A fault diagnosis method based on characteristic mode decomposition with two-stage parameter optimization

Abstract

The present invention relates to the field of fault diagnosis technology and discloses a fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition. In the first stage, an improved tornado optimization algorithm is used as a parameter optimization tool, and an innovatively designed comprehensive evaluation index SKER is used as a fitness function to obtain the optimal filter length and the optimal frequency band division number combination. In the second stage, the optimal parameters from the first stage are used to perform actual FMD decomposition. By constructing a multi-index fusion scoring function based on energy ratio, correlation kurtosis gain, and envelope harmonic ratio, and combining it with a dynamic threshold to control the termination condition of the decomposition, the adaptive determination of the modal number is achieved, avoiding the blindness caused by manual presetting. The entire process embodies a complete logical chain from intelligent and adaptive parameter selection to refined signal decomposition and then to accurate extraction of fault information, aiming to overcome the limitations of traditional FMD methods in parameter setting and noise resistance.

Description

Technical Field

[0001] The present invention relates to the technical field of fault diagnosis, and in particular to a fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition. Background Art

[0002] Rolling bearings are essential components in modern industrial equipment, and their operating status directly impacts the overall performance of mechanical systems. However, due to long-term exposure to high loads, complex operating conditions, and harsh environments, rolling bearings are highly susceptible to fatigue damage and progressive failure, potentially leading to equipment failures and even major safety incidents. To prevent these failures from escalating into catastrophic failures and ensure equipment safety and reliability, rolling bearing fault diagnosis is crucial. When a localized fault occurs in a rolling bearing, the vibration signal exhibits significant nonstationary, nonlinear, and modulated characteristics.

[0003] Currently, commonly used methods for extracting fault features from non-stationary signals can be roughly divided into two categories: Time-Frequency Analysis (TFA) and signal decomposition. To overcome the bottleneck in non-stationary signal analysis, signal decomposition techniques such as Empirical Mode Decomposition (EMD), Intrinsic Time-Scale Decomposition (ITD), Empirical Wavelet Transform (EWT), and VMD have garnered widespread attention. By adaptively decomposing the signal into modal components with clear physical meaning, these techniques eliminate the reliance on pre-set basis functions and effectively suppress the interference of non-target components on transient vibration characteristics.

[0004] Combining adaptive signal decomposition theory and deconvolution principles, pioneers have proposed a new non-stationary signal decomposition method—FMD. This method uses adaptive finite-impulse response (FIR) filter banks and CK optimization to simultaneously consider the signal's impulsiveness and periodicity during the decomposition process, adaptively extracting mechanical fault features and removing redundant modes. Compared to VMD, this method overcomes the limitations of fixed bandwidth and center frequency, significantly improving anti-interference capabilities and decomposition accuracy. However, FMD still relies on manual experience in selecting key parameters (i.e., the number of modes, filter length, and number of frequency band divisions), and the CK objective function may lack robustness in extreme noise environments, affecting its accuracy in fault feature extraction under complex operating conditions. Therefore, adaptive parameter selection and optimization of objective functions are important aspects of FMD research. For example, adaptive methods based on the artificial hummingbird algorithm (AHA) to optimize FMD parameters, adaptive methods guided by the sparsity impact measure index (SIMI) to adaptively adjust filter parameters, and single-valued neutrosophic cross-entropy (SVNCE) to screen modal energy features have been proposed. However, when optimizing FMD parameters, these methods mainly focus on the adaptive adjustment of filter length and the number of frequency band divisions, while ignoring the influence of the number of modes, which may lead to redundant decomposition or insufficient decomposition.

[0005] Therefore, in the field of fault diagnosis, there is an urgent need for a decomposition method that comprehensively considers multiple factors to improve the accuracy of fault feature extraction under non-stationary conditions. Summary of the Invention

[0006] The present invention aims to solve at least one of the technical problems existing in the related art. To this end, the present invention provides a fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition.

