Fault diagnosis method for non-stationary signal and storage medium

Abstract

The invention provides a non-stationary signal fault diagnosis method and a storage medium, and the method comprises the steps: carrying out the discretization of a low-pass fractional order filter, and obtaining a digital filter; optimizing the parameters of the digital filter according to the objective function by using a QPSO algorithm; filtering the non-stationary signal by using the optimized digital filter; extracting characteristic parameters from the filtered non-stationary signals; and performing fault type identification by using a fault diagnosis model based on the characteristic parameters. According to the method, discretization processing is carried out on the low-pass fractional order filter, and parameters of the low-pass fractional order filter are optimized, so that the filtering effect on non-stationary signals is remarkably improved. By means of the optimized digital filter, fault features, such as amplitude entropy, fractional order spectrum kurtosis and dominant frequency components, in non-stationary signals can be extracted more accurately. The support vector machine is adopted as a fault diagnosis model, and the radial basis function is selected as a kernel function, so that the accuracy and robustness of fault recognition are further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial equipment fault diagnosis, and in particular to a fault diagnosis method and storage medium for non-stationary signals. Background Art

[0002] Currently, common methods in the field of fault diagnosis include traditional Fourier transforms (FFTs), wavelet transforms, and standard particle swarm optimization (PSO)-based filter design. Traditional Fourier transforms are only suitable for analyzing stationary signals and lack sufficient time-frequency resolution for non-stationary signals (such as transient shocks and time-varying vibrations). While wavelet transforms can partially address time-frequency analysis, the selection of basis functions relies on empirical experience and is computationally complex. Furthermore, standard PSO algorithms are prone to falling into local optima during filter parameter optimization, limiting the accuracy of fault feature extraction.

[0003] The traditional Fourier transform in existing technologies cannot effectively process non-stationary signals, resulting in incomplete fault feature extraction; the standard particle swarm optimization algorithm converges slowly and is prone to falling into local optimality, affecting the optimization effect of filter parameters; the existing methods are insufficiently adaptable to fractional-order signals (such as fractional-order vibration and electromagnetic noise) under complex working conditions, and the diagnostic accuracy is low. Summary of the Invention

[0004] The present invention aims to at least solve the technical problem of low fault diagnosis accuracy in the prior art, and particularly innovatively proposes a fault diagnosis method and storage medium for non-stationary signals.

[0005] In order to achieve the above-mentioned object of the present invention, the present invention provides a fault diagnosis method for a non-stationary signal, the method comprising: S1, discretize the low-pass fractional-order filter to obtain a digital filter; S2, using the QPSO algorithm to optimize the parameters of the digital filter according to the objective function; S3, filtering the non-stationary signal using the optimized digital filter; S4, extracting characteristic parameters from the filtered non-stationary signal; S5. Identify the fault type using the fault diagnosis model based on the characteristic parameters.

[0006] In another aspect, the present invention further provides a computer-readable storage medium comprising: a memory having a computer program stored thereon; A processor is used to execute the program in the memory to implement the fault diagnosis method for a non-stationary signal.

[0007] Beneficial effects of the present invention: The present invention significantly improves the filtering effect on non-stationary signals by discretizing the low-pass fractional-order filter and optimizing its parameters. By using the optimized digital filter, fault features in non-stationary signals, such as amplitude entropy, fractional-order spectral kurtosis and dominant frequency components, can be extracted more accurately. These characteristic parameters provide a reliable basis for subsequent fault diagnosis. In addition, the present invention adopts a support vector machine as a fault diagnosis model and selects a radial basis function as a kernel function, which further improves the accuracy and robustness of fault identification. The present invention not only solves the problem of low fault diagnosis accuracy in the prior art, but also improves the adaptability and diagnostic efficiency to non-stationary signals.

