A rolling bearing fault method and system based on riesz graph spectrum sparse decomposition

Abstract

The present application belongs to the technical field of time-frequency analysis, and particularly relates to a rolling bearing fault method and system based on Riesz graph sparse decomposition. A new time-frequency analysis method, Riesz four-parameter spectrum time-frequency analysis method, is used to obtain four-parameter information of amplitude, frequency, phase and direction of a vibration signal in a time-frequency domain, so as to improve time-frequency aggregation and anti-noise performance of an analysis result. In order to screen out an optimal parameter spectrum, a sign dynamics entropy is extended to a two-dimensional scale, and a new entropy value calculation method, cosine sign dynamics entropy, is proposed. A parameter optimization component amplitude of a sparse filter is constructed by reconstructing a parameter spectrum component screened out by the entropy, so that the decomposition result has physical significance. The present application analyzes bearing vibration signals under variable speed conditions and bearing vibration signals under constant speed conditions, and on this basis, proposes an RSSD method, so as to realize feature extraction and diagnosis of rolling bearing faults under constant speed and variable speed conditions.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of time-frequency analysis technology, and particularly relates to a method and system for rolling bearing fault analysis based on Riesz graph sparse decomposition. Background Technology

[0002] With the continuous advancement of science and technology, the structure of high-end mechanical equipment is becoming increasingly complex, and key components of this equipment face increasingly extreme service environments and more stringent performance requirements. Among these, the stable and reliable operation of rolling bearings is directly related to the safe operation of mechanical equipment. Rolling bearings typically operate in harsh environments and are highly susceptible to failure. Therefore, to ensure the safe and stable operation of mechanical equipment, it is necessary to collect vibration signals from rolling bearings to identify early and subtle defects, thereby reducing unnecessary losses. However, due to the complex structure of mechanical equipment and the varied operating conditions in actual work, the collected vibration signals are a mixture of noise and multiple component modes. Therefore, accurately extracting fault information from vibration signals containing numerous interfering components is crucial for bearing fault diagnosis.

[0003] Currently, among the methods for extracting fault information from rolling bearing vibration signals, adaptive decomposition algorithms for multi-component signals, represented by Empirical Mode Decomposition (EMD), have been widely studied by scholars both domestically and internationally. To address the problems existing in the EMD decomposition process, a series of improved algorithms have been proposed. These include Integrated Empirical Mode Decomposition (EEMD), which suppresses mode confusion by repeatedly adding Gaussian white noise to the signal; Complementary Set Empirical Mode Decomposition (CEEMD), which adds paired positive and negative Gaussian white noise to eliminate the influence of the introduced Gaussian white noise; Complete Adaptive Noise Integrated Empirical Mode Decomposition (CEEMDAN), which adaptively adjusts the amplitude and distribution of noise based on the decomposition results according to EEMD and CEEMD; and Variational Mode Decomposition (VMD), which determines the frequency center and frequency band of each mode component by iteratively searching for the optimal solution of the variational model, thus achieving adaptive signal partitioning in the frequency domain. These decomposition methods can decompose multi-component signals into different components and have been widely used in the field of mechanical fault diagnosis. However, these methods lack rigorous mathematical support regarding whether the defined single-component signals have physical meaning.

[0004] Time-frequency analysis can intuitively reflect the frequency composition of a signal and the time-varying characteristics of each frequency component. Among linear time-frequency methods, the Short-Time Fourier Transform (STFT) is a commonly used method for analyzing non-stationary signals. Based on the Fourier Transform, STFT uses a window function to divide the time-series signal into multiple time intervals, each of which is stationary. The Wigner-Ville distribution (WVD) has good time-frequency aggregation and high time-frequency resolution when processing single-component signals, but when there are many signal components, it generates severe interference terms, making it impossible to extract accurate fault feature information. Wavelet Transform (WT) achieves different scale decompositions of the signal through wavelet scaling and translation, giving it high time resolution and low frequency resolution, thus ensuring good accuracy in both the time and frequency domains. These methods all have their own drawbacks. The time-frequency resolution of STFT and WT depends on the choice of window and basis function; since these are fixed, they are not effective when processing signals containing many interference components. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and system for rolling bearing fault diagnosis based on Riesz graph sparse decomposition.

[0006] This invention is implemented as follows: a rolling bearing fault diagnosis method based on Riesz graph sparse decomposition, the method comprising:

[0007] S1: A new time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—is used to obtain the four parameters of vibration signal in the time-frequency domain: amplitude, frequency, phase, and direction, thereby improving the time-frequency convergence and noise resistance of the analysis results.

[0008] S2: To select the optimal parameter spectrum, a new entropy calculation method—cosine symbolic dynamic entropy—is proposed, which extends the symbolic dynamic entropy to a two-dimensional scale.

[0009] S3: The parameter spectrum components selected by entropy screening are reconstructed, and the amplitude of the sparse filter parameter optimization components is constructed to make the decomposition results have physical meaning. Based on this, the RSSD method is proposed.

[0010] Furthermore, S1 specifically includes:

[0011] (1) Riesz transform

[0012] Traditional time-frequency analysis methods can only obtain the amplitude and frequency information of the signal in the time-frequency domain, which will introduce bias when analyzing the signal. In order to solve this problem, the Riesz transform is innovatively used to analyze the vibration signal. The Riesz transform can obtain the amplitude, frequency, phase and direction information of the signal, thereby more comprehensively characterizing the fault features and improving the time-frequency convergence and noise resistance of the analysis results.

[0013] For any given one-dimensional real signal f(x) 1D , x∈E, analytic signal f A (x) is defined as the complexification function of the signal, where the real part is the signal itself and the imaginary part (conjugate function) is its Hilbert transform;

[0014] f A (x)=f(x) 1D -if H (x) (1)

[0015] In the formula f H ()=f(x) 1D *h(x) represents the Hilbert transform of the original signal, and the transform kernel is... The corresponding frequency response is H(w) = -jsgn(w);

[0016] Similarly, the Riesz transform can generate analytic signal representations for two-dimensional signals, for any two-dimensional signal f(x). 2D , x∈R 2 Its Riesz transform f R (·) is defined as:

[0017]

[0018] x = (x1, x2) is the position index vector, y = (y1, y2) is the dummy variable, and |||| is the vector norm. The definition of the Riesz transform can be rewritten in the form of a convolution kernel as follows:

[0019]

[0020] Two-dimensional signal f(x) 2D Riesz transform with two directions

[0021]

[0022] Where x′=(x′1,x′2), p·v· represents the Cauchy principal value integral, and the Riesz transform and the first and second transform kernel functions are respectively

[0023]

[0024] f(x) 2D The linear combination with the Riesz transform is f(x). 2D The analytic signal is defined as the monomorphic signal f. M (x)

[0025]

[0026] Where i and j represent two imaginary units, and {i, j, 1} constitutes R. 3 A set of orthogonal bases in the space. Therefore, f(x) 2D Single-stage signals are typically generated using vectorization functions or vector fields f. M :R 2 →R 3 To define,

[0027]

[0028] (2) Riesz four-parameter spectral time-frequency analysis method

[0029] Previous time-frequency transformation methods could only obtain the amplitude and frequency information of a signal in the time-frequency domain. This paper innovatively employs Riesz transform and Log-Gabor filter banks to analyze the signal, thereby simultaneously obtaining four parameters of the signal in the time-frequency domain: amplitude, frequency, phase, and direction. This allows for a more comprehensive characterization of bearing fault features and improves the time-frequency convergence and noise immunity of the analysis results. Based on this, a new time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—is proposed. This method consists of the following steps:

[0030] 1) Perform continuous wavelet transform on the original signal. Given a signal x(t), its CWT can be expressed as:

[0031]

[0032] In the formula, ψ(t) is the Morlet wavelet basis, and τ and s represent the translation and scaling transformations, respectively.