[0007] The present invention provides a fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition,

[0008] A fault diagnosis method based on characteristic mode decomposition with two-stage parameter optimization,

[0009] S1, collect vibration signals, decompose non-stationary signals for parameter initialization, and improve the tornado optimization algorithm for parameter initialization;

[0010] S2, optimizing the key parameters of non-stationary signal decomposition using the improved tornado optimization algorithm, wherein the key parameters of non-stationary signal decomposition include filter length and number of frequency band divisions, and using the SKER index as a fitness function to obtain an optimal combination of the filter length and the optimal number of frequency band divisions;

[0011] S3, based on the combination of the optimal filter length and the optimal number of frequency band divisions, decompose the vibration signal using non-stationary signal decomposition to obtain each eigenmode and its residual;

[0012] S4, calculate the correlation coefficient between each characteristic mode and combine it with the SKER index to eliminate redundant or noise modes, and obtain the effective fault characteristic mode set and the residual of each mode;

[0013] S5, using multi-index fusion scoring and dynamic threshold mechanism, based on the effective fault characteristic mode set and the residual of each mode, adaptively determines the optimal mode number and outputs the final decomposition characteristic mode set and the residual of each mode;

[0014] S6, perform envelope analysis on the final decomposed characteristic mode set and the residual of each mode to extract the fault characteristic frequency and its harmonic components to achieve fault diagnosis.

[0015] Furthermore, the vibration signal acquisition in S1 includes a sampling frequency and an acquisition duration;

[0016] The vibration signal is a vibration signal of a rolling bearing.

[0017] Furthermore, the improved tornado optimization algorithm described in S2 introduces the inertia weight of particle swarm optimization, the mixed speed update mechanism of individual cognitive items and social learning items, adopts the mutation strategy of adaptive mutation probability and dimension adaptive mutation intensity, and combines the mixed perturbation mechanism of Gaussian distribution and Cauchy distribution, adopts the dynamic step size adjustment mechanism based on population distribution entropy, and adopts the boundary reflection strategy to deal with the out-of-bounds individuals in the optimization process, thereby improving the optimization efficiency and global search capability;

[0018] The SKER index is the ratio of the short-term kurtosis error to the slope entropy. Furthermore, the non-stationary signal decomposition in S3 realizes adaptive decomposition of the vibration signal by constructing an adaptive finite impulse response filter bank and iteratively updating the filter coefficients.

[0019] Furthermore, the calculation of the correlation coefficient described in S4 is used to identify highly similar modes, and the modes with more significant fault characteristics are selected through the SKER index. The specific steps include:

[0020] Calculate the correlation coefficient between each mode ,

[0021]

[0022] in is the vibration signal length, 、 are two eigenmode values, 、 is the mean of the two characteristic modes;

[0023] Calculate the correlation coefficients between all modes and obtain the correlation coefficient matrix ;

[0024] For the two modes with the highest correlation coefficient, the mode with the lower SKER value is selected as the effective fault characteristic mode.

[0025] Furthermore, in S5, the multi-index fusion score combines the energy ratio ER, the correlation kurtosis gain CKG and the envelope harmonic ratio EHR, and determines the weight of each index through the entropy weight method.

[0026] Furthermore, in S5, the dynamic threshold mechanism adjusts the decomposition termination condition according to the residual energy and the modal score mean to achieve adaptive determination of the optimal modal number.

[0027] Furthermore, in S6, the envelope analysis performs envelope spectrum calculation on the final decomposed characteristic mode set and the residual of each mode to identify the fault characteristic frequency and its harmonics corresponding to the periodic impact.

[0028] Furthermore, the calculation formula of the SKER is as follows:

[0029]

[0030]

[0031]

[0032]

[0033] in, is a small constant to prevent the denominator from being 0 in the case of a purely periodic signal; Indicates the length is Vibration signal; Indicates that the vibration signal The window length is , the step size is The number of windows after splitting; and They are The mean and standard deviation of the windows; Indicates the kurtosis value of all windows the median; is the value of slope entropy SLE, is the fitness value, For the The vibration signal of each window, is the mean of the vibration signal, and SKE is the short-term kurtosis error.

[0034] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0035] The improved tornado optimization algorithm ITOC proposed in this paper significantly improves the global optimization performance and convergence accuracy by integrating the hybrid particle swarm optimization mechanism, dynamic mutation strategy and diversity driving mechanism.

[0036] The present invention constructs a composite evaluation index, SKER, which integrates SKE and SLE. It replaces the traditional CK index by normalizing the ratio of the median error of the short-time window kurtosis to the local dynamic complexity entropy value, effectively improving the recognition of periodic shock characteristics while suppressing non-stationary noise and harmonic interference.

