Fault diagnosis method based on two-stage parameter optimization characteristic mode decomposition

Abstract

The invention relates to the technical field of fault diagnosis, 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; in the second stage, actual FMD decomposition is carried out by utilizing the optimal parameters in the first stage, and a multi-index fusion scoring function based on an energy ratio, a related kurtosis gain and an envelope harmonic ratio is constructed, and a termination condition of decomposition is controlled by combining a dynamic threshold value, so that the optimal FMD decomposition is realized. The adaptive determination of the modal number is realized, and the blindness caused by manual presetting is avoided. The whole process embodies a complete logic chain from intelligentization and self-adaptive selection of parameters to fine decomposition of signals to accurate extraction of fault information, and aims at overcoming the limitation of a traditional FMD method in the aspects of parameter setting and anti-noise capability.

Description

Technical Field

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

[0002] As an indispensable key component in modern industrial equipment, the operating state of rolling bearings directly affects the overall performance of mechanical systems. However, due to factors such as long-term high load, complex working conditions, and harsh environments, rolling bearings are extremely prone to fatigue damage and progressive failure, which may lead to equipment failures and even major safety accidents. To prevent faults from evolving into serious failures and ensure the safety and reliability of equipment, it is of great significance to implement fault diagnosis of rolling bearings. When a rolling bearing has a local fault, the vibration signal has significant non-stationarity, non-linearity, and modulation characteristics.

[0003] Currently, the methods commonly used to extract fault features of non-stationary signals can be roughly divided into two categories: T-F analysis (Time-Frequency Analysis, TFA) and signal decomposition. To break through the bottleneck of 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 received extensive attention. By adaptively decomposing signals into modal components with clear physical meanings, it gets rid of the dependence on preset basis functions and effectively suppresses the interference of non-target components on transient vibration characteristics.

[0004] Combining the adaptive signal decomposition theory and the deconvolution principle, the pioneers proposed a new non-stationary signal decomposition - FMD. This method synchronously considers the impulsiveness and periodicity of the signal during the decomposition process through an adaptive finite-impulse response (FIR) filter bank and CK optimization, adaptively extracts mechanical fault features, and removes redundant modes. Compared with VMD, it overcomes the limitations of its fixed bandwidth and center frequency, significantly improving the anti-interference ability and decomposition accuracy. However, FMD still relies on manual experience in the selection of key parameters (i.e., the number of modes, filter length, and number of frequency band partitions), and CK, as the objective function, may have insufficient robustness in extreme noise environments, affecting the accuracy of fault feature extraction under complex working conditions. Therefore, adaptive parameter selection and optimization of the objective function are important aspects of FMD research. For example, an adaptive method for optimizing FMD parameters based on the artificial hummingbird algorithm (AHA), guiding the adaptive adjustment of filter parameters by combining the sparsity impact measure index (SIMI), and using the single-valued neutrosophic cross-entropy (SVNCE) to screen modal energy features. However, when optimizing the FMD parameters, these methods mainly focus on the adaptive adjustment of the filter length and the number of frequency band partitions, while ignoring the influence of the number of modes, which may lead to redundant decomposition or under-decomposition.

[0005] Therefore, in the field of fault diagnosis, there is an urgent need for a decomposition method that comprehensively considers various 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. For this reason, the present invention provides a fault diagnosis method based on two-stage parameter optimization feature mode decomposition.

