A bearing fault diagnosis method and system based on multivariate sparse unified decomposition

Abstract

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 multi-element sparse unified decomposition. First, pre-noise reduction of symplectic geometric atoms is achieved by constructing a sparse filter; then, the CAP method is used to achieve unified representation of multi-channel signals; finally, the parameters of the constructed sparse filter are optimized with the regularized singular local linear operator as the optimization target, which not only achieves the modal alignment of the multi-channel signal decomposition results, but also constrains it to a local narrowband signal. The MSSUD method uses the CAP method to process the symplectic geometric atoms to reconstruct the signal. This method can adaptively obtain the projection vector according to the characteristics of the multi-channel signal, and project the multi-channel signal onto a hypersphere to obtain a unified representation of the multi-channel signal. Combined with the sparse filter, it can achieve adaptive frequency band unified segmentation of the multi-channel signal.

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, interference from the signal transmission path, and other components, the single-channel signal collected by the sensor often cannot accurately and comprehensively describe the bearing fault characteristics. However, existing fault diagnosis methods mostly process the single-channel signal 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 the collected signal to a certain extent, and can more accurately and comprehensively characterize the characteristics 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. Classical 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 results are prone to burrs. VMD constructs a variational optimization problem in the frequency domain, constraining the intrinsic mode functions to amplitude-frequency modulated components 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 has been applied to signal processing, providing a new approach to signal analysis. Initially, singular value decomposition (SDD) and singular spectrum analysis (SSA) were both used as signal denoising methods. However, their effectiveness is significantly affected by the reconstruction order and is sensitive to the dimensionality of the constructed matrix. A large matrix increases the burden of the subsequent reconstruction process, while a small matrix results in incomplete signal-to-noise separation. Li et al. proposed using the relative rate of change of the singular envelope spectrum's kurtosis to determine the reconstruction order for SDD. They then combined the filtered signal with the envelope power spectrum to extract the characteristic frequencies of bearing faults. It is generally believed that after matrix decomposition, fault-related characteristic information in the signal is distributed in the resulting eigenvectors. Identifying these information is crucial for fault diagnosis. Symplectic geometric mode decomposition (SMD) assumes that characteristic information is concentrated in the eigenvectors corresponding to the first few eigenvalues. Individual eigenvectors are converted into initial single components. Initial components with similar periods are merged using a cyclic similarity metric, and a threshold for the ratio of normalized mean squared error (NMSE) is set to terminate the merging. This approach combines characteristic information scattered across different eigenvectors while also addressing the additional burden of processing all eigenvectors.

[0005] However, the above methods are only applicable to single-channel signal processing and are not suitable for multichannel signals. Although these methods can process signals from multiple channels individually, this process fails to account for the correlations between the signals in each channel. Therefore, the results obtained from multichannel signal processing using these methods are often difficult to fuse. To address the EMD method's inability to process multichannel signals, MEMD projects the multichannel signals onto a hypersphere, obtaining high-dimensional directional vectors uniformly distributed in space. The local mean of the high-dimensional signal envelope is then calculated to achieve a unified representation of the multivariate signal, ensuring consistency in the number and frequency scale of the signal components across each channel. While the multivariate extension of EMD inherits the original properties of EMD and overcomes the problem of the inability to adaptively select basis functions, it still suffers from drawbacks such as modal aliasing and sensitivity to noise. The MVMD method defines the multivariate signal by constructing a variational optimization and constraining the joint frequency components of each channel, ensuring that all channel signals have a common frequency component, i.e., the mode alignment property. However, like the VMD method, MVMD still requires presetting the number of components and penalty parameters.

[0006] Based on the above analysis, the existing technology has the following technical problems that need to be solved urgently: the existing methods are only suitable for single-channel signal processing and are not suitable for processing multi-channel signals. Although the existing methods can 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 response to the problems existing in the prior art, the present invention provides a bearing fault diagnosis method and system based on multivariate 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 a regularized smoothing operator to obtain the smoothed vibration signals, thereby achieving pre-denoising of the signals of each channel. Then, by taking advantage of the ability of CAP to adaptively obtain projection vectors according to the characteristics of multi-channel signals, the multi-channel signals are projected onto a hypersphere to obtain a unified representation of the multi-channel signals. Finally, with the regularized local narrowband operator as the optimization target, the constructed sparse filter parameters are optimized to achieve unified frequency band segmentation of the 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] Furthermore, 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, and sets 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 after diagonal averaging is obtained = [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 largest to smallest 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 screened 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] Furthermore, step 2 specifically includes:

[0025] 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)] projection signal

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

[0027]

[0028] Furthermore, 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 the 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 banks constructed in F are used to filter the channel signals after symplectic geometric denoising in Y” to achieve unified segmentation of the multi-channel signal bands and obtain the multivariate symplectic sparse modal 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] Consensus segmentation module: used for 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 multivariate 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 multivariate 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 multivariate 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 utilizes symplectic geometry mode decomposition (SGMD) to decompose a time series into several symplectic geometric modal components with independent modes. This method has the advantages of not requiring subjective custom parameters and can effectively reconstruct existing modes and eliminate noise. Based on this theoretical foundation, the MSSUD method is proposed. MSSUD first constructs a symplectic geometric atom library and merges valid atoms by screening them using a regularized complex-valued differential operator, thereby achieving pre-denoising of the signals in each channel. Then, by taking advantage of CAP's ability to adaptively obtain projection vectors based on the characteristics of multi-channel signals, the multi-channel signals are projected onto a hypersphere to obtain the projection signal, thus achieving a unified representation of the multi-channel signals. Finally, with the regularized singular local linear operator as the optimization target, the constructed sparse filter parameters are optimized to achieve unified frequency band segmentation of the multi-channel signals while constraining the decomposition results to local narrowband signals, making the decomposition results physically meaningful. 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 decomposition accuracy and noise resistance. The innovations are as follows:

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

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

[0045] 3. 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 noise resistance.

[0046] Second, as auxiliary evidence for 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. Currently, 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 measurements to a certain extent, and will have a wider range of applications in the future. Based on this, the technology of the present invention expands the original SGMD method technology, enabling it to obtain 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, it is manifested in:

[0050] 1. Utilizing fully adaptive projection technology, we achieve modal alignment, the core processing capability of multichannel signal decomposition algorithms. This links the same modality of signals from different channels, providing intuitive information about each channel's state and facilitating the implementation of subsequent processing techniques.

[0051] 2. The signal decomposition process is constrained by the set singular local linear operator to ensure that each component exhibits amplitude modulation 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 using 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 overlap 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 achieves 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, making it 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, increasing 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 ineffective extraction of fault modes, affecting the efficiency and accuracy of fault diagnosis.

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

[0060] The pre-noise reduction method based on symplectic geometry improves signal quality: This 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] Unified representation of multi-channel signals improves fault diagnosis accuracy: The CAP projection strategy is used to project multi-channel vibration signals onto a hypersphere to generate a unified signal representation. This overcomes the defect of the existing technology that multi-channel signals are difficult to comprehensively process, and can better extract the global characteristics of bearing faults, significantly improving diagnostic accuracy.

[0062] Adaptive frequency band segmentation enhances the sensitivity of fault feature extraction: By optimizing filter parameters and combining a regularized local narrowband operator, the present invention realizes 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 computational effort: By optimizing sparse filter parameters and selecting valid symplectic geometric atoms for reconstruction, this method avoids unnecessary decomposition calculations and significantly reduces computational effort. Furthermore, the decomposition results possess greater physical significance, making the modal characteristics of bearing faults more prominent, thereby improving the efficiency and accuracy of fault diagnosis.

[0064] This paper, using a multivariate sparse unified decomposition method, achieves significant technological advancements in multichannel signal preprocessing, characterization, frequency band segmentation, and sparse decomposition, resolving several bottlenecks in existing technologies. This method not only improves the quality of bearing fault signal extraction but also significantly enhances the accuracy and efficiency of diagnosis, promising broad industrial applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a schematic diagram of the 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 Schematic diagram of MSSMC components obtained by decomposing MSSUD according to an embodiment of the present invention;

[0069] Figure 5 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); and c) is the noise n3(t) added to S3(t);

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

[0072] Figure 8 1 is a schematic diagram of MIMF components obtained by MVMD decomposition according to an embodiment of the present invention;

[0073] Figure 9 Schematic diagram of MIMF components obtained by MEMD decomposition according to an embodiment of the present invention;

[0074] Figure 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); and c) is the noise n3(t) added to S3(t);

[0075] Figure 11 Schematic diagram of MSSMC components obtained by decomposing MSSUD according to an embodiment of the present invention;

[0076] Figure 12 1 is a schematic diagram of MIMF components obtained by MVMD decomposition according to an embodiment of the present invention;

[0077] Figure 13Schematic diagram of MIMF components obtained by MEMD decomposition according to an embodiment of the present invention;

