A bearing fault signal denoising method and system fusing sliding window filtering and PO-MCEEMD

Abstract

This invention proposes a method and system for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD. The method includes: performing frame-based processing on the signal using a sliding window mechanism; then, during the MCEEMD decomposition process within each frame sub-signal, using the Parrot Optimization algorithm to adaptively optimize the NSTD and NE parameters in the MCEEMD decomposition. The invention further includes: inputting the original bearing fault signal x(n) to be processed and performing frame-based processing to obtain several frame sub-signals; using the local minimum envelope entropy as the fitness function, adaptively determining the decomposition parameters NSTD and NE in the MCEEMD method for each frame sub-signal using the PO method; performing MCEEMD decomposition on each frame sub-signal based on the optimal parameters NSTD and NE obtained in step S2 to obtain several IMF components; using cross-correlation coefficient analysis, dividing the IMF components obtained from the decomposition of each sub-signal into correlated and uncorrelated components, and further denoising the correlated components using IWTD; and reconstructing the denoised IMF components to obtain the denoised bearing fault signal d(n).

Description

Technical Field

[0001] This invention proposes a method and system for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD, which relates to the field of mechanical bearing fault diagnosis technology. Background Technology

[0002] As industrial equipment continues to develop towards higher speeds, greater precision, and greater intelligence, rolling bearings, as key fundamental components in rotating machinery such as motors, fans, and compressors, directly affect the safety and stability of the equipment. However, bearings often bear complex alternating loads in actual operating conditions, making them prone to damage or failure. Furthermore, early fault signals are characterized by nonlinearity, non-stationarity, and strong noise interference, often masked by background noise, leading to difficulties in fault feature extraction and decreased diagnostic accuracy. Therefore, effectively suppressing noise interference while maximizing the retention of useful information related to bearing faults, and developing high-fidelity noise reduction methods to extract pure fault signals, has become a critical problem urgently needing to be solved in the field of bearing fault diagnosis. This is of great significance for achieving early fault monitoring and ensuring the safe operation of equipment.

[0003] Several methods have been proposed for denoising bearing fault signals. Some employ adaptive information entropy and wavelet threshold functions: vibration signals are decomposed into multiple intrinsic mode functions (EMFs) through adaptive noise-integrated empirical mode decomposition (EMD), and noisy and noiseless components are distinguished using information entropy thresholds. The noisy components are then denoised and reconstructed using an improved wavelet threshold function, thus improving denoising accuracy and computational efficiency to some extent. However, the key parameters of this method still rely on manual setting, resulting in limited adaptability and a tendency for mode aliasing or insufficient decomposition stability in highly complex noise environments. Other methods propose adaptive bearing fault diagnosis based on multi-basis wavelet fusion. These methods achieve good denoising results under different signal-to-noise ratios by parallel decomposing multiple wavelet bases, weighted fusion, and residual iterative denoising. Fault identification is achieved by combining a convolutional-recurrent-attention network. However, these methods have complex structures, high computational costs, and are sensitive to wavelet base selection, decomposition layer number, and fusion strategy, leading to high implementation costs and insufficient real-time performance in practical engineering applications.

[0004] In summary, there is an urgent need to develop a noise reduction method that can autonomously optimize key parameters, efficiently suppress noise, and fully preserve bearing fault characteristic information under complex noise backgrounds, so as to provide more reliable signal support for subsequent fault identification. Summary of the Invention

[0005] In view of this, and to fill the gaps and deficiencies in the existing technology, this invention proposes a bearing fault signal noise reduction method and system that integrates sliding window filtering and PO-MCEEMD, to solve the problems mentioned in the background technology. This invention can effectively suppress strong noise interference while preserving, to the maximum extent possible, the key features closely related to the fault state in the vibration signal, thereby improving the reliability and accuracy of bearing fault identification.

[0006] This invention proposes a method and system for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD, including the following:

[0007] According to a first aspect of the present invention, a method for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD is proposed. The method is characterized by employing a sliding window mechanism to perform frame-based processing of the signal. Then, during the MCEEMD decomposition process within each frame sub-signal, the Parrot Optimization Algorithm is used to adaptively optimize the NSTD and NE in the MCEEMD decomposition process. Next, the IMF components are distinguished into irrelevant and relevant components using the cross-correlation coefficient method. An improved wavelet thresholding method is introduced to perform secondary denoising processing on the relevant components. Finally, the complete denoised signal is reconstructed based on the overlap-addition method to denoise the bearing fault signal.