[0007] The present invention provides a fault diagnosis method based on two-stage parameter optimization feature mode decomposition, A fault diagnosis method based on two-stage parameter optimization feature mode decomposition, S1, collect vibration signals, perform parameter initialization for non-stationary signal decomposition, and perform parameter initialization for the improved tornado optimization algorithm; S2, optimize the key parameters of non-stationary signal decomposition through the improved tornado optimization algorithm. The key parameters of non-stationary signal decomposition include the filter length and the number of frequency band partitions. Using the SKER index as the fitness function, obtain the combination of the optimal filter length and the optimal number of frequency band partitions; S3. Based on the optimal filter length and the optimal frequency band division number combination, decompose the vibration signal using non-stationary signal decomposition to obtain each intrinsic mode function and its residual; S4. Calculate the correlation coefficients between each intrinsic mode function and combine with the SKER index to eliminate redundant or noisy modes, obtaining an effective fault feature mode set and the residuals of each mode; S5. Utilize the multi-index fusion scoring and dynamic threshold mechanism, based on the effective fault feature mode set and the residuals of each mode, adaptively determine the optimal number of modes, and output the final decomposed feature mode set and the residuals of each mode; S6. Conduct envelope analysis on the final decomposed feature mode set and the residuals of each mode, extract the fault characteristic frequencies and their harmonic components to achieve fault diagnosis.

[0008] Furthermore, the vibration signal acquisition in S1 includes the sampling frequency and the acquisition duration; The vibration signal is the vibration signal of a rolling bearing.

[0009] Furthermore, the improved tornado optimization algorithm in S2 enhances the optimization efficiency and global search ability by introducing a hybrid velocity update mechanism of the inertia weight, individual cognitive term, and social learning term of particle swarm optimization, adopting a mutation strategy with an adaptive mutation probability and a dimension-adaptive mutation intensity, and combining a hybrid perturbation mechanism of Gaussian distribution and Cauchy distribution, adopting a dynamic step size adjustment mechanism based on the population distribution entropy, and using a boundary reflection strategy to handle the out-of-bounds individuals in the optimization process; The SKER index is the ratio of the short-time kurtosis error to the slope entropy. Furthermore, the non-stationary signal decomposition in S3 realizes the adaptive decomposition of the vibration signal by constructing an adaptive finite impulse response filter bank and iteratively updating the filter coefficients.

[0010] Furthermore, the calculation of the correlation coefficients in S4 is used to identify highly similar modes, and the modes with more significant fault features are selected and retained through the SKER index. The specific steps include, Calculate the correlation coefficients between each mode , where is the length of the vibration signal, , are the values of two intrinsic mode functions, , are the means of two intrinsic mode functions; Calculate the correlation coefficients between all modes to obtain the correlation coefficient matrix ; For the two modes with the highest correlation coefficients, select the mode with the lower SKER value as the effective fault feature mode.

[0011] Further, 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 weights of each index through the entropy weight method.

[0012] Further, in S5, the dynamic threshold mechanism adjusts the decomposition termination condition according to the residual energy and the modal score mean, and realizes the adaptive determination of the optimal number of modes.

[0013] Further, in S6, the envelope analysis calculates the envelope spectrum of the final decomposed characteristic mode set and the residuals of each mode, and identifies the fault characteristic frequencies corresponding to the periodic shocks and their harmonics.

[0014] Further, the calculation formula of the SKER is as follows: Wherein, is a tiny constant to prevent the denominator term from being 0 for a pure periodic signal; represents the vibration signal with a length of ; represents dividing the vibration signal into windows with a window length of and a step size of ; and are the mean and standard deviation of the th window respectively; represents the median of the kurtosis values of all windows ; is the value of the slope entropy SLE, is the fitness value, is the vibration signal of the th window, is the mean value of the vibration signal, and SKE is the short-time kurtosis error.

[0015] One or more of the above technical solutions in the embodiments of the present invention have at least one of the following technical effects: The improved tornado optimization algorithm ITOC proposed by the present invention significantly improves the global optimization performance and convergence accuracy by integrating the hybrid particle swarm optimization mechanism, the dynamic mutation strategy, and the diversity-driven mechanism.

[0016] A composite evaluation index SKER that combines SKE and SLE constructed by the present invention replaces the traditional CK index by the ratio of the normalized median kurtosis error of a short-time window to the local dynamic complexity entropy value, effectively improving the recognition rate of periodic impact features while suppressing non-stationary noise and harmonic interference.