[0033] 2) Obtain the Riesz four-parameter spectrum. The Riesz four-parameter spectrum refers to the spectrum obtained from the Riesz four-parameter spectrum. The amplitude spectrum A(τ, s) and phase spectrum constructed after Riesz transform The frequency spectrum f(τ, s) and the directional spectrum θ(τ, s) are given. Considering the influence of noise on the four-parameter spectrum, a Log-Gabor filter is used to filter the four-parameter spectrum. The Log-Gabor filter has the advantages of zero DC component and no bandwidth limitation, and its frequency response function is:

[0034]

[0035] In the formula, ω0 is the center frequency, and σ is the scaling factor for adjusting the bandwidth; to maintain a filter bank with a fixed shape ratio, σ is usually set to a certain value. r =σ / ω0 remains constant; if observed on a logarithmic frequency scale, the Log-Gabor filter has a Gaussian-like frequency response;

[0036] Because the Log-Gabor filter does not have an analytical expression in the time domain, its time domain representation is obtained through inverse Fourier transform;

[0037]

[0038]

[0039] Among them, F -1 This represents the inverse Fourier transform. express The model, yes Fourier stated that yes Two Riesz cores, and They are respectively Differentiate with respect to τ and s.

[0040] Furthermore, S2 specifically includes:

[0041] To further improve the computational efficiency and complexity representation accuracy of symbolic dynamic entropy, this paper utilizes the image block division concept to transform a two-dimensional matrix into a block matrix and calculates the cosine similarity between adjacent block matrices. This transforms the complexity of calculating a two-dimensional matrix into the complexity of calculating a one-dimensional sequence, effectively improving computational efficiency. Based on this, an entropy calculation method—cosine symbolic dynamic entropy—is proposed, with the following steps:

[0042] Taking A(τ, s) as an example, A(τ, s) is first divided into several non-overlapping blocks of the same size, with a block size of 10×10. The block matrix is ​​then converted into vector form to calculate the cosine similarity between adjacent blocks, resulting in a series of cosine similarities. The cosine similarity between two blocks is calculated as follows:

[0043] A(τ, s) = {a1, a2, ... a N*M} (12)

[0044] D = {d1, d2, ..., d} N*M-1}={d(a1-a2), d(a2-a3),..., d(a N*M-1 -a N*M (13)

[0045]

[0046] Where, {a1, a2, ... a N*M} represents the vector form of the block matrix, N = round(length(τ) / 10), M = round(length(s) / 10); Note that the range of cosine similarity d is [-1, 1], and it measures the cosine value of the geometric angle; Note that the range of cosine similarity d is [-1, 1]; The defined cosine similarity d is the similarity between two orbits, and it measures the cosine value of the geometric angle; A larger cosine similarity value indicates that there are similar, predictable, or periodic dynamic changes between the two orbits;

[0047] Divide the D sequence into ε intervals with equal probability according to their size. i It corresponds to one and only one interval, such as the symbol σ. i It then replaced d i This forms the symbol sequence Z{Z k , k = 1, 2, ..., N*M-1}. According to Takens' embedding theorem, subvectors are generated using the embedding dimension m and the time delay μ. Calculate the state pattern probability:

[0048]

[0049] In the formula, ε represents the state pattern of the symbol arrangement of each subvector. m The symbol arrangement state pattern is represented by type(), which represents the mapping relationship from the symbol space to the pattern space, and |||| represents the number of elements in the set.

[0050] When the state pattern has been observed When, the symbol that appears afterward is σ. b The probability of (a = 1, 2, ..., ε) is the state transition probability:

[0051]

[0052] Based on the definition of information entropy, we define the cosine sign dynamic entropy (CSDE). 2D It equals the sum of the state pattern probability entropy and the state transition probability entropy:

[0053]

[0054] If and only if At that time, CSDE 2D The maximum value is obtained as ln(ε) m+1 ). CSDE 2D Normalization:

[0055] CSDE 2D =CSDE 2D / ln(ε m+1 (18)

[0056] CSDE 2D The larger the value, the more random and complex the distribution within the parameter spectrum. CSDE 2D The smaller the value, the more regular the distribution within the parameter spectrum and the less affected it is by noise. Statistical analysis shows that when m=2, ε=10, and μ=1, the complexity within the four-parameter spectrum can be accurately quantified with short computation time.

[0057]

[0058] Furthermore, S3 specifically includes:

[0059] By analyzing the signal using Riesz transform and Log-Gabor filter banks, the obtained four-parameter spectrum is filtered using cosine sign dynamic entropy, and the parameters of the sparse filter constructed from the reconstructed components are optimized to give the decomposition results physical meaning. Based on this, an adaptive signal decomposition method based on time-frequency spectrum—the RSSD method—is proposed. Its main steps are as follows:

[0060] (1) As shown in equations (8)-(10), the filtered result is obtained through Riesz transform and Log-Gabor filter bank. Its time-domain representation is obtained by inverse Fourier transform. The four-parameter spectrum PT(τ, s) is obtained as shown in equation (11);

[0061] (2) Determine the optimal parameter spectrum, as shown in formulas (12)-(18), and use the cosine sign dynamic entropy to calculate the entropy value CSDE of each parameter spectrum. 2D As shown in formula (20), the optimal parameter spectrum PT is obtained. i (τ,s);

[0062] (3) Obtaining local coefficients Given a threshold mean(mean(PT) i (τ,s))), further reducing spurious local minima caused by noise; PT i (τ, s) is divided into several incoherent regions pt, as shown in the image. i (τ, s), in pt i Find the local maximum point max(pt) along s within (τ, s). i (τ,s)), considering applicability, spline interpolation is used to fit the local coefficients to the maximum points.

[0063] (4) Reconstructed component r i (t). Will Perform continuous wavelet inverse transform to reconstruct the component r. i(t) While ensuring reconstruction accuracy, the algorithm's time consumption is reduced; for time-domain signal r i (t), the reconstruction formula is as follows:

[0064]

[0065]

[0066] in, It is the Fourier transform of ψ(t). This indicates taking the real part.

[0067] (5) Sparse component amplitude optimization, which only takes points on the ridge, will lose most of the energy. Therefore, let res1(t) = x(t) to construct the following optimization problem P1:

[0068]

[0069] In the optimization problem P1, the optimization parameters are the magnitudes of each component, η||D(res1(t)-r i (t))|| 2 The objective function is used for regularization optimization. D is a differential operator used to obtain the sparsest representation of the original signal, and its weight η is usually set to 1.

[0070] Construct the following optimization problem P2, where the optimization parameter is the magnitude coefficient μ:

[0071] P2 Minimize||res1(t)-μr i (t)|| 2 (twenty three)

[0072] The purpose of this step is to obtain r i The optimal amplitude of (t) is further ensured to guarantee the sparsity of the decomposition results;

[0073] (6) Set local coefficients Length threshold, When the length is too short, the iteration is terminated during reconstruction, and the entire decomposition process is completed.

[0074] Another objective of this invention is to provide a rolling bearing fault system based on Riesz graph sparse decomposition, which is based on the aforementioned rolling bearing fault method based on Riesz graph sparse decomposition. This system specifically includes:

[0075] The parameter information acquisition module utilizes a novel time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—to acquire the amplitude, frequency, phase, and direction information of the vibration signal in the time-frequency domain, thereby improving the time-frequency convergence and noise resistance of the analysis results.