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

[0079] Figure 15 Schematic diagram of the envelope spectrum of multi-channel bearing fault simulation signals; (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] Figure 16 The component graph obtained by fusion after decomposing the multi-channel bearing fault simulation signal using the MSSUD method;

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

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

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

[0084] Figure 20 Schematic diagram of a bearing fault test bench provided by an embodiment of the present invention;

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

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

[0087] Figure 23 : This 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] Figure 24 1 is a schematic diagram of the fused fault vibration signal components obtained by using MSSUD decomposition according to an embodiment of the present invention;

[0089] Figure 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] Figure 26 2. Schematic diagram of fused fault vibration signal components obtained by using MEMD decomposition according to an embodiment of the present invention;

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

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

[0093] Figure 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 solutions 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 intended 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

[0097] In a wind turbine, bearings are one of the key mechanical components, and their operating status directly affects the performance and reliability of the generator. This method can be used to collect and analyze multi-channel vibration signals from the bearings of a wind turbine. The specific implementation steps are as follows:

[0098] 1. Pre-noise reduction: The vibration signal of the wind turbine is interfered with by environmental noise and other mechanical vibrations. Through symplectic geometry atom library screening and preprocessing, the interference noise is 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 bank to achieve unified frequency band segmentation of the bearing vibration signal, the characteristic frequencies of bearing faults 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 rails, and bearing failures can lead to serious safety hazards. This method can be used to perform online monitoring of locomotive bearings. The specific steps include:

[0103] 1. Pre-noise reduction: The vibration signals of railway locomotives are 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 is improved.

[0104] 2. Multi-channel signal projection: For multi-channel sensor data from different parts of the locomotive, the overall signal representation is obtained through multi-channel unified projection, thereby extracting fault characteristic signals.

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

[0106] These two examples 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. Related 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 the lack of adaptability of projection vectors generated by traditional hypersphere uniform sampling methods such as uniform angle sampling and Hammersley uniform sampling. 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 main 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 The aggregation degree is related to the power imbalance between multi-channel signals.

[0116] (3) The power of a multi-channel signal can be expressed by calculating the square of the power of each channel of the multi-channel 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 multi-channel signal. a can be expressed by formula (3).

[0117]

[0118] The above steps can be used to obtain a fully adaptive projection vector suitable for the multivariate signal itself:

[0119]

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

[0121] Figure 1 The blue and red dots in the figure represent the principal component direction vector and its opposite direction vector, respectively. When a = 0, the projection vectors are uniformly distributed, and the projection degenerates into a Hammersley uniform projection. When a = 1, the projection vectors converge toward the principal component direction vector and its opposite direction vector, respectively. CAP can adaptively determine a based on the characteristics of the signal.

[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 components are represented in turn.

[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 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, and uses a regularized smoothing operator to screen effective atoms for merging to obtain smoothed vibration signals, thereby achieving pre-denoising of the signals of each channel. Then, the advantage of CAP's ability to adaptably obtain projection vectors based on the characteristics of multi-channel signals is used to project the multi-channel signals onto a hypersphere to obtain a unified representation of the multi-channel signals. Finally, with 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 bands while making the decomposition results constrained to local narrowband signals have better physical meaning. The MSSUD method is divided into three main steps: symplectic geometric pre-denoising, multi-channel signal projection, and unified frequency 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, and sets 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 after diagonal averaging is obtained = [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 atomic energy 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 screened 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) itself Then, calculate R(n)=[r1(n),r2(n),…,r M (n)] projection signal

[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 In display.

[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 the 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 banks constructed in F are used to filter the channel signals after symplectic geometric denoising in Y” to achieve unified segmentation of the multi-channel signal bands and obtain the multivariate symplectic sparse modal 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 modal alignment property 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 respectively. 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 can be seen that in Figure 4 Components at the same sorting position in have similar oscillation patterns, while Figure 5 Components in the same order in the α-valued signal do not have similar oscillation modes. This shows that the MSSUD method can link the same signal components from different channels in a multivariate signal, demonstrating the modal alignment property. However, the SSMD method does not have this modal alignment property.

[0156] 2.2 Decomposition performance comparison

[0157] 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. MSSUD, MVMD, and MEMD are used to decompose the signal, 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 As shown. The sampling frequency is 3000Hz and the sampling time is set to 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 same modal alignment property. In addition, MSSUD separates the added noise and has a higher decomposition accuracy than MVMD. Figure 9 In the example, although MEMD also has the property of modal alignment, the noise causes the generated components to undergo modal aliasing. To demonstrate 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 the following example: Figure 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 degrades the decomposition effect of MEMD, the components at different frequencies in MSSUD and MVMD still maintain modal alignment. In terms of decomposition accuracy, because MSSUD separates the noise in the simulation signal more thoroughly than MVMD, the components generated by MSSUD are closer to the original components, resulting in higher decomposition accuracy.