[0008] Furthermore, the method also includes the following:

[0009] Step S1: Input the original bearing fault signal x(n) to be processed and perform frame segmentation to obtain several sub-frame signals;

[0010] Step S2: Using the local minimum envelope entropy as the fitness function, the PO method is used to adaptively determine the decomposition parameters NSTD and NE in the decomposition process of MCEEMD for each frame sub-signal;

[0011] Step S3: Based on the optimal parameters NSTD and NE obtained in step S2, perform MCEEMD decomposition on each frame sub-signal to obtain several IMF components;

[0012] Step S4: Using cross-correlation coefficient analysis, the IMF components obtained from the decomposition of each sub-signal are divided into correlated components and uncorrelated components, and IWTD is used to further denoise the correlated components.

[0013] Step S5: Reconstruct each group of IMF components after noise reduction to obtain the noise-reduced bearing fault signal d(n).

[0014] Further, step S1 includes the following:

[0015] In step S1, the bearing fault signal is processed by frame segmentation using an overlapping sliding window algorithm. This includes dividing the non-stationary long signal into short time frames to capture the time-varying features of the fault; then, the complex decomposition and parameter optimization are confined to local frames to achieve adaptive adjustment of differentiated parameters at different time periods to cope with changes in noise level or impact intensity; finally, the inter-frame overlap and window function are combined to suppress boundary effects and mode mixing, ensuring the continuity of the reconstructed signal and achieving a balance between overall noise reduction and local feature preservation.

[0016] Further, step S2 includes the following:

[0017] Step S21: Initialize the PO population. Let the population size be N and the maximum number of iterations be Maxiter. According to the following formula, randomly generate the parrot individual at the i-th position in the j-th dimension. ;

[0018] ;

[0019] Where rand represents a random number between 0 and 1; UB is defined as the upper boundary; LB is defined as the lower boundary;

[0020] Step S22: Perform envelope demodulation on each IMF component obtained from MCEEMD decomposition to obtain the corresponding envelope signal; after normalizing these envelope signals, calculate their envelope entropy values, and use the minimum envelope entropy as the fitness function to calculate the fitness value of each individual at the current position; where the envelope entropy... The specific definition is:

[0021] ;

[0022] ;

[0023] in, The signal envelope is obtained after Hilbert transform; N represents the total number of sampling points; j is the position number of the sampling point. yes The normalized form;

[0024] And it satisfies: , ;

[0025] Step S23: Define the behavior strategy selection, including: randomly generating a probability value P∈[0,1] for each individual, and selecting one of the following four behaviors according to a preset threshold: foraging behavior; staying behavior; communication behavior; fear of strangers behavior.

[0026] Furthermore, step S2 also includes the following:

[0027] Step S24: Update the position according to the four behaviors of PO, including the following:

[0028] Step S241: Foraging behavior includes global exploration and Levi's flight. Position updates are performed for foraging behavior, where positional movement follows the equation below:

[0029] ;

[0030] In the formula, Indicates the current position; Indicates the location of subsequent updates; Represents the average position within the current group; This represents the Levy distribution, which is used to describe the flight of parrots;

[0031] This represents the position found so far from initialization; t represents the current iteration number. This indicates that the movement is based on the individual's position relative to its owner.

[0032] This indicates that the location of the entire group is being observed to further determine the direction of the food.

[0033] Step S242: Dwelling behavior includes local development and random dwelling. Updating the location of dwelling behavior includes the following:

[0034] ;

[0035] in A vector of all ones representing dimension dim; It indicates flying towards the master, and This refers to the process of randomly stopping at a part of the host's body;

[0036] Step S243: Communication behaviors include social learning or random fly-out. The location of these behaviors is updated, including the following: It is assumed that social learning and random fly-out occur with equal probability, and the average location of the current population is used to represent the population center; this process can be represented as:

[0037] ;

[0038] in, This describes the process of an individual joining a flock of parrots;

[0039] in This indicates the process by which an individual flies away immediately after communicating;

[0040] Step S244: Update the location of the fear of strangers behavior, including the following:

[0041] Fear of strangers includes moving closer to the optimal solution and away from unknown areas, as shown below:

[0042] ;

[0043] in, Showing the process of flying to the owner;

[0044] It shows the process of getting away from strangers;

[0045] Step S25: Boundary control and fitness update, including constraining individuals that exceed the boundary after each iteration's position update; performing MCEEMD decomposition on the updated individual positions containing (NSTD, NE) and calculating the corresponding fitness values. ;

[0046] Step S26: Output the optimal solution, including repeating steps S23-S25 until the current iteration number reaches the preset maximum iteration number, at which point the algorithm terminates and outputs the optimal parrot individual position, thereby obtaining the optimal MCEEMD decomposition parameters NSTD and NE.