[0017] The two-stage parameter collaborative optimization mechanism proposed by the present invention searches for the optimal parameter combination of the filter length and the number of frequency band divisions and adaptively determines the number of modes through two stages, while considering the adaptive adjustment of the filter length and the number of frequency band divisions and the influence of the number of modes; avoiding the problems of redundant decomposition or insufficient decomposition. The additional aspects and advantages of the present invention will be given in part in the following description, will become apparent in part from the following description, or will be understood through the practice of the present invention.

[0018] BRIEF DESCRIPTION OF THE DRAWINGS In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the embodiments or the description of the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019]

[0020] Figure 1 Figure 2 is a flowchart of the fault diagnosis method based on two-stage parameter optimization feature mode decomposition in the present invention; Figure 3 is a standardized result diagram of each index in the present invention under different signal lengths; Figure 4 is a composite fault signal diagram in the present invention under working condition B2; Figure 5 is a performance comparison diagram of each optimization algorithm in the present invention under working condition B2; Figure 6 is a decomposition result diagram of TPOFMD under working condition B2 in the present invention when the filter length is 100 and the number of frequency band divisions is 3; Figure 7 is a decomposition result diagram of FMD under working condition B2 in the present invention when the number of modes is 3, the filter length is 30, and the number of frequency band divisions is 10;

[0021] DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts fall within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0022] 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 the filter length and the number of frequency band divisions 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, and the decomposition termination condition is controlled by a dynamic threshold to realize the adaptive determination of the number of modes, avoiding the problems of modal redundancy or under-decomposition caused by manual presetting, and solving the problems of the existence of artificially set parameters and the instability of the correlated kurtosis (CK) of its objective function under non-stationary conditions.

[0023] FMD, Frequency Modulation Decomposition, non-stationary signal decomposition; ITOC, Improved Tornado Optimization Algorithm, improved tornado optimization algorithm; CK, Correlated Kurtosis, correlated kurtosis of the objective function; TFA, Time-Frequency Analysis, time-frequency analysis; EMD, Empirical Mode Decomposition, empirical mode decomposition; ITD, Intrinsic time-scale decomposition, intrinsic time-scale decomposition; EWT, Empirical Wavelet Transform, empirical wavelet decomposition; VMD, Variational Mode Decomposition, variational mode decomposition; FIR, Finite-impulse response, adaptive finite impulse response; CK, Correlated Kurtosis, correlated kurtosis of the objective function; AHA, Artificial hummingbird algorithm, artificial hummingbird algorithm; SIMI, Sparsity impact measure index, sparsity impact measure index; SVNCE, Single-valued neutrosophic cross-entropy, single-valued neutrosophic cross-entropy; KE, short-time kurtosis error; SLE, slope entropy; SKE, short-time kurtosis error.

[0024] As Figure 1 shown, the flowchart of the two-stage parameter optimization feature pattern decomposition method in the present invention is shown.

[0025] A fault diagnosis method based on two-stage parameter optimization feature pattern decomposition, the steps of which include, 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. At the same time, initialize the population number of the improved tornado optimization algorithm ITOC to 30 and the maximum number of iterations to 20.

[0026] In this embodiment, the bearing dataset of Huazhong University of Science and Technology is used, and the experimental platform is built based on the Spectra-Quest mechanical fault simulator for acquisition. The experimental data acquisition system records the bearing vibration signal at a sampling frequency of 25.6 kHz, and the single acquisition duration is 10.2 seconds. Each sample contains 262,144 data points to ensure the acquisition of high-resolution dynamic feature information.

[0027] The present invention selects condition B2 in two composite fault signals as the research object, and the specific introduction is shown in Table 1: Table 1 Overview of the selected dataset

[0028] Through this set of examples, the following Figure 3 composite fault signal is obtained. From Figure 3 (a) in it, obvious violent fluctuations can be observed, while in Figure 3 the frequency domain partial enlarged view of (b) in it, the fault frequencies of the inner and outer rings are all submerged by background noise and are difficult to identify.