[0037] The two-stage parameter collaborative optimization mechanism proposed in this invention searches for the optimal parameter combination of filter length and frequency band division number and modal number through two stages. The adaptive determination of the filter length and the number of frequency band divisions is considered, and the influence of the number of modes is also considered; the problem of redundant decomposition or insufficient decomposition is avoided.

[0038] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 It is a flow chart of the fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition in the present invention;

[0041] Figure 2 This is a graph showing the standardized results of various indicators under different signal lengths in the present invention;

[0042] Figure 3 This is a composite fault signal diagram under working condition B2 in the present invention;

[0043] Figure 4 This is a performance comparison chart of various optimization algorithms in the present invention under working condition B2;

[0044] Figure 5 This is the decomposition result diagram of TPOFMD under working condition B2 when the filter length is 100 and the number of frequency band divisions is 3 in the present invention;

[0045] Figure 6 This is the decomposition result diagram of FMD under working condition B2 when the mode number is 3, the filter length is 30, and the frequency band division number is 10 in the present invention;

[0046] Figure 7 This is the decomposition result diagram of VMD under working condition B2 when the mode number is 3 and the bandwidth constraint parameter is 2000 in the present invention. DETAILED DESCRIPTION

[0047] To make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0048] In response to the problems in the background technology, the present invention proposes a two-stage parameter collaborative optimization mechanism. In the first stage, the optimal parameters of filter length and frequency band division number are found by combining the ITOC algorithm and SKER. In the second stage, a multi-index fusion scoring function is constructed based on ER, CKG and EHR. The decomposition termination condition is controlled by dynamic threshold to achieve adaptive determination of the modal number, avoid modal redundancy or under-decomposition caused by manual preset, and solve the problems of artificially set parameters and unstable performance of the objective function correlated kurtosis (CK) under non-stationary conditions.

[0049] FMD, Frequency Modulation Decomposition, non-stationary signal decomposition;

[0050] ITOC, Improved Tornado Optimization Algorithm, improved tornado optimization algorithm;

[0051] CK, Correlated Kurtosis, target function correlation kurtosis;

[0052] TFA, Time-Frequency Analysis, time-frequency analysis;

[0053] EMD, Empirical Mode Decomposition, empirical mode decomposition;

[0054] ITD, Intrinsic time-scale decomposition, intrinsic time scale decomposition;

[0055] EWT, Empirical Wavelet Transform, empirical wavelet decomposition;

[0056] VMD, Variational Mode Decomposition, variational mode decomposition;

[0057] FIR, Finite-impulse response, adaptive finite impulse response;

[0058] CK, Correlated Kurtosis, target function correlation kurtosis;

[0059] AHA, Artificial hummingbird algorithm, artificial hummingbird algorithm;

[0060] SIMI, Sparsity impact measure index, sparse impact measurement index;

[0061] SVNCE, Single-valued neutrosophic cross-entropy, single-valued neutrosophic cross entropy;

[0062] KE, short-term kurtosis error;

[0063] SLE, slope entropy;

[0064] SKE, short-term kurtosis error.

[0065] like Figure 1 As shown, a flow chart of the characteristic mode decomposition method based on two-stage parameter optimization in the present invention is shown.

[0066] A fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition, the steps of which include:

[0067] Step 1: Input the vibration signal to be analyzed , and set the maximum number of iterations of the non-stationary signal decomposition theory FMD to 30, and initialize the population number of the improved tornado optimization algorithm ITOC to 30 and the maximum number of iterations to 20.

[0068] This example uses a bearing dataset from Huazhong University of Science and Technology and collects data using an experimental platform built on the Spectra-Quest mechanical fault simulator. The experimental data acquisition system records bearing vibration signals at a sampling frequency of 25.6 kHz. A single acquisition lasts 10.2 seconds, and each sample contains 262,144 data points, ensuring the acquisition of high-resolution dynamic feature information.

[0069] The present invention selects the working condition B2 among the two composite fault signals as the research object, and the specific introduction is shown in Table 1:

[0070] Table 1 Overview of the selected datasets

[0071]

[0072] Through this set of examples, we get Figure 3 Composite fault signal. Figure 3 In (a), obvious and violent fluctuations can be observed, while in Figure 3 In the frequency domain partial magnification diagram in (b), the fault frequencies of the inner and outer rings are submerged by the background noise and are difficult to identify.