[0076] The parameter spectrum screening module, connected to the parameter information acquisition module, extends the symbolic dynamic entropy to a two-dimensional scale to screen out the optimal parameter spectrum, and proposes a new entropy calculation method—cosine symbolic dynamic entropy.

[0077] An amplitude construction module, connected to a parameter spectrum screening module, reconstructs the parameter spectrum components selected by entropy screening, constructs the amplitude of sparse filter parameter optimization components, and makes the decomposition results physically meaningful. Based on this, the RSSD method is proposed.

[0078] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the rolling bearing fault method based on Riesz graph sparse decomposition.

[0079] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the rolling bearing fault method based on Riesz graph sparse decomposition.

[0080] Another objective of this invention is to provide an information data processing terminal for implementing the rolling bearing fault system based on Riesz graph sparse decomposition.

[0081] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0082] First, this invention introduces Riesz transform combined with time-frequency analysis, and proposes a new entropy selection optimal parameter spectrum. It also incorporates sparsity optimization for component amplitudes, analyzing bearing vibration signals under variable speed and constant speed conditions. Based on this, the RSSD method is proposed, enabling feature extraction and diagnosis of rolling bearing faults under constant and variable speed conditions. Specific conclusions are as follows:

[0083] (1) By employing Riesz transform and Log-Gabor filter banks to analyze the signal, and simultaneously obtaining the four parameters of amplitude, frequency, phase, and direction in the time-frequency domain, a Riesz four-parameter spectrum time-frequency analysis method is proposed. In addition, a cosine symbolic dynamic entropy is proposed to improve the computational efficiency and complexity representation accuracy of symbolic dynamic entropy.

[0084] (2) The RSSD method is proposed. This method analyzes the signal by using Riesz transform and Log-Gabor filter bank, filters the obtained four-parameter spectrum using cosine sign dynamic entropy, and optimizes the parameters of the sparse filter constructed by the reconstructed components, so that the decomposition result has better physical meaning. At the same time, RSSD also has good robustness and time-frequency clustering.

[0085] (3) Simulation analysis shows that RSSD has better time-frequency aggregation and robustness compared with EMD and VMD methods. In addition, the analysis results of the vibration signals of rolling bearing faults at variable and constant speeds show that RSSD can accurately extract the fault feature information of rolling bearings at constant or variable speeds, and can effectively realize the fault diagnosis of rolling bearings under different working conditions by combining envelope spectrum or envelope order spectrum.

[0086] Second, the technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully: based on existing rolling bearing fault diagnosis methods and the modal confusion caused by existing technologies, fault features are extracted for rolling bearings under constant speed and variable speed, thereby realizing fault diagnosis.

[0087] Third, this invention solves several key technical problems faced by existing technologies in industrial applications through a rolling bearing fault detection method based on Riesz graph sparse decomposition, and has achieved significant technical progress in practical applications. The following are the solutions to existing technical problems and their technical advancements in industry:

[0088] 1. Problems with existing technologies

[0089] Insufficient noise resistance of time-frequency analysis methods: Traditional time-frequency analysis methods can only obtain the amplitude and frequency information of vibration signals. In cases with large noise or unclear signal characteristics, it is often difficult to accurately capture the fault characteristics of the signal, resulting in reduced diagnostic accuracy.

[0090] Signal feature extraction is singular and incomplete: Existing methods mostly focus on time-domain or frequency-domain analysis of signals, and cannot simultaneously obtain multi-dimensional information such as phase and direction of signals, which limits the accuracy of fault detection and diagnostic effectiveness.

[0091] The computational efficiency of symbolic dynamics entropy is low: Existing complexity analysis methods based on symbolic dynamics have high computational complexity, making them difficult to apply effectively when processing large-scale industrial data, which affects the performance of real-time system monitoring and online fault diagnosis.

[0092] 2. Technological advancements of this invention

[0093] This invention enhances the noise resistance and time-frequency clustering of time-frequency analysis: By introducing the Riesz four-parameter spectrum time-frequency analysis method, it can simultaneously acquire four parameters of vibration signals: amplitude, frequency, phase, and direction. This significantly improves the time-frequency clustering and noise resistance of the analysis results. Compared to traditional time-frequency analysis methods, it can capture fault characteristics in signals more comprehensively and accurately, maintaining high diagnostic accuracy even in high-noise environments.

[0094] A more comprehensive fault feature extraction is achieved: This invention innovatively applies the Riesz transform to rolling bearing fault detection, enabling the acquisition of multi-dimensional signal features, including phase and direction information, overcoming the limitations of traditional methods that can only capture time-frequency domain amplitude and frequency information. Through these multi-dimensional signal representations, the comprehensiveness of fault detection is improved, significantly enhancing the reliability of fault diagnosis.

[0095] The efficiency of entropy calculation is improved: The cosine-signed dynamic entropy method proposed in this invention greatly improves the computational efficiency of signified dynamic entropy by transforming a two-dimensional matrix into a one-dimensional sequence. This method reduces computational complexity, enabling its application to the processing of large-scale industrial data, thereby supporting real-time monitoring and online fault diagnosis, and significantly improving the feasibility of industrial applications in terms of processing speed.

[0096] The invention enhances the physical meaning of the decomposition results and the sparsity of the fault signals: By employing a signal reconstruction method based on sparse filters, this invention ensures the physical meaning of the fault signal decomposition, effectively filters out signal components highly correlated with fault characteristics, and removes useless noise components, further improving the accuracy and efficiency of diagnosis. The sparse decomposition optimization algorithm makes the rolling bearing fault detection method more accurate and efficient, and is particularly suitable for complex industrial environments.

[0097] 3. Significant technological advancements in industrial applications

[0098] Improved accuracy and reliability of rolling bearing fault diagnosis: By introducing multidimensional signal characterization and sparse decomposition technology, rolling bearing fault signals can be extracted efficiently and accurately in complex environments, improving the accuracy of early fault detection and diagnosis and reducing sudden losses from equipment failures.

[0099] Adapting to the needs of large-scale industrial data processing: The cosine-signed dynamic entropy and sparse decomposition optimization algorithm enable this invention to have higher computational efficiency when processing large-scale vibration data, which can meet the needs of real-time online monitoring in industry and provide effective support for intelligent maintenance.

[0100] It improves the predictability of equipment maintenance and saves maintenance costs: This technology has broad application prospects in industrial automation and smart manufacturing. By detecting potential equipment problems earlier, it can effectively reduce unplanned downtime, lower maintenance costs, and extend the service life of equipment.

[0101] In summary, this invention not only solves the key technical problems in existing rolling bearing fault detection, but also significantly improves the accuracy, real-time performance, and efficiency of fault diagnosis in industrial applications. It has important technological advancements and application value for improving the intelligent monitoring and maintenance level of industrial equipment. Attached Figure Description

[0102] Figure 1 This is a flowchart of a rolling bearing fault method based on Riesz graph sparse decomposition provided in an embodiment of the present invention;

[0103] Figure 2 This is a flowchart of the RSSD provided in an embodiment of the present invention;

[0104] Figure 3 These are the mixed signals and their components provided in the embodiments of the present invention;

[0105] Figure 4 This is the RSSD decomposition result provided in the embodiments of the present invention;

[0106] Figure 5 This is the EMD decomposition result provided in the embodiments of the present invention;

[0107] Figure 6 This is the VMD decomposition result provided in the embodiments of the present invention;

[0108] Figure 7 This is the VMD2 decomposition result provided in the embodiments of the present invention;

[0109] Figure 8 These are the time-frequency spectra of each component provided in the embodiments of the present invention; in order, they are the time-frequency spectra of the simulated signal component, the time-frequency spectra of the RSSD component, the time-frequency spectra of the EMD component, and the time-frequency spectra of the VMD component;

