Rolling bearing fault diagnosis method based on parameter optimization FMD and adaptive denoising

Abstract

The invention discloses a rolling bearing fault diagnosis method based on parameter optimization FMD and adaptive denoising. The rolling bearing fault diagnosis method comprises the steps that bearing vibration signals in different operation states are collected based on an acceleration sensor; searching and optimizing FMD decomposition parameters by adopting an improved raccoon optimization algorithm, and performing FMD decomposition on the vibration signals based on an optimal parameter combination to obtain a plurality of IMF components; analyzing each IMF component through a Teager energy operator, and dividing each IMF component into a noise dominant component and a signal dominant component according to a discrimination criterion; performing adaptive denoising processing on the noise dominant component, and reconstructing the noise dominant component and the signal dominant component to obtain a reconstructed signal; calculating a Teager energy operator for the reconstructed signal and constructing a Teager energy spectrum to realize extraction of fault features of the rolling bearing and identification of fault types; the method can effectively reduce the subjectivity of parameter selection and the influence of noise interference on a diagnosis result, and improves the stability and accuracy of rolling bearing fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of mechanical equipment condition monitoring and fault diagnosis technology, and in particular to a rolling bearing fault diagnosis method based on parameter optimization FMD and adaptive noise reduction. Background Technology

[0002] Rolling bearings are critical components widely used in rotating machinery, and their operating condition directly affects the safety and reliability of the mechanical system. In actual working conditions, rolling bearings are susceptible to factors such as load variations, deteriorating lubrication conditions, and environmental noise, leading to various forms of failure in the inner ring, outer ring, or rolling elements. Therefore, accurately extracting rolling bearing fault characteristics from vibration signals under complex, high-noise backgrounds has always been a key research focus in the field of mechanical fault diagnosis.

[0003] Existing methods for diagnosing rolling bearing faults are mostly based on vibration signal analysis, using time-domain analysis, frequency-domain analysis, and time-frequency analysis to assess the bearing's operating state. Among these, modal decomposition methods have attracted widespread attention because they can decompose non-stationary and nonlinear signals into several physically meaningful modal components. However, traditional modal decomposition methods generally suffer from problems in practical applications, such as dependence on experience for decomposition parameters, insufficient stability of decomposition results, and mode aliasing, making it difficult to reliably extract effective fault features under complex operating conditions.

[0004] Feature Mode Decomposition (FMD), as a novel signal decomposition method, improves the mode aliasing problem of traditional methods to some extent by constructing filter banks and iteratively extracting narrowband mode components. However, in practical applications, the decomposition effect of FMD still highly depends on the selection of decomposition parameters. The decomposition results vary greatly under different parameter combinations, and improper parameter selection can easily weaken or mask effective fault information. Therefore, there is an urgent need to optimize the algorithm to determine the selection of parameters.

[0005] To improve the adaptability of mode decomposition methods under complex working conditions, recent studies have attempted to introduce intelligent optimization algorithms to automatically optimize decomposition parameters. Among these, swarm intelligence optimization algorithms, due to their characteristics of not requiring gradient information and being applicable to nonlinear and multimodal optimization problems, have been widely applied in signal processing and mechanical fault diagnosis. For example, by introducing swarm intelligence optimization algorithms to optimize mode decomposition parameters, the decomposition effect can be improved to a certain extent, and the extractability of fault features can be enhanced. The Coati Optimization Algorithm (COA), as a swarm intelligence optimization algorithm based on group cooperation and search behavior, has been proposed and applied to continuous optimization problems in recent years. This algorithm achieves a global search of the target space by simulating the cooperative behavior of a raccoon group during the search process, and has the characteristics of simple structure and few parameters. Therefore, the Coati Optimization Algorithm and its related variants are gradually being introduced into application scenarios such as parameter optimization and signal processing.

[0006] However, in practical applications, COA, as a novel swarm intelligence optimization algorithm, can still be affected by factors such as initial condition settings, a single search strategy, and insufficient population diversity, resulting in unstable convergence speed and susceptibility to local optima. When directly applied to FMD decomposition parameter optimization, it may cause significant fluctuations in decomposition results under different signal or operating conditions, thereby affecting the stability and accuracy of subsequent fault feature extraction and diagnosis results. Therefore, how to rationally design and improve the optimization algorithm based on the parameter characteristics of FMD to enhance the global search capability and stability of the parameter optimization process remains a pressing issue to be addressed in existing technologies.

[0007] Furthermore, rolling bearing vibration signals typically contain significant amounts of environmental noise and random interference. Even after FMD decomposition, the resulting intrinsic mode components (IMFs) may still contain noise-dominant components. If these noise components are not effectively suppressed, direct signal reconstruction or feature extraction can easily lead to unclear fault characteristics, affecting the accuracy of subsequent diagnostic results. Therefore, a rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive denoising is urgently needed to address these issues. Summary of the Invention

[0008] This invention aims to at least partially solve one of the technical problems in the aforementioned technologies. Therefore, the objective of this invention is to propose a rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive denoising, which can effectively reduce the subjectivity of parameter selection and the impact of noise interference on the diagnostic results, thereby improving the stability and accuracy of rolling bearing fault diagnosis.

[0009] To achieve the above objectives, this invention proposes a rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction, comprising: Bearing vibration signals under different operating conditions are collected using an accelerometer; Based on the improved Long-nosed Cobra optimization algorithm, the decomposition parameters of FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal. The improved Long-nosed Cobra optimization algorithm constructs an elite set, calculates the refraction candidate solutions of elite individuals and updates them based on a greedy criterion. It performs Gaussian mutation on the individuals in the elite set to generate refraction candidate solutions and updates them again based on the greedy criterion. Combined with population guidance control, boundary repair and fitness ranking screening, parameter optimization is achieved. The decomposition parameters of FMD are used to control the filter length L, the number of frequency bands C and the number of modes M during the FMD decomposition process. Based on the optimal parameter combination, the bearing vibration signal is decomposed by FMD to obtain several intrinsic mode function (IMF) components. Based on the discrimination criterion of Teager energy median, the IMF components are analyzed and classified into noise-dominant components and signal-dominant components. Adaptive denoising processing is performed on the dominant noise component to obtain the denoised IMF component; The denoised IMF components are reconstructed with the dominant signal components to obtain the reconstructed signal; The reconstructed signal is processed using the Teager energy operator, and the Teager energy spectrum is plotted to extract rolling bearing fault characteristics and identify fault types.

[0010] Preferably, the bearing vibration signal includes: ; in, For a moment The bearing vibration sampling value, The number of sampling points. Sampling frequency, The sampling time is [time], and it satisfies [condition]. .