[0029] The theoretical values of the fault frequencies of the inner and outer rings of the rolling bearing can be calculated according to the following formula: Among them is the failure frequency of the outer ring, is the failure frequency of the inner ring; is the shaft rotation frequency; is the number of balls; is the ball diameter, is the pitch diameter, is the contact angle.

[0030] Step 2: Optimize and improve the ITOC (Improved Tornado Optimization Algorithm) to optimize the filter length and the number of frequency band divisions. Set the search range, with the number of frequency band divisions being [2, 10] and the filter length being [20, 100]; use the SKER index as the fitness function. By minimizing the SKER value and combining global search and local refinement operations, obtain the optimal combination of filter length and the number of frequency band divisions.

[0031] Step 2.1: The initial population consists of individuals randomly generated in the d-dimensional space.

[0032] Step 2.2: Adopt the SKER index as the fitness function, calculate the individual fitness, and divide the population into three categories.

[0033] The following is an explanation of the SKER index: The present invention constructs a comprehensive evaluation index, SKER (Short-Time Kurtosis Error Ratio), which is the ratio of SKE (Short-Time Kurtosis Error) to SLE (Slope Entropy), to replace CK in FMD as the core index for mode selection and evaluation.

[0034] The definition of SKER is as follows: Among them, is a small constant to prevent the denominator term from being 0 in the case of a pure periodic signal; represents the vibration signal with a length of ; represents dividing the vibration signal with a window length of and a step size of (usually ), and the number of divided windows; and are the average value and standard deviation of the th window respectively; represents the median of the kurtosis values of all windows. is the SLE value, That is the fitness value, is the vibration signal of the i-th window, is the mean value of the vibration signal.

[0035] For the SLE value, its solution process is as follows: 1: Let the input signal , and define the slope of adjacent data points as: where N refers to the length of the input signal, refers to the i-th value in the signal.

[0036] 2: Introduce the symbolic mapping function , and discretize the continuous slope values into a finite symbol set. For example, use three-symbol coding: where is a preset threshold for distinguishing significant slope changes.

[0037] 3: For the symbol sequence , divide it into subsequences of length by a sliding window to generate a set of symbol patterns. For example, when , the subsequences may be . Count the occurrence frequencies of all possible subsequences to obtain the probability distribution , where is the total number of patterns.

[0038] 4: Based on the Shannon entropy formula, SLE is defined as: When all patterns appear, the entropy reaches the maximum value , and the sequence complexity is the highest at this time; if only a single pattern appears, the entropy is 0, indicating that the sequence is completely regular.

[0039] To verify the effectiveness of the SKER index, this application constructs a composite test set using the outer race fault simulation signal and its components, and its mathematical model is as follows: where is the periodic pulse signal caused by the outer race fault defect, is the random pulse caused by external shock, is the discrete harmonics of the shaft rotation and the Gaussian white noise with standard deviation .​ is the shaft rotation frequency; is the fault characteristic frequency; represents the th amplitude of the fault pulse, specified as a uniformly distributed random number in and are the resonance frequency and the attenuation coefficient respectively; obeys a uniform distribution , and simulates the time jitter effect caused by slight speed fluctuations, ; and represent the number and amplitude of the random pulses respectively; represents the th occurrence time of the random pulse; and represent the attenuation coefficient and resonance frequency excited by the random pulse respectively; , and represent the amplitude, frequency and phase of the th harmonic respectively.

[0040] Signals #1 to #5 correspond to the outer race fault simulation signal , the periodic pulse signal , the random pulse and the discrete harmonic as well as the Gaussian white noise . At the same time, in order to verify the stability of the SKER index, under the conditions that the signal lengths are 12,800, 25,600 and 51,200 respectively, the normalized response characteristics of SKER are compared with kurtosis, CK and harmonic-to-noise ratio (HNR). The experimental results are as Figure 2 shown. When the signal length is 12,800 and 25,600, both the CK and SKER indices can effectively identify the periodic pulse component, and their discrimination bases are the maximum value of CK and the minimum value of SKER respectively. In contrast, kurtosis shows a high sensitivity to the random pulse component, while HNR is more sensitive to the discrete harmonic component, and neither of these two indices can meet the strict requirements of fault feature extraction. It should be noted that when the signal length increases to 51,200, a significant parameter drift occurs in CK, while SKER remains stable.