[0073] The theoretical value of the failure frequency of the inner and outer rings of rolling bearings can be calculated according to the following formula:

[0074]

[0075]

[0076] in is the fault frequency of the outer race, is the fault frequency of the inner race; is the shaft rotation frequency; is the number of balls; is the ball diameter, is the pitch diameter, is the contact angle.

[0077] Step 2: Optimize the filter length and the number of frequency band divisions by optimizing the improved Tornado optimization algorithm ITOC. Set the search range, the number of frequency band divisions to [2, 10] and the filter length to [20, 100]. Use the SKER index as the fitness function, and obtain the optimal filter length and optimal number of frequency band divisions by minimizing the SKER value and combining global search with local refinement operations.

[0078] Step 2.1: The initial population is randomly generated in d-dimensional space Individual composition.

[0079] Step 2.2: Use the SKER indicator as the fitness function to calculate the individual fitness and divide the population into three categories.

[0080] The following is an explanation of the SKER indicator:

[0081] The present invention constructs a comprehensive evaluation index of the ratio of SKE (short-term kurtosis error) to SLE (slope entropy) - SKER, which replaces CK in FMD as the core index for modality selection and evaluation.

[0082] The definition of SKER is as follows:

[0083]

[0084]

[0085]

[0086]

[0087] in, is a small constant to prevent the denominator from being 0 when there is a pure periodic signal; Indicates the length is Vibration signal; Indicates that the vibration signal The window length is , the step size is (generally ) The number of windows after splitting; and They are The mean and standard deviation of the windows; Indicates the kurtosis value of all windows of the median. is the SLE value, is the fitness value, is the vibration signal of the i-th window, is the mean value of the vibration signal.

[0088] For the SLE value, the solution process is as follows:

[0089] 1: Set input signal , define the slope of adjacent data points as:

[0090]

[0091] Where N is the length of the input signal, Refers to the i-th value in the signal.

[0092] 2: Introducing symbolic mapping functions , discretize the continuous slope value into a finite set of symbols. For example, using a three-symbol encoding:

[0093]

[0094] in is a preset threshold used to distinguish significant slope changes.

[0095] 3: Symbol sequence , divided by sliding window length , generates a set of symbol patterns. For example, when , the subsequence may be . Count the frequencies of all possible subsequences and get the probability distribution ,in is the total number of modes.

[0096] 4: Based on the Shannon entropy formula, SLE is defined as:

[0097]

[0098] When all patterns appear, entropy reaches its maximum , at this time the sequence complexity is the highest; if only a single pattern appears, the entropy is 0, indicating that the sequence is completely regular.

[0099] In order to verify the effectiveness of the SKER indicator, this application uses the outer race fault simulation signal and its components to construct a composite test set, whose mathematical model is as follows:

[0100]

[0101]

[0102]

[0103]

[0104] in It is a periodic pulse signal caused by outer ring fault defect. Random pulses caused by external shocks, is the discrete harmonic of the axis rotation and has a standard deviation Gaussian white noise . is the shaft rotation frequency; is the fault characteristic frequency; Indicates the The amplitude of the fault pulse is specified as Uniform random numbers in ; and are the resonant frequency and attenuation coefficient respectively; Uniform distribution , and simulate the time jitter effect caused by slight speed fluctuations, ; and Respectively represent the number and amplitude of random pulses; Indicates the The occurrence time of a random pulse; and denote the attenuation coefficient and resonance frequency of random pulse excitation, respectively; 、 and Respectively represent Amplitude, frequency, and phase of subharmonics.

[0105] Signals #1 to #5 correspond to outer race fault simulation signals , periodic pulse signal , random pulse and discrete harmonics and Gaussian white noise At the same time, in order to verify the stability of the SKER indicator, the normalized response characteristics of SKER were compared with those of Kurtosis, CK, and Harmonic-to-Noise Ratio (HNR) under the conditions of signal lengths of 12800, 25600, and 51200. The experimental results are as follows: Figure 2 As shown in the figure, when the signal length is 12800 and 25600, both the CK and SKER indicators can effectively identify periodic pulse components, based on the maximum CK value and the minimum SKER value, respectively. In contrast, the kurtosis is highly sensitive to random pulse components, while the HNR is more sensitive to discrete harmonic components. Neither indicator meets the stringent requirements for fault feature extraction. Notably, when the signal length increases to 51200, the CK parameter drifts significantly, while the SKER remains stable.