[0011] Preferably, based on the improved long-nosed raccoon optimization algorithm, the decomposition parameters of the FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal, including: Initialize the population members, where each member corresponds to three parameters: filter length, number of frequency band divisions, and number of modes; Calculate the fitness value of each population member and construct the fitness sequence of the initial population. Based on the fitness sequence of the initial population, determine the globally optimal individual and initialize the convergence record. The fitness value is the envelope spectral entropy (ESE) of the component with the largest kurtosis among the M modal components after FMD decomposition. The guidance method is determined based on the index of each population member; the guidance method includes global optimal position guidance and random guidance; the candidate position of each population member is determined based on the global optimal position and random guidance; Boundary repair is performed on the candidate positions of each population member to determine the search boundary constraints; Sort the fitness values ​​of the population members in ascending order to determine the first sorting index sequence; The first few individuals in the first sorted index sequence are selected to form the first elite set; For each elite individual in the first elite set, calculate the corresponding candidate solution for refraction and calculate the fitness value corresponding to the candidate solution for refraction. Update the solution based on the greedy criterion to obtain the updated sorted index sequence, which is used as the second sorted index sequence. Obtain a preset elite set size coefficient, and determine the size of the second elite set based on the preset elite set size coefficient; select individuals from the second sorting index sequence that are the largest of the second elite set sizes to form the second elite set; Gaussian mutation is performed on each elite individual in the second elite set to generate a corresponding refraction candidate solution for each elite individual. The fitness value corresponding to the refraction candidate solution is calculated and updated based on the greedy criterion to obtain the updated second sorting index sequence, which is used as the third sorting index sequence. Calculate the optimal fitness value in the third sorted index sequence; The optimal fitness value is compared with the global optimal fitness value. When the optimal fitness value is determined to be less than the global optimal fitness value, the optimal parameter combination of the bearing vibration signal is determined.

[0012] Preferably, based on the optimal parameter combination, the bearing vibration signal is decomposed using FMD to obtain several intrinsic mode function (IMF) components, including: Based on the optimal decomposition parameters L, C, and M in the optimal parameter combination, the frequency band is divided into C sub-bands within the normalized frequency range [0,1), where L is the filter length, C is the initial number of sub-bands, and M is the target number of modes. For each sub-band, a corresponding bandpass FIR initial filter is designed based on the Hanning window function, and the bearing vibration signal is copied as C candidate channel inputs to obtain the initial filter group and the initial channel signal. The outer iteration rounds are sequentially executed on each initial channel signal in the bearing vibration signal; After each outer layer iteration, a channel correlation matrix is ​​constructed based on the output signals of all initial channels. The off-diagonal elements are the absolute values ​​of the correlation coefficients between any two channel signals, and the diagonal elements are set to zero. The channel pair with the highest correlation is determined, and the signals of the channel pair are processed to remove the mean. The correlation kurtosis value is calculated based on the estimated period of each channel. The correlation kurtosis values ​​of the two channels are compared, and the channel corresponding to the larger value is retained. The channel corresponding to the smaller value and its filter are removed to determine the number of remaining channels. Determine if the number of remaining channels is equal to M-1. If so, terminate the iteration and use the output signals of the remaining channels as the intrinsic mode functions (IMF) components.

[0013] Preferably, the IMF components are analyzed and classified according to the discrimination criterion based on the Teager energy median, and the IMF components are divided into noise-dominant components and signal-dominant components, including: Calculate the discrete Teager energy operator sequence corresponding to each IMF component; Based on the discrete Teager energy operator sequence, calculate the cumulative Teager energy value for each modal component; A set of Teager energy accumulation values ​​is constructed based on the Teager energy accumulation values ​​of all modal components; the median of the Teager energy accumulation value set is obtained as the adaptive discrimination threshold; A binary discriminant mask is constructed based on the adaptive discrimination threshold; Based on the binary discriminant mask, the IMF components are divided into noise-dominant components and signal-dominant components.

[0014] Preferably, adaptive denoising processing is performed on the dominant noise component to obtain the denoised IMF component, including: The discrete sequences corresponding to the dominant noise components are used as input to construct an initialization set; Set a multiplier coefficient, iterate through the initial set for a certain number of rounds, and calculate the mean and standard deviation of the initial set. The noise threshold is determined based on the multiplier and standard deviation. Based on the noise threshold, the elements of the set are iteratively filtered to determine the target threshold; The noise-dominant component is denoised based on the target threshold to obtain the denoised IMF component.

[0015] Preferably, the denoised IMF component is reconstructed with the dominant signal component to obtain a reconstructed signal, including: ; in, For reconstructing the signal; The dominant component of the signal; This represents the dominant noise component after denoising.

[0016] Preferably, the reconstructed signal is subjected to Teager energy operator calculation, and the Teager energy spectrum is plotted, including: Calculate the discrete Teager-Kaiser energy operator sequence corresponding to the reconstructed signal; The discrete Teager-Kaiser energy operator sequence is subjected to mean-removal processing to obtain a zero-mean sequence; Performing a discrete Fourier transform on the zero-mean sequence yields a complex sequence in the frequency domain; The energy spectral density index value is determined based on the frequency domain complex sequence; Obtain the one-sided Teager energy spectrum and determine the corresponding frequency coordinates; Plot the Teager energy spectrum curve with frequency coordinates on the horizontal axis and energy spectrum values ​​on the vertical axis.

[0017] Preferably, the discrete Teager energy operator sequence corresponding to each IMF component is calculated, including: ; in, Indicates the first Each modal component at the sampling point The output value of the Teager energy operator at that location; Indicates the first Each modal component at the sampling point The value at; The sampling point number; This is the index of the modal components.

[0018] Preferably, for each elite individual in the first elite set, the corresponding candidate solution for refraction is calculated, including: ; in, Let j be the j-th dimension parameter solution of the candidate solution for refraction; Let be the midpoint of the search interval for the j-th dimension parameter; The refractive index is 1. The index of the elite individuals in the first elite set; The first elite group The j-th dimension parameter value of an elite individual.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention introduces a parameter optimization mechanism to adaptively determine the decomposition parameters of Eigenmode Decomposition (FMD), thereby reducing the dependence of the decomposition process on manual empirical parameters and improving the stability and adaptability of the mode decomposition results.

[0020] 2. This invention combines the Teager energy operator to distinguish IMF components, which can effectively differentiate between noise-dominant components and signal-dominant components, providing a reliable basis for subsequent adaptive denoising.

[0021] 3. This invention employs an adaptive denoising method based on statistical characteristics to process the dominant noise components. While suppressing noise interference, it retains effective information related to rolling bearing failure, which is beneficial for highlighting the impact characteristics of the failure.

[0022] 4. This invention reconstructs the denoised IMF components and the dominant signal components, and further constructs the Teager energy spectrum, thereby enhancing the rolling bearing fault characteristics in the energy domain, thus improving the clarity of fault feature extraction and diagnostic accuracy.

[0023] 5. The method of the present invention has a clear overall process, is simple to implement, has good engineering feasibility, and is applicable to fault diagnosis scenarios of rolling bearings under different working conditions.