[0008] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which: Figure 1 It is a flow chart of a fault diagnosis method for non-stationary signals of the present invention; Figure 2 It is a statistical diagram of the filtering situation in the X direction on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 3 It is a statistical diagram of the filtering situation in the Y direction on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 4 It is a statistical diagram of the filtering situation in the Z direction on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 5 It is a statistical diagram of the filtering situation in the X direction on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 6 It is a statistical diagram of the filtering situation in the Y direction on the operating side of a fault diagnosis method for non-stationary signals of the present invention; Figure 7 It is a statistical diagram of the filtering situation in the Z direction on the operating side of a fault diagnosis method for non-stationary signals of the present invention; Figure 8 It is a statistical diagram of the filtering situation in the X direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 9 It is a statistical diagram of the filtering situation in the Y direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 10 It is a statistical diagram of the filtering situation in the Z direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 11 It is a statistical diagram of the filtering situation in the X direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 12 It is a statistical diagram of the filtering situation in the Y direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 13 It is a statistical diagram of the filtering situation in the Z direction on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 14 It is a recursive image schematic diagram of a fault diagnosis method for non-stationary signals of the present invention; Figure 15 Schematic diagram of a recursive image in the X direction on the operating axis side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 16 It is a schematic diagram of a recursive image in the Y direction on the operating axis side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 17 It is a schematic diagram of a recursive image in the Z direction on the operating axis side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 18 It is a schematic diagram of a recursive image in the X direction on the operating axis side of a fault diagnosis method for non-stationary signals of the present invention; Figure 19 It is a schematic diagram of a recursive image in the Y direction on the operating axis side of a fault diagnosis method for non-stationary signals of the present invention; Figure 20 It is a schematic diagram of a recursive image in the Z direction on the operating axis side of a fault diagnosis method for non-stationary signals of the present invention; Figure 21 It is a schematic diagram of a recursive image in the X direction on the transmission shaft side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 22 It is a schematic diagram of a recursive image in the Y direction on the transmission shaft side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 23 It is a schematic diagram of a recursive image in the Z direction on the transmission shaft side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 24 It is a schematic diagram of a recursive image in the X direction on the transmission shaft side of a fault diagnosis method for non-stationary signals of the present invention; Figure 25 It is a recursive image of the Y direction on the transmission shaft side of a non-stationary signal fault diagnosis method of the present invention; Figure 26 It is a schematic diagram of a recursive image in the Z direction on the transmission shaft side of a fault diagnosis method for non-stationary signals of the present invention; Figure 27It is a schematic diagram of an X-recursion graph analysis on the operating side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 28 It is a schematic diagram of a Y-recursion graph analysis on the operating side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 29 It is a schematic diagram of Z recursion graph analysis on the operating side of a fault diagnosis method for non-stationary signals of the present invention; Figure 30 It is a schematic diagram of YZ joint recursive graph analysis on the operating side of a fault diagnosis method for non-stationary signals of the present invention; Figure 31 It is a schematic diagram of an XZ joint recursive graph analysis on the operating side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 32 It is a schematic diagram of an XY joint recursive graph analysis on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 33 It is a schematic diagram of an XYZ joint recursive graph analysis on the operating side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 34 This is a visualization diagram of an X-bearing fault on the operating side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 35 This is a visualization diagram of a Y-bearing fault on the operating side of a non-stationary signal fault diagnosis method of the present invention; Figure 36 It is a visualization diagram of a Z bearing fault on the operating side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 37 This is a visualization diagram of a fault on the operating side lower X bearing of a non-stationary signal fault diagnosis method of the present invention; Figure 38 This is a visualization diagram of a fault on the lower Y bearing on the operating side of a non-stationary signal fault diagnosis method of the present invention; Figure 39 This is a visualization diagram of a fault on the operating side lower Z bearing of a non-stationary signal fault diagnosis method of the present invention; Figure 40 This is a visualization diagram of an X-bearing fault on the transmission side of a fault diagnosis method for a non-stationary signal according to the present invention; Figure 41 This is a visualization diagram of a Y-bearing fault on the transmission side of a fault diagnosis method for a non-stationary signal of the present invention; Figure 42 This is a visualization diagram of a transmission side lower Z bearing fault in a non-stationary signal fault diagnosis method of the present invention; Figure 43This is a visualization diagram of a transmission side lower X-bearing fault in a non-stationary signal fault diagnosis method of the present invention; Figure 44 This is a visualization diagram of a fault on the transmission side lower Y bearing of a non-stationary signal fault diagnosis method of the present invention; Figure 45 It is a visualization diagram of the transmission side lower Z bearing fault of a non-stationary signal fault diagnosis method of the present invention. DETAILED DESCRIPTION

[0010] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0011] Example 1 like Figure 1 As shown, a fault diagnosis method for a non-stationary signal, the method comprising: S1, discretize the low-pass fractional-order filter to obtain a digital filter; It should be noted that in step S1, when discretizing the low-pass fractional-order filter, various numerical methods, such as bilinear transformation method and step response invariance method, can be used to obtain the corresponding digital filter. These digital filters process non-stationary signals in the discrete time domain and can effectively extract characteristic information from the signal.

[0012] S2, using the QPSO algorithm to optimize the parameters of the digital filter according to the objective function; It should be noted that in step S2, after obtaining the digital filter, the present invention further optimizes the filter parameters. Specifically, the quantum particle swarm optimization (QPSO) algorithm can be used to optimize the filter's fractional-order parameters. By adjusting these parameters, the filter's filtering effect on non-stationary signals can be optimized, thereby more accurately extracting fault characteristics from the signal.

[0013] S3, filtering the non-stationary signal using the optimized digital filter; It should be noted that in step S3, the non-stationary signal is filtered using an optimized digital filter. The key to this step is that the optimized filter can more accurately extract key fault characteristics from the non-stationary signal. Specifically, the filtering process can be viewed as a signal transformation that removes noise and interference components while retaining fault-related information, such as amplitude entropy, fractional spectral kurtosis, and dominant frequency components. This information can reflect the operating status and health of the equipment.