[0047] Further, step S3 includes the following:

[0048] Step S31: Add paired complementary white noise with an amplitude of NSTD to each frame sub-signal to obtain two sets of noisy signals;

[0049] Step S32: Perform EMD decomposition on each group of noisy signals to generate two corresponding IMF components; then average the IMF components with matching orders in these two groups.

[0050] Step S33: Repeat the above operation process from S31 to S32 until the preset optimal number of noise additions NE is reached;

[0051] Step S34: Perform median operation on all IMF components obtained through the above decomposition process, and output the operation result as the final IMF component.

[0052] Further, step S4 includes the following:

[0053] Step S41: After the sub-signals are decomposed, calculate each... cross-correlation coefficient , , ..., The cross-correlation coefficients The calculation formula is:

[0054] ;

[0055] in, This indicates the signal that has been decomposed; It is the IMF component obtained from signal decomposition; and These are the average values ​​of the decomposed signal and the nth IMF component, respectively.

[0056] Step S42: Based on the cross-correlation coefficient threshold, filter the IMF components and distinguish them into valid and invalid components; the threshold is calculated as follows:

[0057] ;

[0058] in, Take the maximum cross-correlation coefficient among all IMF components;

[0059] Step S43: Distinguish between relevant IMF components and irrelevant IMF components according to the following formula:

[0060] ;

[0061] Step S44: Establish an improved wavelet threshold function to perform wavelet threshold denoising on the relevant IMF components selected in S43. The function form used is as follows:

[0062] ;

[0063] In the formula, These are the original wavelet coefficients; These are the processed wavelet coefficients; It is the set threshold; Indicates the number of decomposition levels; α and β are position parameters; α and β are shape adjustment factors.

[0064] Step S45: Combining signal and noise characteristics, select an appropriate threshold estimation method; use both the approximation coefficient and the detail coefficient as parameters for threshold shrinkage, and define the threshold calculation as:

[0065] ;

[0066] in, This includes wavelet coefficients for each layer, which contain approximate wavelet coefficients. The length of the wavelet coefficients for each layer.

[0067] According to a second aspect of the present invention, the present invention proposes a bearing fault signal noise reduction system integrating sliding window filtering and PO-MCEEMD, for performing a bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD as described in any one of the present invention, characterized in that it includes the following:

[0068] The signal processing module is used to input the original bearing fault signal x(n) to be processed and to perform frame-by-frame processing to obtain several frame sub-signals;

[0069] The PO and MCEEMD modules use local minimum envelope entropy as the fitness function. For each frame sub-signal, the PO method is used to adaptively determine the key decomposition parameters NSTD and NE in the MCEEMD algorithm. Then, based on the obtained optimal parameters NSTD and NE, MCEEMD decomposition is performed on each frame sub-signal to obtain several IMF components.

[0070] The IMF component module uses cross-correlation coefficient analysis to divide the IMF components obtained from the decomposition of each sub-signal into correlated and uncorrelated components, and uses IWTD to further denoise the correlated components; the denoised IMF components are then reconstructed to obtain the denoised bearing fault signal d(n).

[0071] According to a third aspect of the present invention, the present invention proposes a bearing fault signal noise reduction system that integrates sliding window filtering and PO-MCEEMD, comprising an electronic device, wherein the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of the present invention.

[0072] According to a fourth aspect of the present invention, the present invention provides a bearing fault signal noise reduction system that integrates sliding window filtering and PO-MCEEMD, comprising a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of the present invention.

[0073] The present invention has the following advantages:

[0074] This invention employs an overlapping sliding window framing strategy for preprocessing bearing fault signals. This strategy effectively reconciles the conflict between time resolution and frequency resolution by adjusting the window size. Its advantages are threefold: First, it transforms non-stationary long sequences into approximately stationary short segments, making conventional stationary signal analysis methods applicable and thus accurately extracting the time-varying features of the fault. Second, it confines complex decomposition operations and parameter optimization processes within each frame, supporting adaptive adjustment of differentiated parameters at different time periods to flexibly address fluctuations in noise levels or impact intensity. Third, through the combination of inter-frame overlap design and window functions, it effectively suppresses boundary distortion and mode mixing, achieving a good balance between overall noise reduction performance and local feature preservation while ensuring the continuity of the reconstructed signal. Furthermore, this invention uses the local minimum envelope entropy as a fitness index, introducing PO to adaptively optimize key parameters in MCEEMD, reducing the dependence of parameters on human experience and effectively mitigating mode mixing, thereby improving the stability and reliability of the signal decomposition process. Subsequently, effective IMF components are selected based on their cross-correlation coefficients, and these components are then processed using an improved wavelet threshold denoising technique. This process effectively filters out background noise while preserving as much characteristic information as possible related to the bearing fault state. The overall methodology has a clear architecture and strong adaptability, significantly improving the signal-to-noise ratio of the denoised signal and the identifiability of fault features, thereby enhancing the accuracy and reliability of bearing fault diagnosis. Attached Figure Description

[0075] Figure 1 This is a schematic diagram of the steps of the present invention.