[0024] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0025] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the rolling bearing fault diagnosis method of the present invention; Figure 2 This is a diagram of the original vibration signal of the bearing inner ring acquired by this invention; Figure 3 This is a diagram of the original vibration signal of the bearing outer ring acquired by this invention; Figure 4 These are the reconstructed signal diagram and Teager energy spectrum diagram of the inner ring vibration signal before denoising in this invention; Figure 5 These are the reconstructed signal diagram and Teager energy spectrum of the outer ring vibration signal before denoising in this invention; Figure 6 These are the reconstructed signal diagram and Teager energy spectrum diagram of the inner ring vibration signal after denoising according to the present invention; Figure 7These are the reconstructed signal diagram and Teager energy spectrum of the outer ring vibration signal after denoising according to the present invention. Detailed Implementation

[0027] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0028] Example 1: As Figure 1 As shown, a rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction includes steps S1-S7: S1: Based on the acquisition of bearing vibration signals under different operating conditions using an accelerometer; S2: Based on the improved Long-nosed Cobra optimization algorithm, the decomposition parameters of FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal. The improved Long-nosed Cobra optimization algorithm constructs an elite set, calculates the refraction candidate solutions of elite individuals and updates them based on a greedy criterion. It performs Gaussian mutation on the individuals in the elite set to generate refraction candidate solutions and then updates them again based on the greedy criterion. Combined with population guidance control, boundary repair and fitness ranking screening, parameter optimization is achieved. The decomposition parameters of FMD are used to control the filter length L, the number of frequency bands C and the number of modes M during the FMD decomposition process. S3: Based on the optimal parameter combination, the bearing vibration signal is decomposed by FMD to obtain several intrinsic mode function (IMF) components; S4: Based on the discrimination criterion of Teager energy median, the IMF components are analyzed and classified, and the IMF components are divided into noise-dominant components and signal-dominant components. S5: Perform adaptive denoising processing on the dominant noise component to obtain the denoised IMF component; S6: Reconstruct the denoised IMF component and the dominant signal component to obtain the reconstructed signal; S7: Perform Teager energy operator calculation on the reconstructed signal and plot the Teager energy spectrum to extract rolling bearing fault features and identify fault types.

[0029] In this embodiment, S1, a mechanical bearing data acquisition platform is built, and vibration signals of the outer and inner rings of the rolling bearing are collected using an accelerometer, denoted as follows: , The experimental bearing was a 6205-2RS deep groove ball bearing. Single-point fault machining was performed on the bearing surface using electrical discharge machining (EDM), with a fault diameter of 0.1778 mm and a fault depth of 0.2794 mm. The selected bearing was installed on one side of the motor shaft, and the accelerometer was placed near the bearing. The experimental settings included a motor speed of 1797 r / min, a load of 0, a sampling frequency of 12 kHz, and a sampling time of 1 s. Figure 2 The image shown is a diagram of the original vibration signal of the bearing inner ring; as follows: Figure 3 The image shown is a diagram of the original vibration signal of the bearing outer ring. S2, the acquired signals from the inner and outer rings are respectively... , The parameters were fed into the optimization algorithm for optimization. The number of optimization algorithm populations was set to 30, the number of iterations was set to 30, the maximum number of FMD iterations was set to 30, and the upper and lower bounds of the optimization parameters, filter scale, frequency band division and number of modes were set to 30, 3, 2 and 150, 8, 8 respectively. S3. The optimized parameters obtained in step S2—filter scale, frequency band division, and the number of modes—are 136, 7, and 2 for the inner circle, and 30, 3, and 2 for the outer circle, respectively. Several bandpass filters are constructed based on these decomposition parameters to filter the vibration signal and obtain several initial components. Subsequently, each initial component is iteratively updated to gradually converge into intrinsic mode functions with narrowband characteristics. The iteration terminates when the results of two adjacent iterations meet the preset convergence condition, ultimately yielding several intrinsic mode functions.

[0030] S4. For each intrinsic mode function obtained in step S3, calculate the corresponding Teager energy, perform statistical analysis, and obtain the median of the Teager energy of all IMF components. If the Teager energy of this IMF is greater than the obtained median, this IMF is regarded as the noise-dominant component; otherwise, it is regarded as the signal-dominant component.

[0031] S5. Adaptive denoising processing is performed on the IMF components that are determined to be noise-dominant in step S4.

[0032] S6. The noise-dominant IMF component obtained in step S5 after denoising. The reconstructed signal is obtained by superimposing the IMF component determined to be the dominant signal in step S4. , .

[0033] S7. The reconstructed signal obtained in step S6 , Calculate its Teager energy operator, construct the Teager energy spectrum based on the Teager energy operator, and analyze the fault characteristic frequencies and their energy distribution in the energy spectrum.

[0034] The working principle and beneficial effects of the above technical solution are as follows: By introducing a parameter optimization mechanism to adaptively determine the decomposition parameters of Feature Mode Decomposition (FMD), the dependence of the decomposition process on manual empirical parameters is reduced, and the stability and adaptability of the mode decomposition results are improved; by combining the Teager energy operator to discriminate the IMF components, the noise-dominant components and signal-dominant components can be effectively distinguished, providing a reliable basis for subsequent adaptive denoising; by using an adaptive denoising method based on statistical characteristics to process the noise-dominant components, effective information related to rolling bearing faults is retained while suppressing noise interference, which is beneficial for highlighting fault impact characteristics; by reconstructing the denoised IMF components and signal-dominant components and further constructing the Teager energy spectrum, the rolling bearing fault characteristics are enhanced in the energy domain, thereby improving the clarity and diagnostic accuracy of fault feature extraction; the overall process of the method of this invention is clear, the implementation is simple, and it has good engineering feasibility, making it suitable for fault diagnosis scenarios of rolling bearings under different working conditions.

[0035] Example 2: The bearing vibration signal includes: ; in, For a moment The bearing vibration sampling value, The number of sampling points. Sampling frequency, The sampling time is [time], and it satisfies [condition]. .

[0036] Example 3: Based on the improved Long-nosed Raccoon optimization algorithm, the decomposition parameters of FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal, including: Initialize the population members, where each member corresponds to three parameters: filter length, number of frequency band divisions, and number of modes; Calculate the fitness value of each population member and construct the fitness sequence of the initial population. Based on the fitness sequence of the initial population, determine the globally optimal individual and initialize the convergence record. The fitness value is the envelope spectral entropy (ESE) of the component with the largest kurtosis among the M modal components after FMD decomposition. The guidance method is determined based on the index of each population member; the guidance method includes global optimal position guidance and random guidance; the candidate position of each population member is determined based on the global optimal position and random guidance; Boundary repair is performed on the candidate positions of each population member to determine the search boundary constraints; Sort the fitness values ​​of the population members in ascending order to determine the first sorting index sequence; The first few individuals in the first sorted index sequence are selected to form the first elite set; For each elite individual in the first elite set, calculate the corresponding candidate solution for refraction and calculate the fitness value corresponding to the candidate solution for refraction. Update the solution based on the greedy criterion to obtain the updated sorted index sequence, which is used as the second sorted index sequence. Obtain a preset elite set size coefficient, and determine the size of the second elite set based on the preset elite set size coefficient; select individuals from the second sorting index sequence that are the largest of the second elite set sizes to form the second elite set; Gaussian mutation is performed on each elite individual in the second elite set to generate a corresponding refraction candidate solution for each elite individual. The fitness value corresponding to the refraction candidate solution is calculated and updated based on the greedy criterion to obtain the updated second sorting index sequence, which is used as the third sorting index sequence. Calculate the optimal fitness value in the third sorted index sequence; The optimal fitness value is compared with the global optimal fitness value. When the optimal fitness value is determined to be less than the global optimal fitness value, the optimal parameter combination of the bearing vibration signal is determined.