[0161] 2.3 Simulation fault signal analysis

[0162] To demonstrate the feasibility of MSSUD for rolling element bearing fault diagnosis, further simulation analysis is performed as follows. Multichannel signals collected by sensors are often a mixture of multiple component signals, often accompanied by noise, and signals from different channels can differ from one another. To simulate multichannel rolling element bearing fault signals collected under real-world conditions, the following three raw 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 race 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 Figure 12 The simulated fault signals of the three channels are shown in the figure. The specific process is as follows:

[0168]

[0169] Perform envelope spectrum analysis on channel signals S1(t), S2(t) and S3(t) in turn. The envelope spectrum is as follows: Figure 13 As shown, Figure 13 The red dotted line in the middle is f r and its double frequency, the red dotted line is f i From the envelope spectrum, it is observed that both the rotation frequency and the fault characteristic frequency are masked by noise. Therefore, 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 of 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 richest fault information is selected for envelope spectrum analysis. The envelope spectra corresponding to the three methods are as follows: Figure 17 As shown in the figure. The envelope spectrum corresponding to MSSUD contains the rotation frequency and its double frequency, and the fault characteristic frequency and its double frequency are also relatively obvious, thus extracting the fault characteristic information from the simulated multi-channel bearing fault signal. While the envelope spectrum corresponding to MVMD also contains the rotation frequency and its double frequency, the fault characteristic frequency is not as obvious as that of 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 from 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 Figure 20 The bearing test bench shown in the figure is used for experimental verification. The test bench generally consists of a servo motor, test bearing, support bearing, coupling, acceleration sensor and B&K Pulse signal acquisition system.

[0173] Three acceleration sensors were magnetically fixed to the top and sides of the experimental bearing seat. The sampling rate was set to 65536Hz. When the signal acquisition system was working properly, it could simultaneously record the bearing vibration data from three channels of the three sensors. The test bearing model was 6206, and the parameters are shown in Table 2. An inner race fault was artificially set using electric spark cutting with a cutting depth of 0.2mm. The faulty part was as follows: Figure 21 shown.

[0174] Table 2 Specifications of experimental bearings

[0175]

[0176] Table 3 Fault related frequencies

[0177]

[0178] During the test, the speed was set to 1182 rpm. After the speed stabilized, a total of 43 seconds of bearing inner race fault data was collected. The time domain signals of the three channels at 15-16 seconds were intercepted as follows: Figure 22 As shown in the figure, the signal is used as the experimental signal for fault analysis. First, the envelope spectrum of the experimental signal of the three channels is analyzed. The envelope spectrum is shown in the figure. Figure 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 inner ring fault characteristic frequency f i The frequencies associated with the fault signal and its double frequency are shown in Table 3. Due to the presence of ambient noise in the acquired data, the transfer frequency and fault characteristic frequency in the envelope spectrum are obscured by the noise interference. Therefore, it is clear that direct envelope spectrum analysis cannot directly extract the fault characteristic frequency and transfer frequency information contained in the vibration signals of the three bearing channels.

[0179] Then, the vibration signals of the three channels of the faulty bearing are decomposed 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 of the same sequence number in each channel are directly added together and used as the fused components for subsequent analysis. The obtained signal components are as follows: Figures 24-26 As shown. The envelope spectrum of the signal components obtained by the three methods after fusion is analyzed respectively. The envelope spectrum of the signal components obtained by MSSUD, MVMD and MEMD is shown as follows: Figures 27-29 The envelope spectrum of the components obtained by MSSUD contains the first and second harmonics of the rotation frequency. At the same time, the fault characteristic frequency is also more prominent in the envelope spectrum. Therefore, MSSUD can be used to diagnose the inner race fault of the test bench motor bearing. Figure 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 rest of the frequency information is lost. Figure 27 (b) The envelope spectrum of the components obtained using MEMD only extracts a weak rotation frequency, and the noise significantly affects the accurate extraction of fault information. Therefore, MEMD and MVMD are difficult to accurately and effectively diagnose the inner ring bearing fault of the fault test bench. The above analysis results show that compared with MEMD and MVMD methods, the MSSUD method can accurately extract fault characteristics from the noise in the vibration signal. In combination with the envelope spectrum, it can effectively perform rolling bearing fault diagnosis.