[0076] Figure 2 This is a flowchart of a method according to an embodiment of the present invention.

[0077] Figure 3 This is a time-domain diagram of the bearing fault signal before denoising in an embodiment of the present invention.

[0078] Figure 4 This is a spectrum diagram of the bearing fault signal before noise reduction in an embodiment of the present invention.

[0079] Figure 5 This is a time-domain diagram of the bearing fault signal after denoising in an embodiment of the present invention.

[0080] Figure 6 This is a spectrum diagram of the bearing fault signal after noise reduction in an embodiment of the present invention.

[0081] Figure 7 This is a graph showing the signal-to-noise ratio changes of each window of the bearing fault signal in an embodiment of the present invention.

[0082] Figure 8This is a graph showing the improvement in signal-to-noise ratio for each window of the bearing fault signal in an embodiment of the present invention. Detailed Implementation

[0083] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0084] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0085] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0086] like Figures 1 to 8 As shown, this invention proposes a method and system for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD, including the following:

[0087] This invention discloses a method for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD, relating to the field of mechanical bearing fault diagnosis. Considering that bearing fault signals typically exhibit nonlinearity, non-stationarity, and significant susceptibility to strong noise interference, a sliding window mechanism is employed to perform frame-based processing of the signal, and within each frame sub-signal, the following steps are performed: During the Median Complementary Ensemble Empirical Mode Decomposition (MCEEMD) process,

[0088] This invention introduces the Parrot Optimization (PO) algorithm to adaptively optimize the key parameters of MCEEMD decomposition, namely the Noise Standard Deviation (NSTD) and the Number of Ensembles (NE), overcoming the significant impact of NSTD and NE on the decomposition results and improving its decomposition accuracy for non-stationary and nonlinear signals, effectively suppressing mode aliasing. Furthermore, the Intrinsic Mode Functions (IMF) components are distinguished into irrelevant and relevant components using the cross-correlation coefficient method, and an improved wavelet thresholding method is introduced to perform secondary noise reduction on the relevant components. Finally, a complete denoised signal is reconstructed based on the overlap-addition method, effectively reducing noise in bearing fault signals. The method and system described in this invention are mainly applied in the field of bearing fault signal detection technology. They can effectively suppress noise interference while better preserving the key feature information reflecting the fault state in the signal, thereby improving the accuracy and reliability of fault identification.

[0089] In this invention, the empirical mode decomposition of the median complementary set is expressed as:

[0090] MCEEMD (Median Complementary Ensemble Empirical Mode Decomposition).

[0091] The Parrot Optimization algorithm is represented as PO (Parrot Optimization).

[0092] The noise standard deviation is expressed as NSTD (Noise Standard Deviation).

[0093] The set number is denoted as NE (Number of Ensembles).

[0094] Intrinsic mode functions are represented as IMFs.

[0095] PO-MCEEMD means: empirical mode decomposition of median complementary sets using the parrot optimization algorithm.

[0096] The equivalent Chinese content of the bearing fault signal noise reduction method and system proposed in this invention, which integrates sliding window filtering and PO-MCEEMD, is: A bearing fault signal noise reduction method and system based on sliding window filtering and parrot optimization algorithm to improve empirical mode decomposition.

[0097] According to a first aspect of the present invention, a method for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD is proposed. The method is characterized by employing a sliding window mechanism to perform frame-based processing of the signal. Then, during the MCEEMD decomposition process within each frame sub-signal, the Parrot Optimization Algorithm is used to adaptively optimize the NSTD and NE in the MCEEMD decomposition. Next, the IMF components are distinguished into irrelevant and relevant components using the cross-correlation coefficient method. An improved wavelet thresholding method is introduced to perform secondary denoising processing on the relevant components. Finally, the complete denoised signal is reconstructed based on the overlap-addition method to denoise the bearing fault signal.