[0037] In this embodiment, (1) when dealing with the signal During the FMD decomposition process, the parameters that need to be optimized are the filter length and the filter length. L ( L The integer is lb1≤ L ≤ub1, lb1=30, ub1=150), number of frequency band divisions ( C The integer is lb2≤ C ≤ub2, lb2=2, ub2=8), number of modes ( M The integer is lb3≤ M ≤ub3, lb3=2, ub3=8).

[0038] Initialize population members , in, , The number of population members, The corresponding parameters are L, C, and M. , To meet The smallest prime number, It is a floor function; This is the lower bound of the j-th dimension parameter; This is the upper bound of the j-th dimension parameter; These are the initialization coefficients for chaos. It is the first in the population Each member in the filter length L The value on, It is the first in the population Each member has a number of frequency band divisions The value on, It is the first in the population Each member in modality The value that can be taken on.

[0039] M The envelope spectral entropy of the modal component with the largest kurtosis is ,in -6 , S k To The energy of the one-sided envelope spectrum obtained by the Fourier transform after windowing. , The component with the largest kurtosis among the M modal components exist The value at time, {·} is the Hilbert envelope. yes The mean of. Let The first in the population The appropriate function value of each member, , , These are the three optimization parameters for FMD. The value of is used to calculate the envelope spectral entropy after FMD decomposition. Value Assignment ; · For modulo operation. Initialize iteration. , This represents the maximum number of iterations.

[0040] (2) From the fitness sequence of the initial population Determine the globally optimal individual and initialize the convergence record. Let... ,in This means taking from all population members. The minimum value; further let ,in Indicates to make The member number corresponding to the minimum value is that which satisfies... Based on this, the current global optimal position vector is obtained. .

[0041] (3) For each population member Generate its candidate update positions .

[0042] when When the current globally optimal position vector is used as the guiding individual, denoted as... ,in express The Dimensional components. At this point, candidate positions are generated using the following formula: ,in, , This represents a random number that follows a uniform distribution within the interval (0,1). Used to adjust the stride direction when an individual updates towards the guide position.

[0043] when At that time, construct a randomly guided individual , its first Weiwei And calculate the fitness value corresponding to the randomly guided individual. .

[0044] like If the randomly guided individual is considered superior to the current individual, then candidate positions are generated in a manner that prioritizes the guided individual. Otherwise, it will be generated in a way that is far removed from the guiding individual: .

[0045] Perform boundary repair on the obtained candidate positions to ensure they satisfy the search boundary constraints: .

[0046] The fitness of the candidate individuals is then calculated. ,in Indicates the first Candidate position vectors of each member.

[0047] Update using a greedy criterion: If If so, accept the candidate position and update. ,in, Otherwise, keep the original individual unchanged.

[0048] (4) Sort the current population in ascending order of fitness to obtain the first sorting index sequence. ,satisfy ,in Indicates the sorted order of the first... The index of each individual in the original population. Select the first individual from the first sorted index sequence. Individuals constitute the first elite group ,in To optimize the number of elite individuals Define the vector of the midpoint of the search interval. And define the refractive index that changes with iteration. ,in, This represents the maximum number of iterations. This indicates the current iteration number.

[0049] For each elite individual in the first elite set ( ), construct its refraction candidate solution as and to Perform boundary repair to make it fall into Inside; Index elite individuals. Calculate the fitness of refracted candidate solutions. ,in To avoid reducing randomness by ensuring that refraction enhancement is always fixed on the same elite, from Randomly select one of the candidate solutions for refraction to attempt an update. Let , representing a randomly selected sequence number, then the target elite index is .like Then, replace the corresponding elite individual with the refracted candidate solution: Otherwise, the elite individual remains unchanged.

[0050] (5) Define the shrinking search boundary that varies with the number of iterations as: ,in , They represent the first Dimensional parameters in the first dimension The lower and upper bounds of contraction corresponding to the next iteration, where, Sometimes, , .

[0051] For each population member Generate candidate positions .make and They are mutually independent uniform random numbers that satisfy... Then there is ,in Used to generate perturbation terms in positive and negative directions. Indicates the interval The scale term is randomly selected within the contraction boundary. The candidate locations are then restricted to within the contraction boundary. Calculate the fitness of candidate positions. .like Then update according to the greedy rule. Otherwise, keep the first With each member remaining unchanged, we obtain the updated sorted index sequence, which serves as the second sorted index sequence. It indicates a uniform distribution.

[0052] (6) Sort the second sorted index sequence in ascending order of fitness to obtain the third sorted index sequence. The sorting method is the same as in step (4). Let the size coefficient of the second elite pool be... The size of the second elite pool is defined as follows: Select the first element from the second sorted index sequence. Individuals constitute the second elite pool For each elite individual in the second elite pool A Gaussian mutation is performed to generate candidate solutions. Specifically, three elite indices are randomly selected from the second elite pool, denoted as... ,and The corresponding position vectors are respectively Calculate the geometric centers of the three. And calculate the scale vector. in This indicates the operation of taking the absolute value along the dimension. It generates candidate positions for Gaussian mutation. ,in It is a three-dimensional standard normal random vector. This indicates multiplication by dimension; Represents the scale vector.

[0053] For candidate solutions Perform boundary repair to ensure that the search boundary constraints are met: ; Calculate the fitness of candidate solutions ,like Then use Replace elite individuals And update its fitness: Otherwise, keep the elite individuals unchanged; obtain the updated second sorting index sequence, which serves as the third sorting index sequence.

[0054] (7) Let the optimal fitness value in the third sorted index sequence be... And let the corresponding optimal individual index be ,in This represents the minimum fitness value of the population at the end of this iteration. The individual ID that yielded the minimum value. If Then update the global optimal fitness and optimal position vector: , .

[0055] (8) Order ,like If yes, proceed to step (2); otherwise, proceed to step (9).

[0056] (9) Output the global optimal position vector The corresponding optimal parameter combination is then converted to integers: ,in This represents the rounding function. They are respectively The first to third dimensions.