[0041] Step 2.3: Compared with the TOC original velocity update equation which only depends on the Coriolis force term and does not utilize historical experience information.

[0042] Therefore, ITOC introduces the inertia weight, individual cognitive term and social learning term of PSO into the velocity update equation to form a hybrid velocity update formula: where is the contraction factor, which controls the convergence rate of the velocity update and avoids oscillation or premature convergence; is the fuzzy adaptive kinetic energy, which dynamically adjusts the search step size; is a random parameter, is the Coriolis parameter, is the radius of curvature, is the Coriolis force, is the inertia weight, , ; and are the learning factors, is the individual cognition in PSO, is the social learning in PSO, is the maximum number of iterations, is the current iteration number, is the th iteration of the th individual position, is the th iteration of the th individual velocity, is the velocity of PSO.

[0043] Step 2.4: There are two major problems with the perturbation mechanism of the original TOC algorithm: one is that the influence of dimensions on the search space is not considered in the fixed mutation intensity, which is likely to lead to divergence or insufficient perturbation in high-dimensional problems; the other is that the random perturbation is only triggered when approaching the optimal solution and the direction is single, making it difficult to maintain population diversity.

[0044] Therefore, an adaptive mutation probability and a dimension-adaptive mutation intensity are proposed and defined as follows: where is the maximum number of iterations, is the current iteration number; , the mutation intensity adapts and adjusts with the iteration number and the dimension to avoid excessive perturbation in high-dimensional spaces.

[0045] Furthermore, a mixed perturbation of Gaussian distribution and Cauchy distribution is adopted: Among them, the Gaussian distribution term provides local fine search ability; the Cauchy distribution term enhances the probability of large-range perturbation.

[0046] Step 2.5: The original TOC algorithm uses a fixed contraction factor , which cannot meet the requirements of different search stages: in the initial stage of algorithm iteration, the fixed step size may not be sufficient 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 oscillations near the optimal solution, reducing the convergence accuracy.

[0047] Therefore, a method for dynamically adjusting the step size based on the population distribution entropy is proposed, which is defined as follows: Among them, the initial step size ; is the diversity value of the population, defined as the average Euclidean distance between individuals and the population mean, is the initial population diversity value, is the -th generation population diversity value; is the -th generation population position mean, is the L2 norm.

[0048] In addition, the original TOC algorithm uses the truncation method to handle out-of-bounds individuals, resulting in insufficient utilization of the solution space near the boundary, and after multiple out-of-bounds, individuals pile up at the boundary, reducing diversity.

[0049] Therefore, the boundary reflection strategy is adopted to replace the truncation method, and the out-of-bounds individuals are reflected back into the search space by mirroring, as defined in the formula: Among them represents the displacement of the out-of-bounds individual, represents the lower boundary, represents the upper boundary.

[0050] 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 combination of the optimal filter length and the optimal frequency band segmentation number.

[0051] To verify the performance advantages of the ITOC optimization algorithm proposed in the present invention, based on 12 10-dimensional test functions of the CEC 2022 test set, four classic optimization algorithms, namely PSO, GWO, SSA, and TOC, were selected for comparative experimental research. The 12 test functions can be systematically divided into four typical optimization problems: Unimodal Function (F1), Basic Functions (F2 - F5), Hybrid Functions (F6 - F8), and Composition Functions (F9 - F12), which fully cover various performance test scenarios of the optimization algorithm. The experimental settings were a population size of 100 and a maximum number of iterations of 5000.