[0110] Figure 9 These are the mixed signals and their components provided in the embodiments of the present invention;

[0111] Figure 10 This is the RSSD decomposition result provided in the embodiments of the present invention;

[0112] Figure 11 This is the EMD decomposition result provided in the embodiments of the present invention;

[0113] Figure 12 This is the VMD decomposition result provided in the embodiments of the present invention;

[0114] Figure 13 This is the VMD2 decomposition result provided in the embodiments of the present invention;

[0115] Figure 14 These are the time-frequency spectra of each component provided in the embodiments of the present invention; in order, they are the time-frequency spectra of the simulated signal component, the time-frequency spectra of the RSSD component, the time-frequency spectra of the EMD component, and the time-frequency spectra of the VMD component;

[0116] Figure 15 This is an energy recovery variable speed bearing fault test bench provided in an embodiment of the present invention;

[0117] Figure 16 This is a faulty 6206 bearing part provided by the embodiment of the present invention for electrical discharge cutting;

[0118] Figure 17 These are the bearing speed signal and vibration signal with outer ring fault provided in the embodiments of the present invention;

[0119] Figure 18 This invention provides RSSD decomposition, component angular domain resampling, and envelope order spectrum.

[0120] Figure 19 This invention provides EMD decomposition and component angular domain resampling, as well as envelope order spectrum;

[0121] Figure 20 This invention provides VMD decomposition and component angular domain resampling, as well as envelope order spectrum;

[0122] Figure 21 This is a time-domain diagram of the constant speed bearing outer ring fault signal provided in an embodiment of the present invention;

[0123] Figure 22 This is the envelope spectrum of the constant speed bearing outer ring fault signal provided in the embodiments of the present invention;

[0124] Figure 23 This refers to the fault vibration signal component obtained using RSSD as provided in the embodiments of the present invention;

[0125] Figure 24 This refers to the fault vibration signal components obtained using EMD as provided in the embodiments of the present invention;

[0126] Figure 25 This refers to the fault vibration signal components obtained using VMD as provided in the embodiments of the present invention;

[0127] Figure 26 This is the envelope spectrum of the faulty bearing signal decomposed using RSSD, EMD, and VMD methods provided in the embodiments of the present invention. Detailed Implementation

[0128] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0129] like Figure 1 As shown, a rolling bearing fault method based on Riesz graph sparse decomposition is proposed, which includes:

[0130] S1: A new time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—is used to obtain the four parameters of vibration signal in the time-frequency domain: amplitude, frequency, phase, and direction, thereby improving the time-frequency convergence and noise resistance of the analysis results.

[0131] S2: To select the optimal parameter spectrum, a new entropy calculation method—cosine symbolic dynamic entropy—is proposed, which extends the symbolic dynamic entropy to a two-dimensional scale.

[0132] S3: The parameter spectrum components selected by entropy screening are reconstructed, and the amplitude of the sparse filter parameter optimization components is constructed to make the decomposition results have physical meaning. Based on this, the RSSD method is proposed.

[0133] This invention proposes a rolling bearing fault detection method based on Riesz spectrum sparse decomposition. Firstly, in step S1, the Riesz four-parameter spectrum time-frequency analysis method is employed. This method simultaneously analyzes the amplitude, frequency, phase, and direction of the vibration signal, resulting in higher time-frequency clustering in the analysis results and effectively improving noise immunity even with significant signal noise. Compared to traditional time-frequency analysis techniques, this method can more accurately capture the characteristic changes of the vibration signal, providing a more reliable data foundation for subsequent fault identification.

[0134] Next, in step S2, symbolic dynamic entropy is used as a tool to screen the optimal parameter spectrum. Symbolic dynamic entropy is a quantitative indicator reflecting the complexity of a signal. To more effectively screen parameter spectra that conform to the characteristics of rolling bearing faults, this paper proposes the concept of cosine symbolic dynamic entropy and extends it to a two-dimensional scale. This new entropy calculation method can more accurately capture the complex changes and nonlinear characteristics of signals, thereby improving the accuracy and reliability of fault feature extraction.

[0135] In step S3, the optimal parameter spectrum selected through entropy calculation is reconstructed to form a sparse decomposition model for rolling bearing fault detection. The reconstructed components are further optimized by a sparse filter to give the decomposition results a clearer physical meaning, i.e., the fault signal characteristics are more significant and easier to identify. This sparse decomposition model can effectively eliminate useless information and retain key components related to the fault, thereby improving detection accuracy.

[0136] Finally, based on the above, the RSSD (Riesz Spectral Sparse Decomposition) method is proposed. The RSSD method combines time-frequency analysis, symbolic dynamic entropy, and sparse decomposition techniques, exhibiting high accuracy, strong noise resistance, and clear physical meaning. This method can efficiently extract fault features from rolling bearing vibration signals, making it suitable for equipment fault detection and health monitoring in complex industrial environments, and possesses significant application value.

[0137] S1 specifically includes:

[0138] (1) Riesz transform

[0139] Traditional time-frequency analysis methods can only obtain the amplitude and frequency information of the signal in the time-frequency domain, which will introduce bias when analyzing the signal. In order to solve this problem, the Riesz transform is innovatively used to analyze the vibration signal. The Riesz transform can obtain the amplitude, frequency, phase and direction information of the signal, thereby more comprehensively characterizing the fault features and improving the time-frequency convergence and noise resistance of the analysis results.

[0140] For any given one-dimensional real signal f(x) 1D , x∈R, analytic signal f A (x) is defined as the complexification function of the signal, where the real part is the signal itself and the imaginary part (conjugate function) is its Hilbert transform;

[0141] f A (x)=f(x) 1D -if H (x) (1)

[0142] In the formula f H ()=f(x) 1D *h(x) represents the Hilbert transform of the original signal, and the transform kernel is... The corresponding frequency response is H(w) = -jsgn(w);

[0143] Similarly, the Riesz transform can generate analytic signal representations for two-dimensional signals, for any two-dimensional signal f(x). 2D , x∈R 2 Its Riesz transform f R (·) is defined as:

[0144]

[0145] x = (x1, x2) is the position index vector, y = (y1, y2) is the dummy variable, and |||| is the vector norm. The definition of the Riesz transform can be rewritten in the form of a convolution kernel as follows:

[0146]

[0147] The two-dimensional signal f(x)2D has a Riesz transform in two directions.

[0148]

[0149] Where x′=(x′1,x′2), p·v· represents the Cauchy principal value integral, and the Riesz transform and the first and second transform kernel functions are respectively

[0150]

[0151] f(x) 2D The linear combination with the Riesz transform is f(x). 2D The analytic signal is defined as the monomorphic signal f. M (x)

[0152]

[0153] Where i and j represent two imaginary units, and {i, j, 1} constitutes R. 3 A set of orthogonal bases in the space. Therefore, f(x) 2D Single-stage signals are typically generated using vectorization functions or vector fields f. M :R 2 →R 3 To define,

[0154]

[0155] (2) Riesz four-parameter spectral time-frequency analysis method

[0156] Previous time-frequency transformation methods could only obtain the amplitude and frequency information of a signal in the time-frequency domain. This paper innovatively employs Riesz transform and Log-Gabor filter banks to analyze the signal, thereby simultaneously obtaining four parameters of the signal in the time-frequency domain: amplitude, frequency, phase, and direction. This allows for a more comprehensive characterization of bearing fault features and improves the time-frequency convergence and noise immunity of the analysis results. Based on this, a new time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—is proposed. This method consists of the following steps:

[0157] 1) Perform continuous wavelet transform on the original signal. Given a signal x(t), its CWT can be expressed as:

[0158]

[0159] In the formula, ψ(t) is the Morlet wavelet basis, and τ and s represent the translation and scaling transformations, respectively.