[0057] The working principle and beneficial effects of the above technical solution are as follows: By initializing population members containing three parameters—filter length, number of frequency band divisions, and number of modes—coordinated search and optimization of these key parameters are achieved, thereby ensuring the finding of the optimal parameter combination that comprehensively reflects the characteristics of bearing vibration signals and improving the accuracy of subsequent analysis. The candidate positions of population members are determined by combining global optimal position guidance and random guidance. Global optimal position guidance encourages the population to move closer to known optimal regions, accelerating convergence; random guidance helps the algorithm escape local optima, increasing search diversity and ensuring the search for optimal solutions in a wider search space. Through multiple sorting and filtering processes, an elite set is obtained, and the individuals in the elite set are subjected to refraction candidate solution calculation and updates, as well as Gaussian mutation operations, further improving the quality of the population. These operations can increase the diversity and search ability of the population, continuously explore better solutions, and make the final parameter combination closer to the global optimum, thus improving the performance and stability of the algorithm. The envelope spectral entropy (ESE) of the component with the largest kurtosis among the M modal components after FMD decomposition is used as the fitness value. This index comprehensively considers the kurtosis and envelope spectral entropy characteristics of the signal, and can better reflect the fault characteristic information of the bearing vibration signal. This makes the algorithm optimization goal closely integrated with the actual application requirements, and the optimized parameter combination is more suitable for bearing vibration signal analysis.

[0058] Example 4: Based on the optimal parameter combination, the bearing vibration signal is decomposed using FMD to obtain several intrinsic mode function (IMF) components, including: Based on the optimal decomposition parameters L, C, and M in the optimal parameter combination, the frequency band is divided into C sub-bands within the normalized frequency range [0,1), where L is the filter length, C is the initial number of sub-bands, and M is the target number of modes. For each sub-band, a corresponding bandpass FIR initial filter is designed based on the Hanning window function, and the bearing vibration signal is copied as C candidate channel inputs to obtain the initial filter group and the initial channel signal. The outer iteration rounds are sequentially executed on each initial channel signal in the bearing vibration signal; After each outer layer iteration, a channel correlation matrix is ​​constructed based on the output signals of all initial channels. The off-diagonal elements are the absolute values ​​of the correlation coefficients between any two channel signals, and the diagonal elements are set to zero. The channel pair with the highest correlation is determined, and the signals of the channel pair are processed to remove the mean. The correlation kurtosis value is calculated based on the estimated period of each channel. The correlation kurtosis values ​​of the two channels are compared, and the channel corresponding to the larger value is retained. The channel corresponding to the smaller value and its filter are removed to determine the number of remaining channels. Determine if the number of remaining channels is equal to M-1. If so, terminate the iteration and use the output signals of the remaining channels as the intrinsic mode functions (IMF) components.

[0059] In this embodiment, (1) based on the optimal decomposition parameters in the optimal parameter combination Firstly, in the normalized frequency range Internal Press Divide into equal parts, define the first The left boundary of each sub-band is ,in Sub-band numbering, For the first The normalized left boundary frequency of each sub-band is normalized to 1 using the Nyquist frequency; the first... The normalized passband interval corresponding to each sub-band is: ,in This is a very small positive number, used to avoid the passband endpoint coinciding with 0 or adjacent frequency band endpoints during filter design, thereby reducing the risk of numerical degradation at the endpoints. The construction length is... Hanning window function : ,in Here are the sampling point numbers for the discrete window function. For the first The window function takes values ​​at each sampling point. Using the window as a reference, generate a corresponding bandpass FIR initial filter for each sub-band. ,in Indicates the first The initial filter for each sub-band channel in discrete index The coefficient values ​​at a given point satisfy the above interval constraints in their passband. All initial filters are then grouped into a filter bank. Simultaneously, the original vibration signal is copied as... Road candidate channel input: ,in Indicates the first The input signal of each sub-band channel at the initial moment. It is a time variable.

[0060] (2) For each sub-band channel signal obtained in step (1) Perform iterative updates using Maximum Correlated Kurtosis Deconvolution (MCKD), where... Counting the outermost rounds ( The MCKD method is an adaptive deconvolution method that iteratively updates the filter coefficients to ensure that the filtered output is updated periodically. The shift sequences exhibit stronger correlation kurtosis characteristics, thereby enhancing the periodic impact component and suppressing the non-impact noise component.

[0061] Let the first The number of MCKD inner iterations for each channel in the round is In one implementation method, take ,in This is the maximum number of iterations. For each channel currently retained... In the inner layer The next iteration ( In the given information, let the current filter coefficient sequence be... The channel input signal is The filtered output signal is Introducing the shift order ,in, Positive integers are preferred. In the cycle Lower construction shift output sequence and define the product term. , For shift order index, For the fault cycle, and weighting terms ,in Used to construct the filter update direction; For dummy variables in summation / multiplication; when preferred Sometimes, , .

[0062] Construct the delay embedding matrix formed from the input signal and its Matrix obtained by shifting and order ,in, Indicates by The column vector is formed. Then the filter is updated to... And perform energy normalization on the updated filter: At the same time, define the first The relevant kurtosis index for the next inner iteration is .

[0063] cycle Adaptive estimation is performed using the autocorrelation of the output signal envelope: for the output Constructing envelope sequence Calculate its normalized autocorrelation sequence Determine the first zero-crossing position and order ,in Let represent the value of the independent variable that maximizes the objective function, and let . Rounding; This is the first zero-crossing position.

[0064] Complete the channel After the inner iteration, the channel is obtained at the [number]th iteration. Wheel output ,filter With period and order This serves as the input for correlation determination and channel elimination in step (3).

[0065] (3) in the After the MCKD update is completed, output based on the current channel. Constructing the channel correlation matrix Its elements are defined as ,in The correlation coefficient between two sequences is represented by the coefficient of correlation between the two sequences. This indicates taking the absolute value; and setting the diagonal elements... To exclude autocorrelated terms.

[0066] Among all channel pairs, the two channel indices with the highest correlation are determined as follows: ,in and These represent the two channel numbers with the highest correlation. The mean values ​​of these two channel signals are then removed: ,in This represents the mean of the corresponding sequence.

[0067] Based on the period estimate obtained in step (2) , Calculate the correlation kurtosis values ​​for the two channels, where the shift order of the correlation kurtosis is set to 1: .make ,Compare and Retain channels with higher kurtosis and discard those with lower kurtosis: When removing a channel, its corresponding channel signal is deleted simultaneously. With filters and order When the number of remaining channels satisfies the target number of modes. The removal process is terminated when the corresponding termination condition is met. The termination condition is... When satisfied At that time, output the modal components corresponding to the remaining channels as the FMD decomposition result: If not satisfied, then let Then return to execute steps (2) and (3) until the above termination conditions are met.