[0052] The population size and number of iterations set in the embodiment were for preventing the solution time from being too long and reducing the solution time. And each algorithm was independently run 10 times on each test function, with the result mean as the performance index. The experimental results are shown in Table 2. The ITOC algorithm achieved the optimal fitness value on the vast majority of test functions, fully demonstrating its excellent optimization performance. The various optimization algorithms were also compared in the example. As Figure 4 shown, ITOC began to converge after the first few iterations. Compared with other optimization algorithms, the ITOC algorithm could converge faster, further proving the superiority of the ITOC algorithm.

[0053] Table 2 Results of Each Optimization Algorithm on the CEC 2022 Test Set

[0054] Step 3: Calculate each mode and the residual .

[0055] Step 3.1: Input the optimized combination of the optimal filter length and the optimal number of frequency band divisions in Step 2. Use Hanning windows to construct the initial filter bank, and set the initial value of the number of iterations . For the vibration signal to be analyzed, it needs to be decomposed into a linear combination of characteristic modes ; where is the residual term.

[0056] Step 3.2: Obtain each filtered signal through the filter bank, calculate its autocorrelation spectrum , and find the local maximum value to estimate the period . is the FIR filter coefficients, based on the autocorrelation function , determine the fault period by detecting the local maximum of the autocorrelation spectrum . Specifically, select the time delay corresponding to the first local maximum of the autocorrelation function after the zero crossing as the period estimate value

[0057] Step 3.3: Combine the vibration signal , the filtered signal and the estimated period to update the FIR filter coefficients, and update the iteration count to , repeat steps 3.2 - 3.3 until the FMD preset iteration count in step 1 is reached

[0058] Step 4: Eliminate redundant or noise modes

[0059] Step 4.1: To avoid redundant modes, calculate the correlation coefficient (CorrelationCoefficient, CC) between each mode where is the length of the vibration signal , are two eigenmode values , are the mean values of the two eigenmodes. Calculate the correlation coefficients between all modes to obtain the correlation coefficient matrix ; 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; eliminate redundant or noise modes through the above operations to obtain the effective fault feature mode set and its residual

[0060] Step 5: Adaptively determine the optimal number of modes based on dynamic termination conditions and output the decomposed eigenmode set and the residual

[0061] Step 5.1: Based on the multi - index fusion and dynamic threshold mechanism, first calculate the comprehensive scoring function for each mode of the effective fault feature mode set obtained in step 4. In the multi - index fusion stage, by combining the three key indicators ER, CKG, and EHR, construct the comprehensive scoring function to quantify the significance of the periodic impact components in the signal and the suppression effect of noise interference Among them, the weight is determined by the entropy weight method; is the energy of the first 5 harmonics of the envelope spectrum, is the envelope energy of the full 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 improvement degree of the current mode impact characteristic compared with the previous mode, and suppresses the modes with insufficient gain; EHR reflects the significance of periodic faults.

[0062] Step 5.2: Combine the current residual energy and the scoring distribution of the modes obtained in Step 5.1 to dynamically adjust the threshold of the decomposition termination condition : As the criterion condition, the threshold of the decomposition termination condition is calculated as follows: Among them, is the dynamically adjusted threshold, ; the residual energy weight coefficient ; the scoring mean weight coefficient ; is the mean of the scores of the currently decomposed modes. When the proportion of the residual energy is low ( is small), the threshold is relaxed to capture weak features; when the mean of the scores of the decomposed modes is low ( ), the threshold is tightened to prevent redundancy.

[0063] When is higher than , the decomposition termination condition is not satisfied, and Steps 3.2 to 5 are repeated until the decomposition termination condition is satisfied; conversely, when is lower than , the decomposition process is terminated, so as to adaptively determine the optimal number of modes , and output the decomposed characteristic mode set and the residual.

[0064] Step 6: Perform envelope analysis to extract the fault characteristic frequencies and their harmonic components.

[0065] The specific method of envelope analysis can be selected and adjusted according to actual needs, and will not be elaborated here.