[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 multivariate 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 multivariate 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 rationally arranging multiple acceleration sensors at different positions of the component to be tested, cooperating with a data acquisition system (the acquisition system is generally composed of acquisition card hardware and software system) to collect the vibration signal generated by the equipment during operation, and then storing the signal data and importing it into software analysis tools such as MATLAB or Python. The signal data is analyzed and processed by the multivariate sparse identity decomposition algorithm program compiled according to the technology of this invention, and the original signal is classified into multiple signal components with different characteristics. Finally, the envelope spectrum algorithm program is used 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 demonstrate the practicality of the technology presented in this paper, we have successfully applied it to a bearing failure test bench. By analyzing and processing the multi-channel vibration signal data collected by the test bench, we were able to accurately determine the health of the bearing. 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 1182 rpm, 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 time domain waveform, it can be seen that the collected signal is mixed with a lot of noise and does not show obvious fault characteristics, namely 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 the following figure: Figure 3 As shown in Table 3, it is difficult to find the frequency spectrum corresponding to that in Table 3, which means that the fault status 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 with each other. In order to further enhance the characteristics, the signal components of the same modality will be fused into one component. The final decomposition result is as follows Figure 4 As shown in the figure. 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 the figure. Figure 5 As shown in the figure, the envelope spectrum corresponding to the first component shows significant transfer spectrum lines and fault characteristic frequency spectrum lines, and also contains certain frequency harmonic information. This fully proves that the experimental bearing has an inner ring fault and realizes the fault diagnosis of the experimental bearing.

[0190] Table 1 Specifications of experimental bearings

[0191]

[0192] Table 2 Fault related frequencies

[0193]

[0194] 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 portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, 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. The devices and 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, 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, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0195] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A bearing fault diagnosis method based on multivariate sparse unified decomposition, characterized in that: include: First, a symplectic geometric atom library of vibration signals from each channel is constructed. Effective atoms are then merged using a regularized smoothing operator to obtain smoothed vibration signals, thereby achieving pre-denoising of the signals from each channel. Then, taking advantage of CAP's ability to adaptively obtain projection vectors based on the characteristics of multi-channel signals, the multi-channel signals are projected onto a hypersphere to obtain a unified representation of the multi-channel signals. Finally, with the regularized local narrowband operator as the optimization target, the constructed sparse filter parameters are optimized to achieve unified frequency band segmentation of the multi-channel signals while making the decomposition results constrained to local narrowband signals more physically meaningful. 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; Step 1 specifically includes: S101, for each channel vibration signal S(n) = [s1(n), s2(n), ..., s i (n)], respectively for each s i (n) performs pre-noise reduction, and sets 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 phase space trajectory matrix X, and the symplectic geometry atomic library Y = [y1(n), y2(n),…,y k (n),…]; S102, calculate each symplectic geometric atomic component y in the symplectic geometric atomic library Y k (n) singular local linear operator; 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 smoothing 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 screened 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, y1'(n) and other symplectic geometric atoms [y2'(n),…,y m '(n)] merge, recalculate the singular local linear operator value, merge if it decreases, and obtain the components s after symplectic geometric pre-denoising i '(n), and construct the noise reduction multi-channel signal matrix S'(n); Step 2 specifically includes: S201, let R(n) = S'(n), and use the CAP projection strategy according to the characteristics of R(n) to obtain J projection vectors Then, calculate R(n)=[r1(n),r2(n),…,r M (n)] projection signal S202, averaging the J projection signals to obtain a unified representation signal m(n) of the multi-channel signal; 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 a local narrowband signal, thereby achieving the purpose of adaptive frequency band segmentation; Used to regularize the optimization objective function, D' is the differential operation used to regularize The λ weight is 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 S(n) to achieve unified segmentation of the multi-channel signal bands and obtain the multivariate symplectic sparse modal components of each channel.

2. A bearing fault diagnosis system based on multivariate sparse unified decomposition that implements the bearing fault diagnosis method based on multivariate sparse unified decomposition as claimed in claim 1, characterized in that: include: Pre-denoising module: used for symplectic geometry pre-denoising; Signal projection module: used for multi-channel signal projection; Consensus segmentation module: used for uniform frequency band segmentation.

3. 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 claimed in claim 1.

4. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the bearing fault diagnosis method based on multivariate symplectic sparse unified decomposition as claimed in claim 1.

5. An information data processing terminal, comprising the bearing fault diagnosis system based on multivariate symplectic sparse unified decomposition according to claim 2.

Images