[0014] S4, extracting characteristic parameters from the filtered non-stationary signal; It should be noted that in step S4, the extraction process of characteristic parameters can be achieved by a variety of methods, such as time domain analysis, frequency domain analysis, and time-frequency joint analysis. In an embodiment of the present invention, the preferred characteristic parameters include amplitude entropy, fractional spectral kurtosis, and dominant frequency component. Amplitude entropy can reflect the complexity and irregularity of the signal, fractional spectral kurtosis can highlight the impact component in the signal, and dominant frequency component reveals the main vibration characteristics of the signal. The combined use of these characteristic parameters can comprehensively and accurately describe the state of the non-stationary signal.

[0015] S5. Identify the fault type using the fault diagnosis model based on the characteristic parameters.

[0016] It should be noted that in step S5, the fault diagnosis model determines the fault type of the non-stationary signal based on the extracted feature parameters. In an embodiment of the present invention, a support vector machine (SVM) is used as the fault diagnosis model, which has excellent classification performance and generalization capabilities. The SVM constructs an optimal hyperplane to separate samples of different categories, thereby identifying the fault type. Furthermore, the SVM has strong processing capabilities for high-dimensional data and can handle nonlinear separable problems, which makes it an excellent performer in the fault diagnosis method of the present invention. In the SVM, the choice of kernel function has a significant impact on the classification results. In an embodiment of the present invention, the radial basis function (RBF) is selected as the kernel function, which can map to high-dimensional space, effectively handle nonlinear problems, and further improve the accuracy and robustness of fault identification. Through SVM classification, the fault type of the non-stationary signal can be accurately identified.

[0017] As an optional embodiment of the present invention, optionally, the differential equation of the digital filter is expressed as: in, express The output value of the digital filter at the moment, represents the upper limit of the summation operation, Indicates the The fractional order coefficient of the medium, express The input value of the digital filter at the moment, Indicates the The fractional order coefficient of the medium, express The input value of the digital filter at this moment.

[0018] As an optional embodiment of the present invention, optionally, the QPSO algorithm includes: S201, Random Generation particles, each particle position ,speed ; It should be noted that in step S201, the initial stage of the QPSO algorithm simulates candidate solutions in the search space by randomly generating a certain number of particles. Each particle has a position vector and a velocity vector, representing its current position in the search space and its direction and velocity, respectively. The positions and velocities of these particles are continuously updated as the algorithm iterates to find the optimal solution.

[0019] S202, based on the calculation of particle potential well center Update the particle position; It should be noted that in step S202, the QPSO algorithm guides the particles toward the global optimal solution by calculating the potential well center of each particle. The potential well center is typically calculated based on the historical optimal positions of all particles and the current global optimal position. By continuously updating the particle position and velocity, the particles gradually converge to the potential well center, thereby finding the optimal digital filter parameters.

[0020] S203, performing adaptability evaluation on the particle position after each update to obtain the fitness value of each particle; It should be noted that in step S203, the purpose of the adaptability assessment is to measure the degree of quality of the digital filter parameters represented by each particle in solving the fault diagnosis problem. This is usually achieved by applying the digital filter parameters represented by the particle to the filtering and feature extraction process of the non-stationary signal, and using the fault diagnosis model to classify and identify the extracted feature parameters. Based on the accuracy of the classification and identification or other relevant performance indicators, the fitness value of each particle can be calculated. The higher the fitness value, the better the digital filter parameters represented by the particle perform in solving the fault diagnosis problem.

[0021] S204: Iteratively update the particle position based on the fitness value until the maximum number of iterations is reached or the objective function converges.

[0022] It should be noted that, in step S204, the iterative update process is carried out by comparing the current fitness value of each particle with its historical optimal fitness value and the global optimal fitness value. If the current fitness value is better than the historical optimal fitness value, the historical optimal position of the particle is updated. At the same time, based on the historical optimal positions and the current global optimal position of all particles, the new potential well center is calculated, and the position and velocity of the particle are updated accordingly. This process will be repeated until the preset maximum number of iterations is reached or the objective function converges, that is, the optimization process of the digital filter parameters ends. At this point, the optimal digital filter parameters obtained will be used for subsequent filtering and fault diagnosis processes to improve the accuracy and efficiency of fault diagnosis.

[0023] As an optional embodiment of the present invention, optionally, the calculation of the particle potential well center The calculation expression is: in, represents the individual optimality, Indicates the global optimum.

[0024] As an optional embodiment of the present invention, optionally, the expression of the updated particle position is: in, express The particle position at time t, represents the contraction-expansion coefficient, express The particle position at time t, Represents a random number that follows a uniform distribution in the interval (0,1).