[0160] 2) Obtain the Riesz four-parameter spectrum. The Riesz four-parameter spectrum refers to the spectrum obtained from the Riesz four-parameter spectrum. The amplitude spectrum A(τ, s) and phase spectrum constructed after Riesz transform The frequency spectrum f(τ, s) and the directional spectrum θ(τ, s) are given. Considering the influence of noise on the four-parameter spectrum, a Log-Gabor filter is used to filter the four-parameter spectrum. The Log-Gabor filter has the advantages of zero DC component and no bandwidth limitation, and its frequency response function is:

[0161]

[0162] In the formula, ω0 is the center frequency, and σ is the scaling factor for adjusting the bandwidth; to maintain a filter bank with a fixed shape ratio, σ is usually set to a certain value. r =σ / ω0 remains constant; if observed on a logarithmic frequency scale, the Log-Gabor filter has a Gaussian-like frequency response;

[0163] Because the Log-Gabor filter does not have an analytical expression in the time domain, its time domain representation is obtained through inverse Fourier transform;

[0164]

[0165]

[0166] Among them, F -1 This represents the inverse Fourier transform. express The model, yes Fourier stated that yes Two Riesz cores, and They are respectively Differentiate with respect to τ and s.

[0167] S2 specifically includes:

[0168] To further improve the computational efficiency and complexity representation accuracy of symbolic dynamic entropy, this paper utilizes the image block division concept to transform a two-dimensional matrix into a block matrix and calculates the cosine similarity between adjacent block matrices. This transforms the complexity of calculating a two-dimensional matrix into the complexity of calculating a one-dimensional sequence, effectively improving computational efficiency. Based on this, an entropy calculation method—cosine symbolic dynamic entropy—is proposed, with the following steps:

[0169] Taking A(τ, s) as an example, A(τ, s) is first divided into several non-overlapping blocks of the same size, with a block size of 10×10. The block matrix is ​​then converted into vector form to calculate the cosine similarity between adjacent blocks, resulting in a series of cosine similarities. The cosine similarity between two blocks is calculated as follows:

[0170] A(τ, s) = {a1, a2, ... a N*M} (12)

[0171] D = {d1, d2, ..., d} N*M-1}={d(a1-a2), d(a2-a3),..., d(a N*M-1 -a N+M (13)

[0172]

[0173] Where, {a1, a2, ... a N*M} represents the vector form of the block matrix, N = round(length(τ) / 10), M = round(length(s) / 10); Note that the range of cosine similarity d is [-1, 1], and it measures the cosine value of the geometric angle; Note that the range of cosine similarity d is [-1, 1]; The defined cosine similarity d is the similarity between two orbits, and it measures the cosine value of the geometric angle; A larger cosine similarity value indicates that there are similar, predictable, or periodic dynamic changes between the two orbits;

[0174] Divide the D sequence into ε intervals with equal probability according to their size. i It corresponds to one and only one interval, such as the symbol σ. i It then replaced d i This forms the symbol sequence Z{Z k , k = 1, 2, ..., N*M-1}. According to Takens' embedding theorem, subvectors are generated using the embedding dimension m and the time delay μ. Calculate the state pattern probability:

[0175]

[0176] In the formula, ε represents the state pattern of the symbol arrangement of each subvector. m The symbol arrangement state pattern is represented by type(), which represents the mapping relationship from the symbol space to the pattern space, and |||| represents the number of elements in the set.

[0177] When the state pattern has been observed When, the symbol that appears afterward is σ. bThe probability of (a = 1, 2, ..., ε) is the state transition probability:

[0178]

[0179] Based on the definition of information entropy, we define the cosine sign dynamic entropy (CSDE). 2D It equals the sum of the state pattern probability entropy and the state transition probability entropy:

[0180]

[0181] If and only if At that time, CSDE 2D The maximum value is obtained as ln(ε) m+1 ). CSDE 2D Normalization:

[0182] CSDE 2D =CSDE 2D / ln(ε m+1 (18)

[0183] CSDE 2D The larger the value, the more random and complex the distribution within the parameter spectrum. CSDE 2D The smaller the value, the more regular the distribution within the parameter spectrum and the less affected it is by noise. Statistical analysis shows that when m=2, ε=10, and μ=1, the complexity within the four-parameter spectrum can be accurately quantified with short computation time.

[0184]

[0185] S3 specifically includes:

[0186] By analyzing the signal using Riesz transform and Log-Gabor filter banks, the obtained four-parameter spectrum is filtered using cosine sign dynamic entropy, and the parameters of the sparse filter constructed from the reconstructed components are optimized to give the decomposition results physical meaning. Based on this, an adaptive signal decomposition method based on time-frequency spectrum—the RSSD method—is proposed. Its main steps are as follows:

[0187] (1) As shown in equations (8)-(10), the filtered result is obtained through Riesz transform and Log-Gabor filter bank. Its time-domain representation is obtained by inverse Fourier transform. The four-parameter spectrum PT(τ, s) is obtained as shown in equation (11);

[0188] (2) Determine the optimal parameter spectrum, as shown in formulas (12)-(18), and use the cosine sign dynamic entropy to calculate the entropy value CSDE of each parameter spectrum. 2D As shown in formula (20), the optimal parameter spectrum PT is obtained.i (τ,s);

[0189] (3) Obtaining local coefficients Given a threshold mean(mean(PT) i (τ,s))), further reducing spurious local minima caused by noise; PT i (τ, s) is divided into several incoherent regions pt, as shown in the image. i (τ, s), in pt i Find the local maximum point max(pt) along s within (τ, s). i (τ,s)), considering applicability, spline interpolation is used to fit the local coefficients to the maximum points.

[0190] (4) Reconstructed component r i (t). Will Perform continuous wavelet inverse transform to reconstruct the component r. i (t) While ensuring reconstruction accuracy, the algorithm's time consumption is reduced; for time-domain signal r i (t), the reconstruction formula is as follows:

[0191]

[0192]

[0193] in, It is the Fourier transform of ψ(t). This indicates taking the real part.

[0194] (5) Sparse component amplitude optimization, which only takes points on the ridge, will lose most of the energy. Therefore, let res1(t) = x(t) to construct the following optimization problem P1:

[0195]

[0196] In the optimization problem P1, the optimization parameters are the magnitudes of each component, η||D(res1(t)-r i (t))|| 2 The objective function is used for regularization optimization. D is a differential operator used to obtain the sparsest representation of the original signal, and its weight η is usually set to 1.

[0197] Construct the following optimization problem P2, where the optimization parameter is the magnitude coefficient μ:

[0198] P2 Minimize||res1(t)-μr i (t)|| 2 (twenty three)

[0199] The purpose of this step is to obtain r i The optimal amplitude of (t) is further ensured to guarantee the sparsity of the decomposition results;

[0200] (6) Set local coefficients Length threshold, When the length is too short, the iteration is terminated during reconstruction, and the entire decomposition process is completed.

[0201] I. Specific application areas or related products of this invention.

[0202] This invention provides a rolling bearing fault system based on Riesz graph sparse decomposition, which is based on the aforementioned rolling bearing fault method. The system specifically includes:

[0203] The parameter information acquisition module utilizes a novel time-frequency analysis method—the Riesz four-parameter spectrum time-frequency analysis method—to acquire the four parameters of vibration signal in the time-frequency domain: amplitude, frequency, phase, and direction, thereby improving the time-frequency convergence and noise resistance of the analysis results.

