficult to find the frequency spectrum corresponding to Table 3, which means that the fault state of the experimental bearing cannot be determined by this method.

[0189] The multivariate sparse unified decomposition algorithm compiled by the technology of the present invention is applied to the experimental signal. The algorithm decomposes the signals of the three channels at the same time and aligns the signal components with the same modal characteristics in each channel signal. To further enhance the characteristics, the signal components of the same mode will be merged into one component. The final decomposition result is as follows: Figure 4 As shown in . From this figure, we can clearly observe that the time domain waveforms of different components have different time-frequency characteristics, which are very different from each other. Similarly, the signal components except the residual component in the decomposition result are analyzed by envelope spectrum. The specific envelope spectrum is shown in Figure 5 As shown in the figure, the envelope spectrum corresponding to the first component shows significant frequency spectrum lines and fault characteristic frequency spectrum lines, and also contains certain frequency multiplication information. This fully proves that there is an inner ring fault in the experimental bearing and realizes the fault diagnosis of the experimental bearing.

[0190] Table 1 Experimental bearing specifications

[0191]

[0192] Table 2 Fault related frequencies

[0193]

[0196] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0197] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A bearing fault diagnosis method based on multivariate sparse unified decomposition, characterized in that: include: Firstly, a symplectic geometric atom library of the vibration signals of each channel is constructed. Then, effective atoms are selected and merged through the regularized smoothing operator to obtain the smoothed vibration signals, thereby realizing the pre-denoising of the signals of each channel. Then, the advantage of CAP that can adaptively obtain the projection vector according to the characteristics of multi-channel signals is utilized to project the multi-channel signals onto the hypersphere to obtain a unified representation of the multi-channel signals. Finally, taking the regularized local narrowband operator as the optimization target, the constructed sparse filter parameters are optimized to achieve the unified segmentation of the frequency bands of multi-channel signals while making the decomposition results constrained to local narrowband signals have better physical meaning.

2. The bearing fault diagnosis method based on multivariate sparse unified decomposition according to claim 1 is characterized in that: The bearing fault diagnosis method based on multivariate sparse unified decomposition specifically includes: Step 1: Symplectic geometry pre-denoising; Step 2: Multi-channel signal projection; Step 3: Frequency band uniform division.

3. The bearing fault diagnosis method based on multivariate sparse unified decomposition according to claim 2 is characterized in that: Step 1 specifically includes: S101, for a multivariate signal S(n)=[s1(n),s2(n),…,s l (n)], respectively for each s i (n) performs pre-noise reduction, let r1(n) = s i (n), construct the phase space trajectory matrix X; n is the data length, d is the embedding dimension, which is usually set to n / 3, τ is the delay length, m = n-(d-1)τ, and the embedding dimension d and delay length τ are determined by PSD to obtain the reconstruction matrix X, and the symplectic geometric atomic library Y = [y1(n), y2(n),…,y k (n),…]; S102, calculating the singular local linear operator of each initial single component; in, For evaluating symplectic geometry atoms, The larger the symplectic geometry, the greater the energy of the atom, and the smaller the decomposition residue. k The regularized smoothness operators of (n) are sorted from large to small as follows: Y'=[y1'(n),y2'(n),…,y k '(n),…] S103, construct u=smooth(y k '(n)) / smooth(r1(n)) is used as the reconstruction threshold index, and the symplectic geometric atoms with u>0.001 are selected for reconstruction to obtain the partial symplectic geometric atomic matrix Y"=[y1'(n),y2'(n),…,y m '(n)], the remaining large number of weak invalid components do not participate in the reconstruction process, thereby reducing the amount of calculation and improving the decomposition speed; S104, merge y1'(n) with other symplectic geometry atoms in turn, recalculate the singular local linear operator value, and merge if it decreases, to obtain the components s after symplectic geometry pre-denoising i '(n), and construct the noise reduction multi-channel signal matrix S'(n).

4. The bearing fault diagnosis method based on multivariate sparse unified decomposition according to claim 1 is characterized in that: Step 2 specifically includes: S201, let R(n) = S'(n), and use the CAP projection strategy according to the characteristics of R(t) to obtain J projection vectors Then, calculate R(n)=[r1(n),r2(n),…,r M (n)] S202, averaging the J projection signals to obtain a unified representation signal m(n) of the multi-channel signal; 5. The bearing fault diagnosis method based on multivariate sparse unified decomposition according to claim 1, characterized in that: Step 3 specifically includes: S301, construct filter χ(k|λ), λ=[ω,ω b ,ω c ]: S302, by solving the following optimization problem P1, the optimal filtering parameter λ1=[ω,ω b ,ω c ]: in For As a singular local linear operator, the optimization problem is solved by minimizing The unified representation signal of the filtered multi-channel signal is constrained to be a local narrow-band signal, thereby achieving the purpose of adaptive frequency band segmentation; Used to regularize the optimization objective function, D' is a differential operation used to regularize The λ weight can usually be set to S303, order Repeat S302 to construct the optimal filter parameter matrix F = [λ1, λ2, ..., λ i ,…] until Finally, the filter banks constructed in F are used to filter the channel signals after symplectic geometry denoising in Y” to achieve unified segmentation of multi-channel signal bands and obtain the multivariate symplectic sparse modal components of each channel.

6. A bearing fault diagnosis system based on multivariate sparse unified decomposition for implementing the bearing fault diagnosis method based on multivariate sparse unified decomposition as claimed in any one of claims 1 to 5, characterized in that: include: Pre-denoising module: used for symplectic geometry pre-denoising; Signal projection module: used for multi-channel signal projection; Consent segmentation module: used to perform uniform frequency band segmentation.

7. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the bearing fault diagnosis method based on multivariate sparse unified decomposition as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the bearing fault diagnosis method based on multivariate symplectic sparse unified decomposition as claimed in any one of claims 1 to 5.

9. An information data processing terminal, comprising the bearing fault diagnosis system based on multivariate symplectic sparse unified decomposition as claimed in claim 6.

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