[0098] Furthermore, the method also includes the following:

[0099] Step S1: Input the original bearing fault signal x(n) to be processed and perform frame segmentation to obtain several sub-frame signals;

[0100] Step S2: Using the local minimum envelope entropy as the fitness function, the PO method is used to adaptively determine the decomposition parameters NSTD and NE in the MCEEMD method for each frame sub-signal;

[0101] Step S3: Based on the optimal parameters NSTD and NE obtained in step S2, perform MCEEMD decomposition on each frame sub-signal to obtain several IMF components;

[0102] Step S4: Using cross-correlation coefficient analysis, the IMF components obtained from the decomposition of each sub-signal are divided into correlated components and uncorrelated components, and IWTD is used to further denoise the correlated components.

[0103] Step S5: Reconstruct each group of IMF components after noise reduction to obtain the noise-reduced bearing fault signal d(n).

[0104] Correspondingly, in one embodiment of the present invention, step S1 includes the following:

[0105] S1 employs an overlapping sliding window algorithm to perform frame-based processing on the bearing fault signal. This algorithm can dynamically adjust the window size based on the local stationarity of the signal to better balance the contradiction between time resolution and frequency resolution. Based on this, the sliding window framing mechanism has the following advantages: First, it divides non-stationary long signals into approximately stationary short frames, enabling the effective application of stationary signal analysis methods and thus accurately capturing the time-varying characteristics of the fault; second, it confines complex decomposition and parameter optimization within local frames, allowing for adaptive adjustment of differentiated parameters at different time periods, and finely responding to changes in noise level or impact intensity; finally, the combination of inter-frame overlap and window functions can effectively suppress boundary effects and mode mixing, ensuring the continuity of the reconstructed signal and achieving a better balance between overall noise reduction and local feature preservation.

[0106] Correspondingly, in one embodiment of the present invention, step S2 includes the following:

[0107] Step S21: Initialize the PO population. Let the population size be N (number of parrots) and the maximum number of iterations be Maxiter. Randomly generate the parrot individual at the i-th position in the j-th dimension according to the following formula. ;

[0108] ;

[0109] Where rand represents a random number between 0 and 1; UB is defined as the upper boundary; LB is defined as the lower boundary;

[0110] Step S22: Perform envelope demodulation on each IMF component obtained from MCEEMD decomposition to obtain the corresponding envelope signal. After normalizing these envelope signals, calculate their envelope entropy values, and use the minimum envelope entropy as the fitness function to calculate the fitness value of each individual at the current position. Envelope Entropy The specific definition is

[0111] ;

[0112] ;

[0113] In the formula, The signal envelope is obtained after Hilbert transform; N represents the total number of sampling points; j is the position number of the sampling point. yes The normalized form;

[0114] And it satisfies: , ;

[0115] Step S23: Behavioral Strategy Selection. For each individual, a probability value P∈[0,1] is randomly generated. Based on a preset threshold (e.g., divided into 0.25 equal parts), one of the following four behaviors is selected: Behavior 1: Foraging behavior; Behavior 2: Staying behavior; Behavior 3: Communication behavior; Behavior 4: Fear of strangers.

[0116] Step S24: Location update (corresponding to the four behaviors of PO).

[0117] (1) Foraging behavior (global exploration + Levy flight). In the foraging behavior of parrots, they mainly estimate the approximate location of food by observing its location or considering the location of their owner, and then they fly to the corresponding location. Therefore, the location movement follows the equation below:

[0118] ;

[0119] In the formula, Indicates the current position; This indicates the location of subsequent updates. Represents the average position within the current group; This represents the Levy distribution, which is used to describe the flight of parrots; This indicates the position from initialization to the current best position found. Indicates the current iteration number;

[0120] This indicates that the movement is based on the individual's position relative to its owner. This indicates that the location of the entire group is being observed to further determine the direction of the food.

[0121] (2) Persistent Behavior (Local Development + Random Persistence). Parrots are highly sociable creatures, and their persistent behavior mainly involves suddenly flying to any part of their owner's body, where they remain still for a period of time. This process can be represented as:

[0122] ;

[0123] in This represents a vector of all 1s of dimension dim. It indicates flying towards the master, and This refers to the process of randomly stopping at a part of the host's body.

[0124] (3) Communication Behavior (Social Learning or Random Flight). Parrots are inherently social animals, characterized by close communication within the group. This communication behavior includes both flying towards and away from the group. In PO, it is assumed that both behaviors occur with equal probability, and the average position of the current population is used to symbolize the center of the population. This process can be represented as:

[0125] ;

[0126] in, This refers to the process of an individual joining a flock of parrots. This represents the process of an individual flying away immediately after communication. Both of these behaviors are feasible, therefore, they are implemented using P, which is randomly generated in the range [0, 1].