[0025] As an optional embodiment of the present invention, optionally, the expression for filtering the non-stationary signal using the optimized digital filter is: in, express The non-stationary signal after time filtering, represents the fractional Fourier transform, represents the frequency domain response of the optimized filter, express Non-stationary signal at any moment.

[0026] As an optional embodiment of the present invention, optionally, the fault diagnosis model uses a support vector machine to identify the fault type, and the kernel function in the support vector machine selects a radial basis function.

[0027] It should be noted that the radial basis function is chosen as the kernel function in the support vector machine (SVM) primarily because it can map input data into a high-dimensional feature space, making problems that are originally linearly inseparable linearly separable. In the fault diagnosis method of the present invention, by selecting the radial basis function as the kernel function, the complex features in non-stationary signals can be effectively processed, improving the accuracy and robustness of fault identification. Furthermore, parameters of the radial basis function, such as the width coefficient, can also be optimized to further improve the classification performance of the SVM.

[0028] As an optional embodiment of the present invention, optionally, the expression of the radial basis function is: in, Represents the radial basis function (RBF) at the sample point and The function value at Indicates the feature vectors, Indicates the feature vectors, represents the exponential function, represents the Euclidean norm.

[0029] As an optional embodiment of the present invention, optionally, the characteristic parameters include amplitude entropy, fractional-order spectral kurtosis and dominant frequency components.

[0030] The technical solution advantages of the present invention are: (1) Fractional-order flexibility: by optimizing and , the filter can adaptively match the non-stationary signal characteristics under different working conditions; (2) Global convergence: The QPSO algorithm avoids falling into local optimality and ensures high-precision optimization of filter parameters; (3) End-to-end diagnosis: Forming a closed loop from signal processing to fault classification to improve system reliability and real-time performance.

[0031] The key points of the present invention are: (1) Improvement of quantum particle swarm optimization algorithm: introducing quantum behavior mechanism, describing particle state through wave function, expanding search space and avoiding local optimum, significantly improving the optimization efficiency of fractional filter parameters; (2) Application of fractional Fourier transform: By adjusting the fractional order, the time-frequency characteristics of the signal can be adaptively matched to enhance the time-frequency resolution of non-stationary signals; (3) Collaborative optimization mechanism: The combination of QPSO and FRFT realizes the closed-loop feedback of signal analysis and parameter optimization, ensuring the accuracy and robustness of fault feature extraction.

[0032] The fault diagnosis accuracy of the present invention is improved by 20% to 30%, and it is particularly suitable for early fault detection in complex mechanical systems such as gearboxes and bearings. The computational efficiency is improved by 40% compared with the traditional PSO algorithm, and the optimized fractional-order filter parameters converge faster. The ability to suppress fractional-order noise (such as 1 / f noise) is significantly enhanced, and the signal-to-noise ratio (SNR) is improved by more than 15dB.

[0033] like Figures 2 to 13 As shown in the figure, for the data collected in the factory, the signal is filtered using a fractional-order filter and the quantum particle swarm optimization algorithm to select appropriate parameters. The three figures respectively reflect the filtering conditions in the X, Y, and Z directions on the operating side. It can be clearly seen that the original signal is messy, and the fault characteristic signal is prominent after filtering.

[0034] This method is used to process the original signals of the corresponding X, Y, Z directions on the operating side, X, Y, Z on the transmission side, and X, Y, Z on the transmission side, which can make the original signals more stable. The corresponding fault characteristic signals are observed and no prominent fault characteristic signals are found. It is known that no fault occurs in the X, Y, Z directions on the operating side, X, Y, Z on the transmission side, and X, Y, Z on the transmission side.

[0035] Recursive plots are used to illustrate the similarity of the time series structure of signals collected from different locations on the rolling mill (in the X, Y, and Z directions, above and below the operating shaft and above and below the drive shaft). By comparing the signal states at different time points, the repetitive and periodic characteristics of the signals are graphically displayed.

[0036] The Markov transition field image is a further development of the recursive image. It is primarily used to reveal the transition probabilities and dynamic patterns between mill signal states. By quantifying the frequency and likelihood of transitions between different states, it helps us understand the state evolution trends during mill operation.

[0037] The differences in color and pattern in these images reflect the state transition characteristics of signals in different parts and directions. Areas with darker colors or more complex patterns may indicate that the transitions between corresponding states are more frequent or have a higher probability, which may be related to factors such as the operating mode of the rolling mill in that part, load changes, or mechanical structure characteristics. For example, in a certain direction, if there is an obvious dark block area in the image, it may mean that the transitions between certain states of the rolling mill signal in that direction are more concentrated, which may be due to the inherent behavior patterns of the mechanical components in that direction under specific operating conditions. By comparing the Markov transition field images of different parts and directions, the differences between various parts during the operation of the rolling mill and potential abnormal state transition patterns can be discovered, providing clues for fault diagnosis and performance optimization.