[0106] Step 2.3: Compared to the TOC original velocity update equation, which only relies on the Coriolis force term, it does not utilize historical experience information.

[0107] Therefore, ITOC introduces the inertia weight, individual cognitive term and social learning term of PSO into the speed update equation to form a hybrid speed update formula:

[0108]

[0109]

[0110]

[0111] in is the shrinkage factor, which controls the convergence speed of the velocity update to avoid oscillation or premature convergence; For fuzzy adaptive kinetic energy, the search step size is dynamically adjusted; is a random parameter, is the Coriolis parameter, is the radius of curvature, is the Coriolis force, is the inertia weight, , ; and is the learning factor, is the individual cognition in PSO, For social learning in PSO, is the maximum number of iterations, is the current iteration number, For the In the iteration individual positions, For the In the iteration Individual speed, is the speed of PSO.

[0112] Step 2.4: There are two major problems with the perturbation mechanism of the original TOC algorithm: First, the fixed mutation intensity does not consider the impact of dimension on the search space, and high-dimensional problems are prone to divergence or insufficient perturbation; second, random perturbation is only triggered when close to the optimal solution and has a single direction, making it difficult to maintain population diversity.

[0113] Therefore, the adaptive mutation probability is proposed and dimensional adaptive variation strength , defined as follows:

[0114]

[0115]

[0116] in is the maximum number of iterations, is the current iteration number; , mutation intensity With the number of iterations and dimensions Adaptive adjustment to avoid excessive disturbance in high-dimensional space.

[0117] Furthermore, a mixed perturbation of Gaussian distribution and Cauchy distribution is used:

[0118]

[0119] Among them, the Gaussian distribution term Provides local fine search capability; Cauchy distribution term Increase the probability of large-scale disturbances.

[0120] Step 2.5: Original TOC algorithm using fixed shrinkage factor , cannot adapt to the needs of different search stages: in the early stage of algorithm iteration, the fixed step size may not be enough to cover the vast search space, resulting in missing the global optimum; in the later stage of algorithm iteration, the fixed step size may cause oscillation near the optimal solution, reducing the convergence accuracy.

[0121] To this end, a method for dynamically adjusting the step size based on population distribution entropy is proposed, which is defined as follows:

[0122]

[0123]

[0124] Among them, the initial step length ; is the diversity value of the population, defined as the average Euclidean distance between the individual and the population mean, is the initial population diversity value, For the Generation population diversity value; For the The position mean of the generation population, is the L2 norm.

[0125] In addition, the original TOC algorithm uses the truncation method to deal with out-of-bounds individuals, which leads to insufficient utilization of the solution space near the boundary, and individuals accumulate at the boundary after multiple out-of-bounds, reducing diversity.

[0126] To this end, the boundary reflection strategy is used instead of the truncation method, and the out-of-bounds individuals are reflected back to the search space as a mirror image. The definition is shown in the formula:

[0127]

[0128] in Indicates the displacement of the individual that crosses the boundary, represents the lower boundary, Indicates the upper boundary.

[0129] Step 2.6: When the number of iterations is less than the maximum set value, repeat steps 2.1-2.5 until the set value is reached, and output the optimal combination of filter length and optimal number of frequency band divisions.

[0130] To verify the performance advantages of the proposed ITOC optimization algorithm, a comparative experimental study was conducted using 12 10-dimensional test functions from the CEC 2022 test set. Four classic optimization algorithms, namely PSO, GWO, SSA, and TOC, were selected. These 12 test functions can be systematically divided into four typical optimization problem categories: unimodal functions (F1), basic functions (F2-F5), hybrid functions (F6-F8), and composition functions (F9-F12), fully covering various performance testing scenarios for optimization algorithms. The experiment was performed with a population size of 100 and a maximum number of iterations of 5000.

[0131] The population size and number of iterations set in the embodiment are to prevent the solution time from being too long and to reduce the solution time. Each algorithm is independently run 10 times on each test function, and the average of the results is used as the performance indicator. The experimental results are shown in Table 2. The ITOC algorithm has achieved the optimal fitness value on most test functions, fully demonstrating its excellent optimization performance. The various optimization algorithms are also compared in the examples, such as Figure 4 As shown in the figure, ITOC begins to converge after the first few iterations. Compared with other optimization algorithms, ITOC algorithm can converge faster, which further proves the superiority of ITOC algorithm.