[0127] (4) Fear of Strangers Behavior (Approaching the Optimal Solution + Moving Away from the Unknown Area). Generally, birds exhibit an innate fear of strangers, and parrots are no exception. They maintain distance from unfamiliar people and seek safety with their owners to find a safe environment, as shown below:

[0128] ;

[0129] in, Showing the process of flying to the owner;

[0130] in It shows the process of distancing oneself from strangers.

[0131] Step S25: Boundary Control and Fitness Update. After each iteration's position update, constraints are applied to individuals exceeding the boundary (boundary absorption or reflection). The updated individual positions (NSTD, NE) are then subjected to MCEEMD decomposition, and the corresponding fitness values ​​are calculated. .

[0132] Step S26: Output the optimal solution. Repeat steps S23-S25 until the current iteration count reaches the preset maximum iteration count. The algorithm then terminates and outputs the optimal parrot individual position, thereby obtaining the optimal MCEEMD decomposition parameters NSTD and NE.

[0133] Correspondingly, in one embodiment of the present invention, step S3 includes the following:

[0134] Step S31: Add paired complementary white noise with an amplitude of NSTD (step S26) to each frame sub-signal to obtain two sets of noisy signals;

[0135] Step S32: Perform EMD decomposition on each group of noisy signals to generate two corresponding IMF components; then average the IMF components with matching orders in these two groups.

[0136] Step S33: Repeat the above operation process from S31 to S32 until the preset optimal number of noise additions NE is reached;

[0137] Step S34: Perform median operation on all IMF components obtained through the above decomposition process, and output the operation result as the final IMF component.

[0138] Correspondingly, in one embodiment of the present invention, step S4 includes the following:

[0139] Step S41: After the sub-signals are decomposed, calculate each... cross-correlation coefficient , , ..., The cross-relationship number The calculation formula is:

[0140] ;

[0141] in, This indicates the signal that has been decomposed; It is the IMF component obtained from signal decomposition; and These are the average values ​​of the decomposed signal and the nth IMF component, respectively.

[0142] Step S42: The larger the cross-correlation coefficient value, the stronger the correlation between the IMF component and the original decomposed signal, and the richer the effective fault information contained therein. Based on the cross-correlation coefficient threshold, IMF components can be filtered and classified into effective and invalid components. The threshold is calculated as follows:

[0143] ;

[0144] in, Take the maximum cross-correlation coefficient among all IMF components;

[0145] Step S43: Distinguish between relevant IMF components and irrelevant IMF components according to the following formula:

[0146] ;

[0147] Step S44: Establish an improved wavelet threshold function to perform wavelet threshold denoising on the relevant IMF components selected in S43. The function form used is as follows:

[0148] ;

[0149] In the formula, These are the original wavelet coefficients; These are the processed wavelet coefficients; It is the set threshold; Indicates the number of decomposition levels; α is the position parameter; β and α are shape adjustment factors.

[0150] Step S45: Combining signal and noise characteristics, select an appropriate threshold estimation method. Here, the approximation coefficient and detail coefficient are used simultaneously as parameters for threshold shrinkage. The threshold is calculated as follows:

[0151] ;

[0152] in, These are the wavelet coefficients for each layer (including approximate wavelet coefficients). The length of the wavelet coefficients for each layer.

[0153] According to a second aspect of the present invention, the present invention proposes a bearing fault signal noise reduction system integrating sliding window filtering and PO-MCEEMD, for performing a bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD as described in any one of the present invention, characterized in that it includes the following:

[0154] The signal processing module is used to input the original bearing fault signal x(n) to be processed and to perform frame-by-frame processing to obtain several frame sub-signals;

[0155] The PO and MCEEMD modules use local minimum envelope entropy as the fitness function. For each frame sub-signal, the PO method is used to adaptively determine the key decomposition parameters NSTD and NE in the MCEEMD algorithm. Then, based on the obtained optimal parameters NSTD and NE, MCEEMD decomposition is performed on each frame sub-signal to obtain several IMF components.

[0156] The IMF component module uses cross-correlation coefficient analysis to divide the IMF components obtained from the decomposition of each sub-signal into correlated and uncorrelated components, and uses IWTD to further denoise the correlated components; the denoised IMF components are then reconstructed to obtain the denoised bearing fault signal d(n).

[0157] According to a third aspect of the present invention, the present invention proposes a bearing fault signal noise reduction system that integrates sliding window filtering and PO-MCEEMD, comprising an electronic device, wherein the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of the present invention.

[0158] According to a fourth aspect of the present invention, the present invention provides a bearing fault signal noise reduction system that integrates sliding window filtering and PO-MCEEMD, comprising a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of the present invention.

[0159] In one embodiment of the present invention, the following is included:

[0160] Figure 2 This is a flowchart of a method according to an embodiment of the present invention.