[0038] The Gram Matrix (GAF) transform image converts the mill signal from the time domain to a new feature space, presenting the signal's intrinsic structure and correlation information in the form of a two-dimensional matrix. This transformation helps to more intuitively observe the relationship between the signal at different time points and extract the signal's global characteristics.

[0039] like Figure 14 As shown in the figure, the changes in color and texture in the image reflect the characteristic distribution of the signal after the GAF transformation. An image with uniform color and regular texture may indicate that the signals in the corresponding area have good temporal correlation and stability. For example, in a normally operating rolling mill, the signals in certain directions may show such regular image characteristics after transformation, indicating that the operation in that direction is relatively stable and the relationship between the signals is relatively consistent.

[0040] like Figure 15 As shown, images with significant color variations or cluttered textures may indicate weak temporal signal correlation or abnormal fluctuations and variations. For example, when a part of a rolling mill experiences a fault or unstable operation, the GAF transform image in the corresponding direction may exhibit varying color depths and irregular textures. This helps us quickly locate the problematic area and direction for further in-depth analysis and diagnosis.

[0041] like Figure 16 As shown, the image exhibits a relatively uniform blue color, with dense, relatively regular distribution of lines. This indicates that the original normal mill signals exhibit strong similarity and regularity. This means that during normal mill operation, the signal changes over time are relatively stable, without significant abnormal fluctuations or sudden changes. For example, key mill parameters such as rolling speed and rolling force likely vary smoothly within a set range, with various components working well together and unaffected by external interference or internal faults, resulting in a high degree of consistency in the signal state at different time points.

[0042] like Figure 17 As shown, in the X-direction on the operating axis side, the blue areas in the image are relatively concentrated, and the lines show a certain regularity. This indicates that the signals in the X-direction on the operating axis side have high similarity within certain time periods, possibly reflecting the periodic characteristics of the rolling mill operation in this direction. For example, the movement of the operating axis in the X-direction may be subject to certain periodic forces, such as the meshing period of the transmission gears, causing the signals to exhibit similar states within these cycles. However, there are also some green areas, indicating that the signal has some degree of variation at certain moments, possibly due to slight fluctuations in the incoming material thickness or other transient interference factors, but overall it remains relatively stable.

[0043] like Figure 16As shown, in the Y direction on the operating axis side, the blue and green areas in the image are interlaced, and the color distribution is relatively uneven. This suggests that the signal in the Y direction on the operating axis side exhibits complex temporal variations, with periods of relative stability (blue areas) and moments of significant variation (green areas). This direction may be affected by a combination of factors, such as vertical vibration of the operating axis and deformation of the mill stand. These factors lead to significant variations in signal similarity at different time points. This may require further attention to the mill's operating status in this direction to identify potential issues or areas requiring adjustment.

[0044] like Figure 18 As shown, in the Z direction on the operating axis side, the image shows a relatively large green area and a rather chaotic color distribution. This indicates that the time series of signals in the Z direction on the operating axis side have low similarity, exhibiting significant variability and uncertainty. Frequent and abnormal signal fluctuations may be caused by unstable mechanical components in this direction, such as inaccurate positioning of the operating axis in the Z direction, worn or loose bearings, etc. This condition may affect the mill's machining accuracy and product quality, and requires prompt inspection and maintenance.

[0045] like Figure 18 、 19 As shown in Figure 20, the images in the X, Y, and Z directions below the operating shaft are relatively uniform in color, primarily green, but with varying shades of color and line density. Overall, the signals below the operating shaft vary relatively smoothly over time, but some differences still exist. For example, the X direction below the operating shaft may be less affected by ground vibration or other external factors, resulting in a relatively stable signal. The Y direction below the operating shaft may have a different signal variation pattern due to its mechanical connection or force compared to the Y direction above the operating shaft. The Z direction below the operating shaft may be affected by the mill's bottom support structure, resulting in a signal with specific variation characteristics. These differences require further analysis based on the specific structure and operating conditions of the mill to determine if they are normal.

[0046] like Figure 21 、 22As shown in Figure 23, the distribution of blue and green areas in the three images of the drive shaft in the X, Y, and Z directions varies. The relatively concentrated blue areas in the X-direction image on the drive shaft side may indicate that the drive shaft's movement in this direction is relatively regular, cooperating well with other components of the transmission system, and the signals have high similarity in the time series. The more even distribution of colors in the Y-direction image on the drive shaft side may indicate that the signal in this direction is affected by a combination of factors, with relatively stable changes but no obvious periodic characteristics. The preponderance of green areas in the Z-direction image on the drive shaft side may indicate that there are some unstable factors in the drive shaft's operation in this direction, such as shaft imbalance or loose couplings, which lead to significant signal variations and require further inspection and analysis.