[0066] The present invention uses the rotation frequency Taking the severe compound fault data under the 80Hz working condition as the research object, the analysis duration is 1s. According to theoretical calculations, the fault frequencies of the inner and outer rings of the bearing are 434.05Hz and 285.95Hz respectively. Figures 5 to 7 The results comparison between different decomposition methods is shown. Figure 5 The decomposition results of the TPOFMD method are shown. Since the optimal number of modes is 2, the number of Modes is set according to the optimal number of modes, so it is decomposed into Mode#1 and Mode#2, where the Mode#1 component clearly presents 、 and its harmonic components. As a comparison, Figure 6 and Figure 7 respectively show the decomposition results of the traditional FMD and VMD. Although and its harmonic components can be identified from both the Mode#2 and BLIMF#2 components, in terms of extracting the inner ring fault characteristics, only can be identified and its harmonic components cannot be detected, resulting in difficulty in accurately determining the inner ring fault characteristic frequency. This comparison further highlights the superiority of the TPOFMD method in fault feature extraction, and it can extract the fault frequency more fully.

[0067] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault diagnosis method based on two-stage parameter optimization feature mode decomposition, characterized in that S1, collect vibration signals, perform parameter initialization for non-stationary signal decomposition, and improve the tornado optimization algorithm for parameter initialization; S2, use the improved tornado optimization algorithm to optimize the key parameters of non-stationary signal decomposition. The key parameters of non-stationary signal decomposition include filter length and frequency band division number. Use the SKER index as the fitness function to obtain the optimal filter length and optimal frequency band division number combination; S3, based on the optimal filter length and optimal frequency band division number combination, use non-stationary signal decomposition to decompose the vibration signal to obtain each characteristic mode and its residual; S4, calculate the correlation coefficient between each characteristic mode and combine the SKER index to eliminate redundant or noise modes to obtain an effective fault characteristic mode set and the residual of each mode; S5, use the multi-index fusion scoring and dynamic threshold mechanism, based on the effective fault characteristic mode set and the residual of each mode, adaptively determine the optimal number of modes, and output the final decomposed 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, extract the fault characteristic frequency and its harmonic components to achieve fault diagnosis.

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

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

4. The fault diagnosis method based on two-stage parameter optimization feature mode decomposition according to claim 1, characterized in that In S3, the non-stationary signal decomposition realizes the 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 feature mode decomposition according to claim 1, characterized in that The calculation of the correlation coefficient in S4 is used to identify highly similar modes, and the mode with more significant fault characteristics is selected through the SKER index. The specific steps include Calculate the correlation coefficients between each modality , wherein is the length of the vibration signal, and are two characteristic mode values, and are the means of two characteristic modes; Calculate the correlation coefficients between all modalities to obtain the correlation coefficient matrix ; For the two modes with the highest correlation coefficient, select the mode with the lower SKER value as the effective fault characteristic mode.

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

7. The fault diagnosis method based on two-stage parameter optimization feature mode decomposition according to claim 1, wherein In S5, the dynamic threshold mechanism adjusts the decomposition termination condition according to the residual energy and the mean value of the modal score, and realizes the adaptive determination of the optimal number of modes.

8. The fault diagnosis method based on two-stage parameter optimization feature mode decomposition according to claim 1, wherein In S6, the envelope analysis calculates the envelope spectrum of the final decomposed feature mode set and the residuals of each mode to identify the fault characteristic frequencies corresponding to the periodic shocks and their harmonics.

9. The fault diagnosis method based on two-stage parameter optimization feature mode decomposition according to claim 1, wherein The calculation formula of the SKER is as follows: Among them, is a tiny constant to prevent the denominator term from being 0 in a pure periodic signal; represents a vibration signal with a length of ; represents dividing the vibration signal by a window length of , with a step size of , and the number of divided windows; and are the mean and standard deviation of the -th window respectively; represents the median of the kurtosis values of all windows ; is the value of the slope entropy SLE, which is the fitness value, is the vibration signal of the -th window, is the mean of the vibration signal, and SKE is the short-time kurtosis error.

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