[0161] Figure 3 This is a time-domain diagram of the bearing fault signal before denoising in an embodiment of the present invention.

[0162] Figure 4 This is a spectrum diagram of the bearing fault signal before noise reduction in an embodiment of the present invention.

[0163] Figure 5 This is a time-domain diagram of the bearing fault signal after denoising in an embodiment of the present invention.

[0164] Figure 6 This is a spectrum diagram of the bearing fault signal after noise reduction in an embodiment of the present invention.

[0165] Figure 7 This is a graph showing the signal-to-noise ratio changes of each window of the bearing fault signal in an embodiment of the present invention.

[0166] Figure 8 This is a graph showing the improvement in signal-to-noise ratio for each window of the bearing fault signal in an embodiment of the present invention. Figure 8 Each point in the diagram represents the signal-to-noise ratio improvement value of each window signal. Figure 8 The signal is divided into eleven window sub-signals through a sliding window mechanism, corresponding to eleven points on the graph.

[0167] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for denoising bearing fault signals by integrating sliding window filtering and PO-MCEEMD, characterized in that, A sliding window mechanism is used to segment the signal into frames. Then, during the decomposition of MCEEMD in each frame sub-signal, the parrot optimization algorithm is used to adaptively optimize NSTD and NE in the MCEEMD decomposition process. Then, the IMF component is distinguished into irrelevant and relevant components by the cross-correlation coefficient method. An improved wavelet thresholding method is introduced to perform secondary noise reduction on the relevant components. Finally, the complete denoised signal is reconstructed based on the overlap addition method to reduce the noise of the bearing fault signal.

2. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 1, characterized in that, The method also includes the following: Step S1: Input the original bearing fault signal x(n) to be processed and perform frame segmentation to obtain several sub-frame signals; Step S2: Using the local minimum envelope entropy as the fitness function, the PO method is used to adaptively determine the decomposition parameters NSTD and NE in the decomposition process of MCEEMD for each frame sub-signal; Step S3: Based on the optimal parameters NSTD and NE obtained in step S2, perform MCEEMD decomposition on each frame sub-signal to obtain several IMF components; Step S4: Using cross-correlation coefficient analysis, the IMF components obtained from the decomposition of each sub-signal are divided into correlated components and uncorrelated components, and IWTD is used to further denoise the correlated components. Step S5: Reconstruct each group of IMF components after noise reduction to obtain the noise-reduced bearing fault signal d(n).

3. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 2, characterized in that, Step S1 includes the following: In step S1, the bearing fault signal is processed by frame segmentation using an overlapping sliding window algorithm. This includes dividing the non-stationary long signal into short time frames to capture the time-varying features of the fault; then, the complex decomposition and parameter optimization are confined to local frames to achieve adaptive adjustment of differentiated parameters at different time periods to cope with changes in noise level or impact intensity; finally, the inter-frame overlap and window function are combined to suppress boundary effects and mode mixing, ensuring the continuity of the reconstructed signal and achieving a balance between overall noise reduction and local feature preservation.

4. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 2, characterized in that, Step S2 includes the following: Step S21: Initialize the PO population. Let the population size be N and the maximum number of iterations be Maxiter. According to the following formula, randomly generate the parrot individual at the i-th position in the j-th dimension. ; ； Where rand represents a random number between 0 and 1; UB is defined as the upper boundary; LB is defined as the lower boundary; Step S22: Perform envelope demodulation on each IMF component obtained from MCEEMD decomposition to obtain the corresponding envelope signal; after normalizing these envelope signals, calculate their envelope entropy values, and use the minimum envelope entropy as the fitness function to calculate the fitness value of each individual at the current position; where the envelope entropy... The specific definition is: ； ； in, The signal envelope is obtained after Hilbert transform; N represents the total number of sampling points; j is the position number of the sampling point; yes The normalized form; And it satisfies: , ; Step S23: Define the behavior strategy selection, including: randomly generating a probability value P∈[0,1] for each individual, and selecting one of the following four behaviors according to a preset threshold: foraging behavior; staying behavior; communication behavior; fear of strangers behavior.

5. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 2, characterized in that, Step S2 also includes the following: Step S24: Update the position according to the four behaviors of PO, including the following: Step S241: Foraging behavior includes global exploration and Levi's flight. Position updates are performed for foraging behavior, where positional movement follows the equation below: ； In the formula, Indicates the current position; Indicates the location of subsequent updates; Represents the average position within the current group; This represents the Levy distribution, which is used to describe the flight of parrots; This represents the position found so far from initialization; t represents the current iteration number. This indicates that the movement is based on the individual's position relative to its owner. This indicates that the location of the entire group is being observed to further determine the direction of the food. Step S242: Dwelling behavior includes local development and random dwelling. Updating the location of dwelling behavior includes the following: ； in A vector of all ones representing dimension dim; It indicates flying towards the master, and This refers to the process of randomly stopping at a part of the host's body; Step S243: Communication behaviors include social learning or random fly-out. The location of these behaviors is updated, including the following: It is assumed that social learning and random fly-out occur with equal probability, and the average location of the current population is used to represent the population center; this process can be represented as: ； in, This describes the process of an individual joining a flock of parrots; in This indicates the process by which an individual flies away immediately after communicating; Step S244: Update the location of the fear of strangers behavior, including the following: Fear of strangers includes moving closer to the optimal solution and away from unknown areas, as shown below: ； in, Showing the process of flying to the owner; It shows the process of getting away from strangers; Step S25: Boundary control and fitness update, including constraining individuals that exceed the boundary after each iteration's position update; performing MCEEMD decomposition on the updated individual positions containing (NSTD, NE) and calculating the corresponding fitness values. ; Step S26: Output the optimal solution, including repeating steps S23-S25 until the current iteration number reaches the preset maximum iteration number, at which point the algorithm terminates and outputs the optimal parrot individual position, thereby obtaining the optimal MCEEMD decomposition parameters NSTD and NE.

6. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 2, characterized in that, Step S3 includes the following: Step S31: Add paired complementary white noise with an amplitude of NSTD to each frame sub-signal to obtain two sets of noisy signals; Step S32: Perform EMD decomposition on each group of noisy signals to generate two corresponding IMF components; then average the IMF components with matching orders in these two groups. Step S33: Repeat the above operation process from S31 to S32 until the preset optimal number of noise additions NE is reached; Step S34: Perform median operation on all IMF components obtained through the above decomposition process, and output the operation result as the final IMF component.

7. The bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD according to claim 2, characterized in that, Step S4 includes the following: Step S41: After the sub-signals are decomposed, calculate each... cross-correlation coefficient , , ..., The cross-correlation coefficients The calculation formula is: ； in, This indicates the signal that has been decomposed; It is the IMF component obtained from signal decomposition; and These are the average values ​​of the decomposed signal and the nth IMF component, respectively. Step S42: Based on the cross-correlation coefficient threshold, filter the IMF components and distinguish them into valid and invalid components; the threshold is calculated as follows: ； in, Take the maximum cross-correlation coefficient among all IMF components; Step S43: Distinguish between relevant IMF components and irrelevant IMF components according to the following formula: ； Step S44: Establish an improved wavelet threshold function to perform wavelet threshold denoising on the relevant IMF components selected in S43. The function form used is as follows: ； In the formula, These are the original wavelet coefficients; These are the processed wavelet coefficients; It is the set threshold; Indicates the number of decomposition levels; α and β are position parameters; α and β are shape adjustment factors. Step S45: Combining signal and noise characteristics, select an appropriate threshold estimation method; use both the approximation coefficient and the detail coefficient as parameters for threshold shrinkage, and define the threshold calculation as: ； in, This includes wavelet coefficients for each layer, which contain approximate wavelet coefficients. The length of the wavelet coefficients for each layer.

8. A bearing fault signal noise reduction system integrating sliding window filtering and PO-MCEEMD, used to perform a bearing fault signal noise reduction method integrating sliding window filtering and PO-MCEEMD as described in any one of claims 1 to 7, characterized in that, Includes the following: The signal processing module is used to input the original bearing fault signal x(n) to be processed and to perform frame-by-frame processing to obtain several frame sub-signals; The PO and MCEEMD modules use local minimum envelope entropy as the fitness function. For each frame sub-signal, the PO method is used to adaptively determine the key decomposition parameters NSTD and NE in the MCEEMD algorithm. Then, based on the obtained optimal parameters NSTD and NE, MCEEMD decomposition is performed on each frame sub-signal to obtain several IMF components. The IMF component module uses cross-correlation coefficient analysis to divide the IMF components obtained from the decomposition of each sub-signal into correlated and uncorrelated components, and uses IWTD to further denoise the correlated components; the denoised IMF components are then reconstructed to obtain the denoised bearing fault signal d(n).

9. A bearing fault signal noise reduction system integrating sliding window filtering and PO-MCEEMD, comprising an electronic device, wherein the electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of claims 1 to 7.

10. A bearing fault signal noise reduction system integrating sliding window filtering and PO-MCEEMD, comprising a computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a bearing fault signal noise reduction method that integrates sliding window filtering and PO-MCEEMD as described in any one of claims 1 to 7.

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