[0068] The working principle and beneficial effects of the above technical solution are as follows: The frequency band is divided into C sub-bands within the normalized frequency range [0, 1), and a corresponding bandpass FIR initial filter is designed based on the Hanning window function. This frequency band division and filter design method helps to effectively separate the bearing vibration signal in different frequency bands, highlighting the characteristics of each frequency component. After each outer-layer iteration, a channel correlation matrix is ​​constructed. By analyzing the correlation between channels, the channel pair with the highest correlation is identified. This method can identify redundant or similar channel signals, providing a basis for subsequent screening. The signal of the channel pair with the highest correlation is subjected to mean removal processing, and the correlation kurtosis value is calculated. By comparison, channels with larger correlation kurtosis values ​​are retained, while smaller channels and their filters are removed. The correlation kurtosis value reflects the impact characteristics of the signal; retaining channels with more obvious impact characteristics helps to extract more valuable fault feature information. The iteration termination condition is whether the number of remaining channels is equal to M - 1. When this condition is met, the iteration is terminated in time, and the output signal of the remaining channels is used as the intrinsic mode function (IMF) component. This explicit termination condition avoids unnecessary calculations, improves decomposition efficiency, and enables the algorithm to quickly obtain the required decomposition results.

[0069] Example 5: Based on the discrimination criterion of Teager energy median, the IMF components are analyzed and classified, and the IMF components are divided into noise-dominant components and signal-dominant components, including: Calculate the discrete Teager energy operator sequence corresponding to each IMF component; Based on the discrete Teager energy operator sequence, calculate the cumulative Teager energy value for each modal component; A set of Teager energy accumulation values ​​is constructed based on the Teager energy accumulation values ​​of all modal components; the median of the Teager energy accumulation value set is obtained as the adaptive discrimination threshold; A binary discriminant mask is constructed based on the adaptive discrimination threshold; Based on the binary discriminant mask, the IMF components are divided into noise-dominant components and signal-dominant components.

[0070] In this embodiment, (1) the intrinsic mode function (IMF) components are denoted as ,in The first Each modal component is represented as a discrete sequence. ,in , This represents the number of sampling points.

[0071] (2) For each modal component Calculate the Teager energy operator sequence . Given by the discrete Teager-Kaiser energy operator: ,in, Indicates the first Each modal component at the sampling point The output value of the Teager energy operator at that location.

[0072] (3) Define the first The Teager energy scalar representation of each modal component is... ,in This indicates taking the absolute value. Indicates the first The cumulative Teager energy of each modal component.

[0073] (4) For all modal components Use the median as the adaptive discrimination threshold: ,in, This represents the median operation, which involves sorting the data by size and taking the median value.

[0074] (5) Based on threshold Construct a discriminant mask variable : Based on this, the IMF components are divided into a set of noise-dominant components. With the set of dominant signal components : ,in To meet The set of modal indices, This is the set of the remaining modal indices.

[0075] The working principle and beneficial effects of the above technical solution are as follows: By calculating the discrete Teager energy operator sequence and Teager energy accumulation value of each IMF component, the signal characteristics in the IMF component can be highlighted. The Teager energy operator is sensitive to the instantaneous energy changes of the signal and can effectively capture the abrupt changes in the signal, which can enhance the distinction between signal and noise and provide a more reliable basis for subsequent classification. The median of the set of Teager energy accumulation values ​​of all modal components is used as the adaptive discrimination threshold. This threshold can be dynamically determined according to the actual energy distribution of the IMF component, avoiding the misjudgment problem that may occur under different operating conditions or signal characteristics with a fixed threshold, making the classification results more consistent with the actual signal situation. A binary discriminant mask is constructed based on the adaptive discrimination threshold. Through a simple comparison operation, the IMF component can be divided into noise-dominant components and signal-dominant components. The calculation process is simple, reducing the computational complexity and improving the classification efficiency, which is suitable for application scenarios with high real-time requirements. After accurately dividing the IMF component into noise-dominant components and signal-dominant components, different types of components can be processed in a targeted manner. For the dominant signal component, fault features can be further extracted for fault diagnosis; for the dominant noise component, noise reduction processing or direct rejection can be performed, thereby improving the accuracy and reliability of subsequent fault diagnosis, condition monitoring and other analyses.

[0076] Example 6: Adaptive denoising processing is performed on the dominant noise component to obtain the denoised IMF component, including: The discrete sequences corresponding to the dominant noise components are used as input to construct an initialization set; Set a multiplier coefficient, iterate through the initial set for a certain number of rounds, and calculate the mean and standard deviation of the initial set. The noise threshold is determined based on the multiplier and standard deviation. Based on the noise threshold, the elements of the set are iteratively filtered to determine the target threshold; The noise-dominant component is denoised based on the target threshold to obtain the denoised IMF component.

[0077] In this embodiment, (1) the noise dominant component set is obtained by step S4. For any To correspond to the modal components discrete sequence ( Using this as input, we obtain the denoised modal components. : ,in, This is an adaptive denoising operator.

[0078] (2) The adaptive denoising operator The threshold is determined based on an iterative three-standard-deviation criterion. First, an initialization set is constructed from the input sequence. and define the multiplier coefficient. Preferred For the first iteration Calculate the set Mean and standard deviation: And construct the threshold: ,in and The first The mean and standard deviation of each iteration. This corresponds to the threshold.

[0079] (3) Based on the threshold Filter the elements in the set to obtain the next set: If an element is removed, the iteration continues; if no element is removed, the iteration terminates; the final threshold is obtained upon termination. ,in This represents the number of iterations at which the iteration terminates.

[0080] (4) Based on the final threshold For the original modal components Perform hard thresholding to zero denoising to obtain the denoised modal components: ,in For the first The output after denoising the dominant noise component.

[0081] (5) Set of dominant signal components any of No noise reduction processing is performed; the code is directly set to... Thus, the denoising results corresponding to all modal components are obtained. The result is then output to step S6 for reconstruction.

[0082] The working principle and beneficial effects of the above technical solution are as follows: By setting a multiplier coefficient, the initial set is iterated to calculate the mean and standard deviation, and a noise threshold is determined based on these statistics. Finally, the target threshold is iteratively selected. This method can dynamically adjust the threshold according to the actual data characteristics of the dominant noise component, adapting to changes in noise characteristics under different operating conditions, and avoiding the over- or under-denoising problems that may occur with fixed threshold denoising. Specific denoising of the dominant noise component allows for focused processing of the main noise parts of the signal, reducing noise interference with subsequent analysis. After denoising, the effective signal characteristics in the IMF component are more prominent, significantly improving signal quality. The denoised IMF component provides a more reliable data foundation for subsequent fault diagnosis, feature extraction, and other analytical work. Accurate signals can more clearly reflect the operating status and fault information of equipment, helping to improve the accuracy and reliability of fault diagnosis and timely detection of potential equipment faults.

[0083] Example 7: Reconstructing the denoised IMF component with the dominant signal component to obtain a reconstructed signal, including: ; in, For reconstructing the signal; The dominant component of the signal; This represents the dominant noise component after denoising.