[0204] The parameter spectrum screening module, connected to the parameter information acquisition module, extends the symbolic dynamic entropy to a two-dimensional scale to screen out the optimal parameter spectrum, and proposes a new entropy calculation method - cosine symbolic dynamic entropy.

[0205] An amplitude construction module, connected to a parameter spectrum screening module, reconstructs the parameter spectrum components selected by entropy screening, constructs the amplitude of sparse filter parameter optimization components, and makes the decomposition results physically meaningful. Based on this, the RSSD method is proposed.

[0206] This invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the rolling bearing fault method based on Riesz graph sparse decomposition.

[0207] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the rolling bearing fault method based on Riesz graph sparse decomposition.

[0208] This invention provides an information data processing terminal for implementing the rolling bearing fault system based on Riesz graph sparse decomposition.

[0209] II. Evidence related to the technical effects obtained by the embodiments of the present invention.

[0210] 1. Simulation Analysis

[0211] To demonstrate the superiority and accuracy of the RSSD method in mixed-signal decomposition, its decomposition capabilities are compared in detail with those of the EMD and VMD methods. First, a simulation model s(t) is constructed, consisting of an amplitude-modulated frequency-modulated component s1(t), an oscillation-damped component s2(t), and a frequency-converted component s3(t). 5 dB of intermittent Gaussian white noise nt is added to the signal. The time domain representations of the simulated signal and its components are shown below. Figure 3 As shown.

[0212]

[0213] The simulated signal was decomposed using RSSD, EMD, and VMD methods respectively. The decomposition results are shown below. Figure 4 , Figure 5 and Figure 6 .Depend on Figure 4 It can be seen that RSSD successfully separates the signal components from intermittent noise, and the phase of the decomposed result matches the phase of the components in the original signal, while the amplitude of the decomposed components is almost identical to the amplitude of the components in the original signal. Figure 5 The EMD decomposition results show that the IMF components still contain noise and modal confusion between components, thus proving that the decomposition capability of EMD is weaker than that of RSSD. Figure 6 We know that VMD successfully separated the noise, and IMF1 appears to be completely noise-free. Therefore, we perform another VMD decomposition on IMF1, and the result is as follows... Figure 7 As shown.

[0214] from Figure 7 As can be seen, VMD2 separates the signal components. The amplitude modulation (AM) and frequency modulation (FM) components are separated relatively well. However, in IMF1, IMF3, and IMF4, mode confusion exists between the frequency conversion component and the oscillation decay component during the decomposition process, leading to incomplete decomposition. The time-domain signal of IMF4 contains both frequency conversion and oscillation decay components. Therefore, it is preliminarily concluded that RSSD decomposition is indeed more accurate in handling intermittent noise compared to EMD and VMD.

[0215] Plot the time-frequency spectrum of the simulated signal and the components obtained by each decomposition method, such as... Figure 8 The time-frequency spectrum is represented as a three-dimensional grayscale image, depicting the instantaneous frequency and amplitude of each component. Amplitude is expressed in grayscale levels; brighter pixels indicate larger amplitudes. Figure 8As can be seen, the low-frequency energy of the EMD decomposed components is mixed together; the 100Hz component is significantly affected by intermittent noise, with gaps appearing in the 0.1–0.3s and 0.7–0.8s intervals. The frequency-converted components in the RSSD and VMD2 decomposed components have almost the same time-frequency spectrum as the simulated signal components; while the 100Hz component is slightly affected by intermittent noise, showing some fluctuations in the 0.1–0.3s and 0.7–0.8s intervals, but overall consistent with the simulated signal components; in the 30Hz component, due to mode confusion in the VMD2 decomposed component, the amplitude of the VMD2 component is lower than that of the simulated signal component in the 0.1–0.4s interval, which corroborates the VMD decomposed results in the previous paragraph. Therefore, it is tentatively concluded that RSSD does have certain advantages compared to EMD and VMD.

[0216] Component quantization of RSSD, VMD, and EMD decompositions, and the correlation coefficient r between the correlation coefficient and the original signal. j The orthogonality index IO and computation time T are used to compare the orthogonality and computation speed of the methods. Table 1 shows that the correlation coefficient of RSSD is slightly larger than that of VMD, and larger than that of EMD. This indicates that RSSD has the best component-to-original signal decomposition performance. Furthermore, RSSD has the smallest orthogonality index; the smaller the IO, the better the orthogonality. It is worth noting that the decomposition speed of RSSD is lower than that of EMD, but faster than that of VMD.

[0217] Table 1 Evaluation Indicators of Decomposition Results

[0218]

[0219] To further illustrate the superiority of RSSD in signal processing, the following simulation model s(t) was created. s(t) consists of an oscillation decay component s1(t), a frequency-modulated component s2(t) with gradually increasing amplitude, and an amplitude-frequency modulated component s3(t). To better simulate reality, 5dB of Gaussian white noise nt was added to the signal. The time domain of the simulated signal and its components is shown in the figure below.

[0220]

[0221] We will still use EMD, VMD, and RSSD for decomposition and comparison. The decomposition diagram is as follows: Figures 10-12 As shown. From Figure 10 It can be seen that the components decomposed by RSSD, in terms of both amplitude and frequency, are consistent with the components of the simulated signal, effectively separating the signal components from the noise. (Comparison) Figure 11 According to the EMD decomposition results, the EMD components still contain noise and require further processing. Figure 12 and Figure 6 Similarly, VMD isolates the signal components, meaning that IMF1 contains signal components.

[0222] right Figure 12 The IMF1 component in the matrix is ​​then decomposed again using VMD, and the decomposition results are as follows: Figure 13 .from Figure 13 As can be seen, s1(t), s2(t), and s3(t) all exhibit mode confusion during the decomposition process. Among them, s1(t) and s2(t) interfere with each other because their frequencies are similar. Figure 13 The IMF2 and IMF4 in the model are clearly reflected, and s3(t) is also slightly affected, splitting into IMF1 and IMF3. In conclusion, RSSD has a stronger decomposition capability than EMD and VMD.

[0223] Plot the time-frequency spectrum of the simulated signal and the components obtained by each decomposition method, such as... Figure 14 .from Figure 14 It can be seen that the components decomposed by EMD are masked by noise. In the VMD2 component, the amplitude-modulated and frequency-modulated signals are affected, and the energy in the vicinity is relatively dispersed; while the oscillation decay and the frequency conversion component interfere with each other, causing the oscillation decay component point to be relatively dim, and the latter part of the frequency conversion component disappears completely with dispersed energy. From the time spectrum of the RSSD component, it can be seen that the time spectrum of the RSSD component is almost the same as that of the simulated signal component. Therefore, RSSD does indeed have a better decomposition effect compared to EMD and VMD.

[0224] Component quantization of RSSD, VMD, and EMD decompositions, and the correlation coefficient r between the correlation coefficient and the original signal. i The orthogonality index IO and computation time T compare the orthogonality and computation speed of the methods. Table 2 shows that the correlation coefficient of RSSD is greater than that of EMD. It is worth mentioning that the three correlation coefficients r of VMD... i r3 represents the amplitude-frequency modulation (AM / FM) component, and its correlation coefficient with RSSD is close. The other two coefficients are smaller than those of RSSD, which is consistent with the results above. This indicates that the RSSD component has the best decomposition performance with the original signal. Furthermore, RSSD has the smallest orthogonality index; the smaller the I / O, the better the orthogonality. It is worth noting that RSSD's decomposition speed is lower than EMD, but faster than VMD.