[0047] like Figure 24 、 25 As shown in Figure 26, the images in the X, Y, and Z directions of the lower drive shaft are primarily green, with a relatively uniform color distribution and fine lines. This indicates that the signals at the lower drive shaft exhibit relatively little temporal variation and are operating in a relatively stable manner. This may be due to the relatively low external interference experienced at the lower drive shaft, or to the rational design and installation of the transmission system in this area, resulting in a relatively stable signal. However, a comprehensive assessment of these areas, combined with other monitoring data and actual operating conditions, is still necessary to ensure the overall performance and reliability of the rolling mill.

[0048] Recurrence Plot (RP) is a visualization tool used to analyze the dynamic characteristics of time series, especially for revealing repetitive patterns, periodicity or chaotic behavior in nonlinear systems.

[0049] Here are its core points: 1. Basic Concepts Definition: A recurrence graph compares the state at each moment in a time series with the state at other moments, determining whether they are "similar" and marking them with black dots (1) or blanks (0) in a two-dimensional matrix. Its essence is the "self-repeating" nature of the system's trajectory in phase space.

[0050] Mathematical expression: recursive matrix Defined as: in, is the state vector of the time series in the phase space, is the similarity threshold, is a step function (takes 1 when the distance is less than the threshold, otherwise takes 0).

[0051] 2. Key Features and Interpretation The patterns in the recurrence graph can reflect the dynamic nature of the system: Diagonal Lines: Continuous diagonal lines indicate deterministic or periodic behavior (such as a sine wave).

[0052] Outliers: Signs of randomness or chaotic systems (such as white noise).

[0053] Vertical / horizontal lines: suggest transient mutations or stagnant states.

[0054] Block structure: piecewise stationarity, common in non-stationary systems.

[0055] 3. Application areas Fault detection: Recurrence plots of mechanical vibration signals can identify abnormal patterns (such as bearing wear).

[0056] Physiological signal analysis: Detecting pathological features in electrocardiogram (ECG) and electroencephalogram (EEG).

[0057] 4. Multivariate joint analysis For multivariable systems (xz-yz joint, xy joint, etc.), the recurrence diagram can be expanded to: Joint Recurrence Plot (JRP): It satisfies the conditions of similar states of multiple variables at the same time and is used to analyze the coupling relationship between variables.

[0058] Cross Recurrence Plot (CRP): Compare the similarities between two different time series and quantify their synchronization or causal relationship.

[0059] The original signal containing a fault in the x direction and the same fault in the y and z directions at the same time is subjected to separate recursive graph analysis and joint recursive graph analysis. The joint recursive graph analysis used here is like Figure 27 As shown, the figure is primarily dark blue, with only a few lighter blue lines. This indicates that the recursive nature of the system state in the x-direction is weak, and the similarity or reproducibility between state points is low. The lighter lines may represent occasional state similarities, but overall, the dynamic behavior in the x-direction is relatively scattered, lacking frequent state recurrence patterns. The system's evolution in this direction may be highly random or complex.

[0060] like Figure 28 As shown, the overall background is dark blue with a few sparse light-colored lines. This indicates that the recursive phenomenon of the system state in the y-direction is not strong, and the frequency of state recurrence is low. These sparse light-colored lines suggest that at certain specific moments, the system state exhibits a certain degree of similarity, but overall, the system's dynamic changes in the y-direction rarely show repetitive patterns, which may indicate a more complex and unpredictable trend.

[0061] like Figure 29 As shown, the image is primarily dark blue, with fewer light-colored lines. This reflects the limited recursiveness of the system's state in the z-direction, with a low number of similar events occurring between state points. This suggests that the system's dynamic behavior in the z-direction is relatively unstable, with difficulty exhibiting regular state recurrence. This is likely due to the influence of multiple complex factors, resulting in a relatively random state evolution.

[0062] like Figure 30 As shown, a grid-like structure composed of light-colored lines is distributed across a dark blue background. This indicates that when the Y and Z directions intersect, there is a certain degree of state recursion, but it is not very dense. This grid-like structure indicates that under certain state combinations, the system states in the Y and Z directions will show similarities, but this similarity does not occur frequently. The dynamic behavior of the system in the joint Y and Z dimensions has certain regularities, but also has certain complexity and uncertainty.

[0063] like Figure 31 As shown, light-colored lines interweave against a dark blue background. This indicates state recursion when the X and Z directions intersect. This interweaving of lines indicates that within the X and Z state space, there are specific regions where the system states repeat or are similar. However, overall, this recursive phenomenon is not dominant, indicating that the dynamic changes of the system in the X and Z joint dimensions have both certain regularities and a variety of non-recursive and complex variations.

[0064] like Figure 32 As shown, the image is primarily dark blue, with sparse light-colored lines forming a pattern. This indicates that the recursive nature of the system state in the XY cross-direction is weak, and state recurrence is relatively rare. The sparse lines indicate that in the XY state space, system states exhibit similarity only in a few cases. The dynamic evolution of the system in this joint dimension is relatively complex, and the correlation and recurrence patterns between states are difficult to capture.