[0084] In this embodiment, (1) step S5 obtains the denoised modal components, denoted as Among them, for The modal components have undergone adaptive denoising processing. The modal components remain unchanged; (2) The denoised IMF component and the dominant signal component are used together for reconstruction, and the reconstructed signal is defined as follows: Its discrete sequence is denoted as Then there is ; (3) Equivalently, according to the set partitioning form obtained in step S4, the reconstructed signal can also be expressed as The first term represents the signal-dominant component that directly participates in the reconstruction, while the second term represents the noise-dominant component that participates in the reconstruction after denoising.

[0085] (4) Output reconstructed signal Step S7 is used for calculating the Teager energy spectrum and extracting fault features.

[0086] Example 8: Performing Teager energy operator calculations on the reconstructed signal and plotting the Teager energy spectrum, including: Calculate the discrete Teager-Kaiser energy operator sequence corresponding to the reconstructed signal; The discrete Teager-Kaiser energy operator sequence is subjected to mean-removal processing to obtain a zero-mean sequence; Performing a discrete Fourier transform on the zero-mean sequence yields a complex sequence in the frequency domain; The energy spectral density index value is determined based on the frequency domain complex sequence; Obtain the one-sided Teager energy spectrum and determine the corresponding frequency coordinates; Plot the Teager energy spectrum curve with frequency coordinates on the horizontal axis and energy spectrum values ​​on the vertical axis.

[0087] In this embodiment, (1) the reconstructed signal is represented as a discrete sequence. ,in , This represents the number of sampling points. Calculate the Teager energy operator sequence : ,in, Indicates the reconstructed signal at the sampling point The Teager energy value at that location.

[0088] (2) To reduce the influence of the DC component on the spectrum, After performing mean removal processing, the following is obtained: : ; (3) To Perform a discrete Fourier transform to obtain the frequency domain sequence. : ,in For frequency domain indexing, The imaginary unit is defined as the square of the Teager energy spectrum amplitude. .

[0089] (4) Use the single-sided spectrum for plotting. Let Then the one-sided Teager energy spectrum is The corresponding frequency coordinates are defined as follows: .by The Teager energy spectrum curve is plotted to achieve Teager energy spectrum analysis of the reconstructed signal.

[0090] The working principle and beneficial effects of the above technical solution are as follows: The discrete Teager-Kaiser energy operator is sensitive to the instantaneous energy changes of a signal, highlighting abrupt changes and local features in the signal. By calculating the operator sequence, the energy characteristics of the signal can be effectively amplified, making weak fault features that might otherwise be masked by noise more apparent, facilitating subsequent analysis. The zero-mean sequence is obtained by removing the mean from the discrete Teager-Kaiser energy operator sequence, eliminating the DC component in the signal and avoiding interference from the DC component in subsequent frequency domain analysis, thus making the frequency domain analysis results more accurately reflect the actual frequency components of the signal. The zero-mean sequence is transformed to the frequency domain using the discrete Fourier transform, resulting in a frequency domain complex sequence, which is then used to determine the energy spectral density index value. This helps to clearly display the energy distribution of the signal at different frequencies, intuitively identifying the main frequency components and fault characteristic frequencies in the signal, providing crucial information for fault diagnosis. Finally, a Teager energy spectrum curve is plotted with frequency as the horizontal axis and energy spectrum as the vertical axis, presenting the frequency domain energy distribution of the signal in an intuitive graphical form. Technicians can quickly determine the operating status of equipment and whether there is a fault by observing the shape and peak position of the energy spectrum curve, thereby improving the efficiency and accuracy of fault diagnosis.

[0091] Example 9: Calculate the discrete Teager energy operator sequence corresponding to each IMF component, including: ; in, Indicates the first Each modal component at the sampling point The output value of the Teager energy operator at that location; Indicates the first Each modal component at the sampling point The value at; The sampling point number; This is the index of the modal components.

[0092] The working principle and beneficial effects of the above technical solution are as follows: The discrete Teager energy operator can effectively extract the instantaneous energy characteristics of the signal, highlight the local changes and abrupt changes in the signal, and help to analyze the dynamic characteristics of the signal; in the fields of mechanical fault diagnosis and power system fault detection, the Teager energy operator can be used to detect fault characteristics in the signal, thereby improving the accuracy and timeliness of fault diagnosis.

[0093] Example 10: Calculate the corresponding candidate solution for each elite individual in the first elite set, including: ; in, Let j be the j-th dimension parameter solution of the candidate solution for refraction; Let be the midpoint of the search interval for the j-th dimension parameter; The refractive index is 1. The index of the elite individuals in the first elite set; The first elite group The j-th dimension parameter value of an elite individual.

[0094] The working principle and beneficial effects of the above technical solution are as follows: By calculating refracted candidate solutions, the search space can be expanded based on the original elite individuals, allowing the algorithm to explore more possible solutions, helping to escape local optima and increasing the probability of finding the global optimum; the refracted candidate solutions differ from the original elite individuals, increasing the diversity of solutions. In optimization algorithms, solution diversity is crucial for preventing premature convergence and improving optimization performance. The newly generated refracted candidate solutions can provide more choices for subsequent iterations, enriching the diversity of the population.

[0095] refer to Figure 4 and Figure 5 The images shown are the reconstructed signal diagrams of the inner and outer rings before denoising in this invention, and the Teager energy spectrum, respectively. Figure 6 and Figure 7 These are the reconstructed signal images of the inner and outer rings after denoising according to this invention, and their corresponding Teager energy spectra; for comparison. Figure 4 and Figure 6 ,from Figure 4 It can be seen that in the reconstructed signal before noise reduction, the relay frequency fr, the fault frequency fo, and the sidebands near the fault frequency are not prominent enough, and a large amount of fault information is masked by noise; while from Figure 6 It is clearly visible that the reconstructed signal after denoising has prominent frequency shift (fr) and its harmonics (2fr, 4fr, 5fr); fault frequency (fo) and its harmonics (2fo, 3fo); as well as sidebands near the fault frequency; in comparison... Figure 5 and Figure 7 Similarly, the reconstructed outer ring signal after denoising can be clearly seen, which has rich frequency conversion fi, fault frequency fi and sidebands near the fault frequency.

[0096] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction, characterized in that, include: Bearing vibration signals under different operating conditions are collected using an accelerometer; Based on the improved Long-nosed Cobra optimization algorithm, the decomposition parameters of FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal. The improved Long-nosed Cobra optimization algorithm constructs an elite set, calculates the refraction candidate solutions of elite individuals and updates them based on a greedy criterion. It performs Gaussian mutation on the individuals in the elite set to generate refraction candidate solutions and updates them again based on the greedy criterion. Combined with population guidance control, boundary repair and fitness ranking screening, parameter optimization is achieved. The decomposition parameters of FMD are used to control the filter length L, the number of frequency bands C and the number of modes M during the FMD decomposition process. Based on the optimal parameter combination, the bearing vibration signal is decomposed by FMD to obtain several intrinsic mode function (IMF) components. Based on the discrimination criterion of Teager energy median, the IMF components are analyzed and classified into noise-dominant components and signal-dominant components. Adaptive denoising processing is performed on the dominant noise component to obtain the denoised IMF component; The denoised IMF components are reconstructed with the dominant signal components to obtain the reconstructed signal; The reconstructed signal is processed using the Teager energy operator, and the Teager energy spectrum is plotted to extract rolling bearing fault characteristics and identify fault types.

2. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, The bearing vibration signal includes: ； in, For a moment The bearing vibration sampling value, The number of sampling points. Sampling frequency, The sampling time is [time], and it satisfies [condition]. .

3. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, Based on the improved Long-nosed Raccoon optimization algorithm, the decomposition parameters of the FMD are searched and optimized to determine the optimal parameter combination of the bearing vibration signal, including: Initialize the population members, where each member corresponds to three parameters: filter length, number of frequency band divisions, and number of modes; Calculate the fitness value of each population member and construct the fitness sequence of the initial population. Based on the fitness sequence of the initial population, determine the globally optimal individual and initialize the convergence record. The fitness value is the envelope spectral entropy (ESE) of the component with the largest kurtosis among the M modal components after FMD decomposition. The guidance method is determined based on the index of each population member; the guidance method includes global optimal position guidance and random guidance; the candidate position of each population member is determined based on the global optimal position and random guidance; Boundary repair is performed on the candidate positions of each population member to determine the search boundary constraints; Sort the fitness values ​​of the population members in ascending order to determine the first sorting index sequence; The first few individuals in the first sorted index sequence are selected to form the first elite set; For each elite individual in the first elite set, calculate the corresponding candidate solution for refraction and calculate the fitness value corresponding to the candidate solution for refraction. Update the solution based on the greedy criterion to obtain the updated sorted index sequence, which is used as the second sorted index sequence. Obtain a preset elite set size coefficient, and determine the size of the second elite set based on the preset elite set size coefficient; select individuals from the second sorting index sequence that are the largest of the second elite set sizes to form the second elite set; Gaussian mutation is performed on each elite individual in the second elite set to generate a corresponding refraction candidate solution for each elite individual. The fitness value corresponding to the refraction candidate solution is calculated and updated based on the greedy criterion to obtain the updated second sorting index sequence, which is used as the third sorting index sequence. Calculate the optimal fitness value in the third sorted index sequence; The optimal fitness value is compared with the global optimal fitness value. When the optimal fitness value is determined to be less than the global optimal fitness value, the optimal parameter combination of the bearing vibration signal is determined.

4. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, Based on the optimal parameter combination, the bearing vibration signal is decomposed using FMD to obtain several intrinsic mode function (IMF) components, including: Based on the optimal decomposition parameters L, C, and M in the optimal parameter combination, the frequency band is divided into C sub-bands within the normalized frequency range [0,1), where L is the filter length, C is the initial number of sub-bands, and M is the target number of modes. For each sub-band, a corresponding bandpass FIR initial filter is designed based on the Hanning window function, and the bearing vibration signal is copied as C candidate channel inputs to obtain the initial filter group and the initial channel signal. The outer iteration rounds are sequentially executed on each initial channel signal in the bearing vibration signal; After each outer layer iteration, a channel correlation matrix is ​​constructed based on the output signals of all initial channels. The off-diagonal elements are the absolute values ​​of the correlation coefficients between any two channel signals, and the diagonal elements are set to zero. The channel pair with the highest correlation is determined, and the signals of the channel pair are processed to remove the mean. The correlation kurtosis value is calculated based on the estimated period of each channel. The correlation kurtosis values ​​of the two channels are compared, and the channel corresponding to the larger value is retained. The channel corresponding to the smaller value and its filter are removed to determine the number of remaining channels. Determine if the number of remaining channels is equal to M-1. If so, terminate the iteration and use the output signals of the remaining channels as the intrinsic mode functions (IMF) components.

5. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, Based on the Teager energy median criterion, the IMF components are analyzed and classified into noise-dominant components and signal-dominant components, including: Calculate the discrete Teager energy operator sequence corresponding to each IMF component; Based on the discrete Teager energy operator sequence, calculate the cumulative Teager energy value for each modal component; A set of Teager energy accumulation values ​​is constructed based on the Teager energy accumulation values ​​of all modal components; the median of the Teager energy accumulation value set is obtained as the adaptive discrimination threshold; A binary discriminant mask is constructed based on the adaptive discrimination threshold; Based on the binary discriminant mask, the IMF components are divided into noise-dominant components and signal-dominant components.

6. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, Adaptive denoising processing is performed on the dominant noise component to obtain the denoised IMF component, including: The discrete sequences corresponding to the dominant noise components are used as input to construct an initialization set; Set a multiplier coefficient, iterate through the initial set for a certain number of rounds, and calculate the mean and standard deviation of the initial set. The noise threshold is determined based on the multiplier and standard deviation. The set elements are iteratively filtered based on the noise threshold to determine the target threshold; The noise-dominant component is denoised based on the target threshold to obtain the denoised IMF component.

7. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, The denoised IMF components are then reconstructed together with the dominant signal components to obtain the reconstructed signal. include: ； in, For reconstructing the signal; The dominant component of the signal; This represents the dominant noise component after denoising.

8. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 1, characterized in that, The reconstructed signal is subjected to Teager energy operator calculation, and the Teager energy spectrum is plotted, including: Calculate the discrete Teager-Kaiser energy operator sequence corresponding to the reconstructed signal; The discrete Teager-Kaiser energy operator sequence is subjected to mean-removal processing to obtain a zero-mean sequence; Performing a discrete Fourier transform on the zero-mean sequence yields a complex sequence in the frequency domain; The energy spectral density index value is determined based on the frequency domain complex sequence; Obtain the one-sided Teager energy spectrum and determine the corresponding frequency coordinates; Plot the Teager energy spectrum curve with frequency coordinates on the horizontal axis and energy spectrum values ​​on the vertical axis.

9. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 5, characterized in that, Calculate the discrete Teager energy operator sequence corresponding to each IMF component, including: ； in, Indicates the first Each modal component at the sampling point The output value of the Teager energy operator at that location; Indicates the first Each modal component at the sampling point The value at; The sampling point number; This is the index of the modal components.

10. The rolling bearing fault diagnosis method based on parameter-optimized FMD and adaptive noise reduction as described in claim 3, characterized in that, For each elite individual in the first elite set, calculate the corresponding candidate solution for refraction, including: ； in, Let j be the j-th dimension parameter solution of the candidate solution for refraction; Let be the midpoint of the search interval for the j-th dimension parameter; The refractive index is 1. The index of the elite individuals in the first elite set; The first elite group The j-th dimension parameter value of an elite individual.

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