[0225] Table 2 Evaluation Indicators of Decomposition Results

[0226]

[0227] 2. Application of RSSD method in rolling bearing diagnosis

[0228] 2.1 Application of RSSD method in the diagnosis of variable speed bearings

[0229] To verify the feasibility of RSSD in practical applications, this method was used in actual variable speed bearing fault diagnosis. The energy recovery variable speed bearing fault test bench was constructed as follows: Figure 15 As shown. The outer ring of the bearing is cut using electrical discharge machining (EDM), as follows. Figure 16 As shown in (c), the experimental platform mainly consists of a generator, torque sensor, speed sensor, acceleration sensor, coupling, test bearing, Siemens PLC, and data acquisition equipment. The test bearing is an SKF 6206 deep groove ball bearing with a fault depth set to 0.2 mm and a sampling frequency of 1024 Hz.

[0230] The characteristic order K of the outer ring fault is calculated using the formula for calculating the characteristic frequency of the outer ring fault, and is found to be 3.568. First, the bearing speed variation is analyzed, such as... Figure 17 As shown, the speed increases from 0 to 810 r / min within 0–14 s. The time-domain plot of the vibration signal shows that the amplitude increases with the increase of rotational speed, thus proving that the vibration signal is related to the rotational speed signal.

[0231]

[0232] To verify the effectiveness of RSSD decomposition of the experimental signal, it was compared with EMD and VMD methods. Envelope order spectrum analysis was combined for fault diagnosis of the outer ring of a variable speed bearing. The vibration signal was decomposed using each method, and the first four components were taken from the decomposition result. The first component with a higher center frequency was selected for angular domain resampling to obtain a more stable component. Finally, the angular domain signal was subjected to envelope Fourier transform to obtain the envelope order spectrum, which was then analyzed. The decomposition results are shown below. Figure 18 (a) Figure 19 (a) and Figure 20 As shown in (a), the corner domain resampled signal is as follows: Figure 18 (b) Figure 19 (b) and Figure 20 As shown in (b), the envelope order spectrum is as follows: Figure 18 (c) Figure 19 (c) and Figure 20 As shown in (c).

[0233] Through the Figure 19 Analysis shows that the characteristic order corresponding to the outer ring fault of the variable speed bearing cannot be found in the envelope order spectrum obtained by EMD decomposition and angular domain resampling of the experimental signal, therefore, outer ring fault diagnosis is impossible. Figure 20In the envelope order spectrum of the variable speed bearing, a relatively high peak appears at 3.5603, which approximates the characteristic order corresponding to the outer ring fault of the variable speed bearing. However, only one characteristic order appears, so the diagnosis result for the outer ring fault is not particularly obvious. In contrast, the envelope order spectrum of RSSD clearly shows multiple high peaks, three of which are 3.5658, 7.1373, and 10.7087, approximately 1, 2, and 3 times the characteristic order of the variable speed bearing outer ring fault, respectively. Furthermore, their amplitudes are higher than the characteristic order amplitudes of VMD, indicating more obvious extracted fault features. Experimental results show that the RSSD method proposed in this invention can effectively extract fault features from variable speed signals. Moreover, compared to EMD and VMD, RSSD is superior in processing variable speed signals, effectively extracting fault features and achieving effective diagnosis of outer ring faults in variable speed bearings.

[0234] 2.2 Application of RSSD method in constant speed bearing diagnosis

[0235] To further verify the effectiveness of the RSSD method in rolling bearing fault diagnosis, the RSSD method was introduced to... Figure 15 The outer ring fault data of the experimental platform shown is decomposed, and the outer ring faults are as follows: Figure 16 As shown in (c), the sampling rate is 1024Hz, the switching frequency f0 is set to 13.5Hz, and the fault characteristic frequency f is calculated by formula (26). r 48.168Hz. Envelope spectrum analysis was performed on the time-domain data, and the time-domain plot and envelope spectrum of the bearing fault signal are shown below.

[0236] Neither the time-domain plot nor the envelope spectrum revealed any fault characteristics in the bearing's outer ring. Therefore, RSSD, EMD, and VMD were used to decompose the vibration signal, and the obtained components are as follows: Figure 23-25 .

[0237] Each component is used for subsequent analysis. The component containing the richest fault information is selected for envelope spectrum analysis, and the resulting envelope spectrum is as follows: Figure 26 As shown, the RSSD component envelope spectrum shows a prominent rotational frequency and accurately extracts the fault characteristic frequency. Therefore, RSSD can accurately diagnose outer ring faults in energy recovery bearing test benches. Meanwhile, it can be seen that the VMD component envelope spectrum has a prominent rotational frequency and harmonics, while the fault characteristic frequency is weak. Therefore, VMD cannot be used to diagnose bearing outer ring faults. The fault characteristic frequency in the EMD envelope spectrum is also not very obvious, making it difficult to effectively diagnose bearing faults.