[0132] Table 2 Results of each optimization algorithm on the CEC2022 test set

[0133]

[0134] Step 3: Calculate each mode and residuals .

[0135] Step 3.1: Input the optimal filter length and optimal number of frequency band divisions optimized in step 2. The initial filter bank is constructed using a Hanning window, and the initial value of the number of iterations is set. For the vibration signal to be analyzed , which needs to be decomposed into Eigenmodes A linear combination of

[0136]

[0137] in, is the residual term.

[0138] Step 3.2: Obtain each filtered signal through the filter bank , calculate its autocorrelation spectrum , find the local maximum to estimate the period . For the FIR filter coefficients, based on the autocorrelation function , determine the fault period by detecting the local maximum of the autocorrelation spectrum Specifically, the time delay corresponding to the first local maximum of the autocorrelation function after the zero crossing is selected. As a period estimate.

[0139] Step 3.3: Combine vibration signals , filtered signal and estimated period Update the FIR filter coefficients and update the number of iterations to , repeat steps 3.2-3.3 until the preset number of FMD iterations in step 1 is reached.

[0140] Step 4: Eliminate redundant or noisy modes.

[0141] Step 4.1: To avoid redundant modes, calculate the correlation coefficient between each mode (CorrelationCoefficient,CC):

[0142]

[0143] in is the vibration signal length, 、 are two eigenmode values, 、 is the mean of the two characteristic modes. Calculate the correlation coefficients between all modes and obtain the correlation coefficient matrix ;

[0144] Step 4.2: For the two modes with the highest correlation coefficient, select the mode with the lower SKER value as the effective fault feature mode; through the above operation, eliminate redundant or noisy modes and obtain the effective fault feature mode set and its residual.

[0145] Step 5: Adaptively determine the optimal number of modes based on dynamic termination conditions And output the decomposed characteristic mode set and residuals.

[0146] Step 5.1: Based on the multi-index fusion and dynamic threshold mechanism, first calculate the comprehensive scoring function of each mode of the effective fault feature mode set obtained in step 4 In the multi-index fusion stage, a comprehensive scoring function is constructed by combining the three key indicators of ER, CKG and EHR. , to quantify the significance of the periodic impulse components in the signal and the suppression effect of noise interference:

[0147]

[0148]

[0149]

[0150]

[0151] Among them, the weight Determined by entropy weight method; is the energy of the first five harmonics of the envelope spectrum, is the envelope energy of the entire frequency band; CK is an improved kurtosis index, ER measures the energy contribution of the mode to the original signal, and a low ER value indicates that it may be noise; CKG quantifies the degree of improvement of the current mode's impact characteristics compared to the previous mode, suppressing modes with insufficient gain; EHR reflects the significance of periodic faults.

[0152] Step 5.2: Combine the current residual energy and the score distribution of the mode obtained in step 5.1 to dynamically adjust the decomposition termination condition threshold :

[0153] As a criterion condition,

[0154] Decomposition termination condition threshold The calculation formula is as follows:

[0155]

[0156] in, To dynamically adjust the threshold, ; Residual energy weight coefficient ; Rating mean weight coefficient ; is the mean of the currently decomposed modal scores. When the decomposed modal score is low ( ), tighten the threshold to prevent redundancy.

[0157] when Higher than When , the decomposition termination condition is not met, and steps 3.2 to 5 are repeated until the decomposition termination condition is met; otherwise, when Lower than When , the decomposition process is terminated, thereby adaptively determining the optimal mode number , and output the decomposed eigenmode set and residuals.

[0158] Step 6: Perform envelope analysis to extract the fault characteristic frequency and its harmonic components.

[0159] The specific method of envelope analysis can be selected and adjusted according to actual needs and will not be described in detail here.