[0065] like Figure 33 As shown, the overall color scheme is dark blue, with some light-colored lines scattered throughout. This indicates that when the three dimensions (X, Y, and Z) are combined, the recurrence of the system state is not significant. Although a small number of light-colored lines suggest some similar states, overall, the system's state recurrence in the three-dimensional joint space is relatively rare. This indicates that the system's dynamic behavior under the combined effects of the three dimensions (X, Y, and Z) is extremely complex and difficult to show clear regularity.

[0066] Visual analysis of bearing faults Bearing fault visualization is a technology that uses advanced technology to process and analyze multi-source data such as vibration and temperature during bearing operation and convert them into intuitive and easy-to-understand graphics. Its implementation process usually involves first processing and analyzing the collected bearing vibration signals and other data, extracting features such as kurtosis, entropy, and fractal values, and then using deep learning models such as WDCNN to learn and classify fault features. Finally, through dimensionality reduction algorithms such as t-SNE and PCA, the high-dimensional feature data is mapped to two-dimensional or three-dimensional space for visualization, or with the help of model interpretation tools such as SHAP to interpret the model's prediction results, so as to intuitively present the data distribution, classification boundaries, and the contribution of each feature to the fault diagnosis results under different fault types, helping operation and maintenance personnel and researchers to understand the bearing fault situation more quickly and accurately, so that appropriate repair and maintenance measures can be taken in a timely manner to ensure the stable operation of the equipment.

[0067] like Figure 34 As shown, the overall signal is relatively stable with a relatively small amplitude, but significant spikes appear at a few locations, such as a large positive spike near 800. This may indicate a localized impact fault in the bearing, such as localized damage to the ball or raceway, or surface fatigue spalling. It may also be caused by a sudden external impact force on the bearing during operation.

[0068] like Figure 35 As shown in the figure, similar to the X-direction, the overall signal is relatively stable, but a significant positive peak appears near 800, with some fluctuations around 800. This peak also indicates a possible localized impact fault in the bearing, such as a localized failure of the raceway or cage. Furthermore, continuous fluctuations may indicate a certain degree of cyclical wear or misalignment in the bearing.

[0069] like Figure 36 As shown, the signal fluctuation amplitude is slightly larger than in the X and Y directions, with some spikes and slight fluctuations in certain areas. This may indicate slight raceway wear or ball damage, causing the signal spikes and fluctuations. Alternatively, it could be due to a certain degree of imbalance in the bearing installation or uneven axial load distribution.

[0070] like Figure 37 As shown, the fluctuation amplitude is large, especially in the negative direction, with obvious periodic fluctuations, and the amplitude of the fluctuation changes relatively regularly. This may indicate that the bearing has severe wear or misalignment problems. Periodic fluctuations suggest that there may be periodic damage to the rolling elements or raceways, such as ball wear and uneven raceway wear.

[0071] like Figure 38As shown, similar to the X-direction, the fluctuation amplitude is large, with obvious periodic fluctuations and sharp peaks at certain locations. This may indicate severe damage to the raceway or balls, such as severe raceway wear or ball surface spalling, resulting in significant fluctuations and spikes in the signal. Alternatively, it may be due to the bearing being subjected to large alternating loads, exacerbating wear and fatigue damage.

[0072] like Figure 39 As shown, the fluctuation amplitude is large, with obvious peaks and periodic fluctuations, and the fluctuation amplitude changes are relatively complex. This may indicate that the bearing has severe wear, fatigue spalling, or impact damage. The appearance of peaks indicates localized impact failure, while the periodic fluctuations further confirm the presence of periodic damage to the rolling elements or raceways.

[0073] like Figure 40 As shown, the fluctuation amplitude is large, with obvious peaks and dramatic fluctuations, and the overall fluctuation range of the signal is wide. This may indicate severe wear, impact damage, or quality defects on the drive-side bearing, causing the severe fluctuations and spikes in the signal. For example, severe wear of the balls or raceways, deformation or damage to the cage, etc., can cause increased impact vibration during bearing operation.

[0074] like Figure 41 As shown, the fluctuation amplitude is large, with obvious peaks and dramatic fluctuations, similar to the signal characteristics in the X direction. This may indicate that the transmission-side bearing has severe wear, impact damage, or quality defects, such as severe raceway wear, ball cracking, and loose cage, resulting in strong vibration and impact signals during operation.

[0075] like Figure 42 As shown, the fluctuation amplitude is large, with obvious peaks and dramatic fluctuations. The fluctuation shape is complex and has a certain degree of irregularity. This may indicate a serious combined fault on the transmission side bearing, such as raceway wear, ball damage, cage damage, and excessive axial clearance, resulting in complex vibration signals during bearing operation.