[0238] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as 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 circuitry 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., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0239] The above description is merely 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 those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A rolling bearing fault detection system based on Riesz graph sparse decomposition, characterized in that the system... include: The time-frequency analysis module uses the Riesz four-parameter spectrum time-frequency analysis method to obtain the amplitude, frequency, phase and direction four-parameter spectrum information of the rolling bearing vibration signal; The entropy calculation module uses the cosine sign dynamic entropy calculation method to characterize the complexity of the signal in order to select the optimal parameter spectrum. The sparse decomposition module reconstructs the components of the optimal parameter spectrum and optimizes the sparse filter parameters. The control module uses the Riesz graph sparse decomposition method-RSSD method to achieve adaptive decomposition and fault diagnosis of rolling bearing fault signals. The Riesz graph sparse decomposition-based rolling bearing fault detection system is used to execute a Riesz graph sparse decomposition-based rolling bearing fault detection method, which includes: S1: Use the Riesz four-parameter spectral time-frequency analysis method to obtain the amplitude, frequency, phase and direction four-parameter spectral information of the vibration signal in the time-frequency domain; S2: Extending the symbolic dynamic entropy to a two-dimensional scale, we propose the cosine symbolic dynamic entropy, which is used to screen out the optimal parameter spectrum; S3: The optimal parameter spectrum reconstruction component is selected by screening the cosine sign dynamic entropy, and the amplitude of the sparse filter parameter optimization component is constructed. Based on this, the RSSD method is proposed. S1 specifically includes: (1) Riesz transform The Riesz transform can obtain the amplitude, frequency, phase and direction information of a signal, thereby more comprehensively characterizing fault features and improving the time-frequency convergence and noise resistance of the analysis results. For any given one-dimensional real signal f(x) 1D , x∈R, analytic signal f A (x) is defined as the complexification function of the signal, where the real part is the signal itself and the imaginary part is the Hilbert transform; f A (x)=f(x) 1D -if H (x) (1) In the formula f H ()=f(x) 1D *h(x) represents the Hilbert transform of the original signal, and the transform kernel is... The corresponding frequency response is H(w) - jsgn(w); The Riesz transform generates an analytic signal representation of a two-dimensional signal, for any two-dimensional signal f(x). 2D , x∈R 2 Its Riesz transform f R (·) is defined as: x = (x1, x2) is the position index vector, y = (y1, y2) is the dummy variable, and ||x|| is the vector norm; the definition of the Riesz transform is rewritten in the form of a convolution kernel as follows: Two-dimensional signal f(x) 2D Riesz transform with two directions Where x' = (x'1, x'2), pv represents the Cauchy principal value integral, and the first and second Riesz transform kernel functions are respectively... f(x) 2D The linear combination with the Riesz transform is f(x). 2D The analytic signal is defined as the monomorphic signal f. M (x) Where i and j represent two imaginary units, and {i, j, 1} constitutes R. 3 A set of orthogonal bases in the space; therefore, f(x) 2D The single-stage signal is obtained by using a vectorization function or vector field f M :R 2 →R 3 To define, (2) Riesz four-parameter spectral time-frequency analysis method The signal is analyzed using Riesz transform and Log-Gabor filter banks, enabling simultaneous acquisition of four parameters—amplitude, frequency, phase, and direction—in the time-frequency domain. Based on this, a time-frequency analysis method—the Riesz four-parameter spectral time-frequency analysis method—is proposed, which consists of the following steps: 1) Perform continuous wavelet transform on the original signal. Given a signal x(t), its CWT is expressed as: In the formula, ψ(t) is the Morlet wavelet basis, and τ and s represent the translation and scaling transformations, respectively. 2) Obtain the Riesz four-parameter spectrum. The Riesz four-parameter spectrum refers to the spectrum obtained from the Riesz four-parameter spectrum. The amplitude spectrum A(τ, s) and phase spectrum constructed after Riesz transform The frequency spectrum f(τ, s) and the directional spectrum θ(τ, s) are given. Considering the influence of noise on the four-parameter spectrum, a Log-Gabor filter is used to filter the four-parameter spectrum. The Log-Gabor filter has the advantages of zero DC component and no bandwidth limitation, and its frequency response function is: In the formula, ω0 is the center frequency, and σ is the scaling factor for adjusting the bandwidth; to maintain a filter bank with a fixed shape ratio, σ is... r =σ / ω0 remains constant; if observed on a logarithmic frequency scale, the Log-Gabor filter has a Gaussian-like frequency response; Because the Log-Gabor filter does not have an analytical expression in the time domain, its time domain representation is obtained through inverse Fourier transform; Among them, F -1 This represents the inverse Fourier transform. express The model, yes Fourier stated that yes Two Riesz cores, and They are respectively Differentiate with respect to τ and s; S2 specifically includes: By utilizing the concept of image segmentation to transform a two-dimensional matrix into a block matrix and calculating the cosine similarity between adjacent block matrices, the computational complexity of calculating a two-dimensional matrix is ​​transformed into the complexity of calculating a one-dimensional sequence, effectively improving computational efficiency. Based on this, an entropy calculation method—cosine sign dynamic entropy—is proposed, with the following steps: First, divide A(τ, s) into several non-overlapping blocks of the same size, each block being 10×10. Convert the block matrix into vector form to calculate the cosine similarity between adjacent blocks, resulting in a series of cosine similarities. The cosine similarity between two blocks is calculated as follows: A(τ,s)={a1,a2,...a N*M } (12) D={d1,d2,...,d N*M-1 }={d(a1-d2),d(a2-a3),…,d(a N*M-1 -a N*M )} (13) Where, {a1, a2, ... a N*M } represents the vector form of the block matrix, N = round(length(τ) / 10), M = round(length(s) / 10); the range of cosine similarity d is [-1, 1], and it measures the cosine value of the geometric angle; note that the range of cosine similarity d is [-1, 1]; the defined cosine similarity d is the similarity between two orbits, and it measures the cosine value of the geometric angle; a larger cosine similarity value indicates that there are similar, predictable or periodic dynamic changes between the two orbits; Divide the D sequence into ε intervals with equal probability according to their size. i It corresponds to one and only one interval, such as the symbol σ. i It then replaced d i This forms the symbol sequence Z{Z k , k = 1, 2, ..., N*M-1; According to Takens' embedding theorem, subvectors are generated using the embedding dimension m and the time delay μ. Calculate the state mode probabilities for z(j+μ), ..., z(j+(m-1))). In the formula, The state pattern represents the symbol arrangement of each subvector, a = 1, 2, ..., ε m , ε m The symbol arrangement state pattern is represented by type(), which represents the mapping relationship from the symbol space to the pattern space, and |||| represents the number of elements in the set. When the state pattern has been observed When, the symbol that appears afterward is σ. b The probability of transition is the state transition probability, b = 1, 2, ..., ε: Based on the definition of information entropy, we define the cosine sign dynamic entropy (CSDE). 2D It equals the sum of the state pattern probability entropy and the state transition probability entropy: If and only if At that time, CSDE 2D The maximum value is obtained as ln(ε) m+1 ); CSDE 2D Normalization: CSDE 2D =CSDE 2D / ln(e m+1 ) (18) CSDE 2D The larger the value, the more random and complex the distribution within the parameter spectrum; CSDE 2D The smaller the value, the more regular the distribution within the parameter spectrum and the less affected by noise; when m=2, ε=10, μ=1, the complexity within the four-parameter spectrum can be accurately quantified and the computation time is short. S3 specifically includes: The steps of the RSSD method are as follows: (1) Obtaining local coefficients Given a threshold mean(mean(PT) i (τ,s))), further reduce the number of pseudo-local minima caused by noise; PT i (τ, s) is divided into several incoherent regions pt, as shown in the image. i (τ, s), in pt i Find the local maximum point max(pt) along s within (τ,s). i (τ,s)) uses spline interpolation to fit the local coefficients to the maximum points. (2) Reconstructed component r i (t); will Perform continuous wavelet inverse transform to reconstruct the component r. i (t) While ensuring reconstruction accuracy, the algorithm time is reduced; for the reconstructed component r i (t), the reconstruction formula is as follows: in, It is the Fourier transform of ψ(t). Indicates taking the real part; (3) Sparse component amplitude optimization, which only takes points on the ridge, will lose most of the energy; therefore, let res1(t) = x(t) to construct the following optimization problem P1: P1 Minimize In the optimization problem P1, the optimization parameters are the magnitudes of each component, η||D s (res1(t)-r i (t))|| 2 Used to regularize the optimization objective function, D is a differential operator whose weight η is set to 1; Construct the following optimization problem P2, where the optimization parameter is the magnitude coefficient μ: P2 Minimize||res1(t)-μr i (t)|| 2 (23) The purpose of this step is to obtain r i The optimal amplitude of (t) is further ensured to guarantee the sparsity of the decomposition results; (4) Set local coefficients Length threshold, If the length is too short, terminate the iteration and complete the entire decomposition process.

2. The rolling bearing fault detection system based on Riesz map sparse decomposition as described in claim 1, characterized in that, The time-frequency analysis module further includes: The Riesz transform unit acquires the amplitude, frequency, phase, and direction information of the signal in the time-frequency domain; The Log-Gabor filter bank is used to filter signals in a four-parameter spectrum after Riesz transform.

3. The rolling bearing fault detection system based on Riesz map sparse decomposition as described in claim 1, characterized in that, The entropy calculation module includes: The cosine similarity calculation unit is used to calculate the cosine similarity between adjacent blocks based on the four-parameter spectrum block matrix obtained from the time-frequency analysis module. The symbol sequence generation unit performs sequence segmentation and symbolization of the signal based on symbol dynamic entropy, generates state patterns of symbol arrangement, and calculates state transition probabilities.

4. The rolling bearing fault detection system based on Riesz map sparse decomposition as described in claim 1, characterized in that, The sparse decomposition module is implemented through the following steps: The signal is reconstructed using the optimal parameter spectrum; The signal components are reconstructed using the inverse continuous wavelet transform method; Sparsity optimization is performed on the component amplitudes to construct the sparsest representation of the component amplitudes in the optimization problem, thus ensuring the sparsity of the decomposition results.

5. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of a rolling bearing fault detection method based on Riesz graph sparse decomposition for a rolling bearing fault detection system based on Riesz graph sparse decomposition as described in any one of claims 1-4.

6. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the rolling bearing fault detection system based on Riesz graph sparse decomposition as described in claim 1.

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