[0160] The present invention uses the rotation frequency The study focused on severe composite fault data at 80Hz, with an analysis duration of 1s. According to theoretical calculations, the fault frequencies of the bearing inner and outer rings are 434.05Hz and 285.95Hz, respectively. Figures 5 to 7 A comparison of the results between different decomposition methods is shown. Figure 5 The decomposition results of the TPOFMD method are shown. Since the optimal mode number is 2, the number of modes is set according to the optimal mode number, so it is decomposed into Mode#1 and Mode#2, among which the Mode#1 component clearly shows 、 and its harmonic components. In contrast, Figure 6 and Figure 7 The decomposition results of traditional FMD and VMD are shown respectively. Although both Mode#2 and BLIMF#2 components can be identified and its harmonic components, but in terms of inner race fault feature extraction, only However, the harmonic components cannot be detected, making it difficult to accurately determine the characteristic frequency of the inner race fault. This comparison further highlights the superiority of the TPOFMD method in fault feature extraction, which can more fully extract the fault frequency.

[0161] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition, characterized in that: S1, collect vibration signals, decompose non-stationary signals for parameter initialization, and improve the tornado optimization algorithm for parameter initialization; S2, optimizing the key parameters of non-stationary signal decomposition using the improved tornado optimization algorithm, wherein the key parameters of non-stationary signal decomposition include filter length and number of frequency band divisions, and using the SKER index as a fitness function to obtain an optimal combination of the filter length and the optimal number of frequency band divisions; S3, based on the combination of the optimal filter length and the optimal number of frequency band divisions, decompose the vibration signal using non-stationary signal decomposition to obtain each eigenmode and its residual; S4, calculate the correlation coefficient between each characteristic mode and combine it with the SKER index to eliminate redundant or noise modes, and obtain the effective fault characteristic mode set and the residual of each mode; S5, using multi-index fusion scoring and dynamic threshold mechanism, based on the effective fault characteristic mode set and the residual of each mode, adaptively determines the optimal mode number and outputs the final decomposition characteristic mode set and the residual of each mode; S6, perform envelope analysis on the final decomposed characteristic mode set and the residual of each mode to extract the fault characteristic frequency and its harmonic components to achieve fault diagnosis; The calculation formula of the SKER is as follows: in, is a small constant to prevent the denominator from being 0 in the case of a purely periodic signal; Indicates the length is Vibration signal; Indicates that the vibration signal The window length is , the step size is The number of windows after splitting; and They are The mean and standard deviation of the windows; Indicates the kurtosis value of all windows the median; is the value of slope entropy SLE, is the fitness value, For the The vibration signal of each window, is the mean of the vibration signal, SKE is the short-term kurtosis error; Non-stationary signals are decomposed into FMD.

2. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: The vibration signal acquisition in S1 includes sampling frequency and acquisition duration; The vibration signal is a vibration signal of a rolling bearing.

3. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: The improved tornado optimization algorithm described in S2 introduces the inertia weight of particle swarm optimization, the hybrid speed update mechanism of individual cognitive items and social learning items, adopts the mutation strategy of adaptive mutation probability and dimension adaptive mutation intensity, and combines the hybrid perturbation mechanism of Gaussian distribution and Cauchy distribution, adopts the dynamic step size adjustment mechanism based on population distribution entropy, and adopts the boundary reflection strategy to deal with out-of-bounds individuals in the optimization process, thereby improving the optimization efficiency and global search capability; The SKER index is the ratio of the short-term kurtosis error to the slope entropy.

4. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: The non-stationary signal decomposition in S3 realizes adaptive decomposition of the vibration signal by constructing an adaptive finite impulse response filter bank and iteratively updating the filter coefficients.

5. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: The calculation of the correlation coefficient described in S4 is used to identify highly similar modes and select the mode with more significant fault characteristics through the SKER index. The specific steps include: Calculate the correlation coefficient between each mode , in is the vibration signal length, 、 are two eigenmode values, 、 is the mean of the two characteristic modes; Calculate the correlation coefficients between all modes and obtain the correlation coefficient matrix ; For the two modes with the highest correlation coefficient, the mode with the lower SKER value is selected as the effective fault characteristic mode.

6. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: In S5, the multi-index fusion score combines the energy ratio ER, the correlation kurtosis gain CKG and the envelope harmonic ratio EHR, and determines the weight of each index through the entropy weight method.

7. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: In S5, the dynamic threshold mechanism adjusts the decomposition termination condition according to the residual energy and the modal score mean to achieve adaptive determination of the optimal number of modes.

8. The fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition according to claim 1 is characterized in that: In S6, the envelope analysis performs envelope spectrum calculation on the final decomposed characteristic mode set and the residual of each mode to identify the fault characteristic frequency and its harmonics corresponding to the periodic impact.

Images