[0076] like Figure 43 As shown, the fluctuation amplitude is large, with obvious peaks and dramatic fluctuations, and the fluctuation amplitude changes frequently. This may indicate that the bearing in the lower X direction on the transmission side has severe wear, impact damage, or quality defects, such as severe ball wear, cracks or spalling in the raceway, resulting in strong and unstable vibration signals during bearing operation.

[0077] like Figure 44As shown, the fluctuation amplitude is large, with obvious peaks and dramatic fluctuations, similar to the signal in the X direction on the drive side. This indicates that the bearing may have suffered severe damage, such as severe wear or spalling of the raceway, cracked rolling elements, or deformed cages. Such damage can cause severe vibration and impact during bearing operation, resulting in large fluctuations and spikes.

[0078] like Figure 45 As shown, the fluctuation amplitude is large, with obvious peaks and violent fluctuations, and the fluctuation shape is complex and irregular. This may indicate that the bearing has a serious combined fault, such as raceway wear, ball damage, cage damage, and excessive axial clearance. The simultaneous existence of multiple faults results in a complex and strong vibration signal during bearing operation.

[0079] Example 2 A computer-readable storage medium comprising: a memory having a computer program stored thereon; A processor is used to execute the program in the memory to implement the fault diagnosis method for a non-stationary signal in Example 1.

[0080] It should be noted that the electronic device according to the embodiment of the present disclosure includes a processor and a memory for storing processor executable instructions, wherein the processor is configured to implement any of the above-mentioned methods for diagnosing a fault with a non-stationary signal when executing the executable instructions.

[0081] It should be noted that the number of processors can be one or more. Furthermore, the electronic device in the embodiments of the present disclosure may also include an input device and an output device. The processor, memory, input device, and output device may be connected via a bus or other means, which are not specifically limited here.

[0082] Memory, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and various modules, such as the program or module corresponding to the fault diagnosis method for non-stationary signals in the embodiments of the present disclosure. The processor executes the software programs or modules stored in the memory to perform various functional applications and data processing of the electronic device.

[0083] The input device can be used to receive input numbers or signals. The signals can be key signals related to user settings and function control of the device / terminal / server. The output device can include a display device such as a display screen.

[0084] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and alterations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A fault diagnosis method for non-stationary signals, characterized in that: The method comprises: S1, discretize the low-pass fractional-order filter to obtain a digital filter; S2, using the QPSO algorithm to optimize the parameters of the digital filter according to the objective function; S3, filtering the non-stationary signal using the optimized digital filter; S4, extracting characteristic parameters from the filtered non-stationary signal; S5. Identify the fault type using the fault diagnosis model based on the characteristic parameters.

2. The fault diagnosis method for non-stationary signals according to claim 1, wherein: The differential equation of the digital filter is expressed as: in, express The output value of the digital filter at the moment, represents the upper limit of the summation operation, Indicates the The fractional order coefficient of the medium, express The input value of the digital filter at the moment, Indicates the The fractional order coefficient of the medium, express The input value of the digital filter at this moment.

3. The fault diagnosis method for non-stationary signals according to claim 2, wherein: The QPSO algorithm includes: S201, Random Generation particles, each particle position ,speed ; S202, based on the calculation of particle potential well center Update the particle position; S203, performing adaptability evaluation on the particle position after each update to obtain the fitness value of each particle; S204: Iteratively update the particle position based on the fitness value until the maximum number of iterations is reached or the objective function converges.

4. The fault diagnosis method for non-stationary signals according to claim 3, wherein: The calculated particle potential well center The calculation expression is: in, represents the individual optimality, Indicates the global optimum.

5. The fault diagnosis method for non-stationary signals according to claim 3, wherein: The expression for the updated particle position is: in, express The particle position at time t, represents the contraction-expansion coefficient, express The particle position at time t, Represents a random number that follows a uniform distribution in the interval (0,1).

6. The fault diagnosis method for non-stationary signals according to claim 2, wherein: The expression for filtering non-stationary signals using the optimized digital filter is: in, express The non-stationary signal after time filtering, represents the fractional Fourier transform, represents the frequency domain response of the optimized filter, express Non-stationary signal at any moment.

7. The fault diagnosis method for non-stationary signals according to claim 1, wherein: The fault diagnosis model uses a support vector machine to identify the fault type, and the kernel function in the support vector machine selects a radial basis function.

8. The fault diagnosis method for non-stationary signals according to claim 7, wherein: The expression of the radial basis function is: in, Represents the radial basis function (RBF) at the sample point and The function value at Indicates the feature vectors, Indicates the feature vectors, represents the exponential function, represents the Euclidean norm.

9. The method for diagnosing a non-stationary signal fault according to claim 1, wherein: The characteristic parameters include amplitude entropy, fractional spectral kurtosis and dominant frequency components.

10. A computer-readable storage medium, characterized in that include: a memory having a computer program stored thereon; A processor, configured to execute the program in the memory to implement the fault diagnosis method for a non-stationary signal according to any one of claims 1 to 9.

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