CN114813123A - Rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD - Google Patents

Abstract

The invention provides a rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD, which is characterized in that for collected vibration signals, a PSO algorithm is firstly utilized to optimize a VMD algorithm, and based on the result of the VMD after decomposing weak fault signals, the optimal modal component is selected. Secondly, determining PSO to MCKD algorithm according to the outstanding frequency range in the envelope spectrum of the optimal modal componentTThe optimization range of (1); and optimizing the MCKD algorithm by using the PSO, and enhancing fault impact components in the optimal component signals based on the MCKD algorithm. And finally, extracting weak fault characteristics of the bearing by using an envelope spectrum and comparing the weak fault characteristics with theoretical fault frequency to obtain a fault diagnosis result. The method solves the problem that parameters in a VMD algorithm and an MCKD algorithm are difficult to determine, achieves signal noise reduction and obtains a prominent fault frequency range by adopting the VMD algorithm, further enhances fault impact components by adopting the MCKD algorithm, and is more accurate in diagnosis of weak faults of the rolling bearing.

Description

Rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD

Technical Field

The invention belongs to the field of fault diagnosis of rotary machinery, and particularly relates to a rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD.

Background

The failure of the rolling bearing is one of important factors influencing the normal operation of the rotary machinery. Because the impact generated by the early failure of the bearing is very weak and is easily interfered by system noise, and the vibration transmission path of the rolling bearing is complex, the extraction of the failure characteristics of the rolling bearing is very difficult. Therefore, how to effectively reduce noise of the original fault signal of the rolling bearing and enhance the weak impact component in the signal is the key for carrying out early fault diagnosis on the components.

The fault signal of the rolling bearing is a nonlinear and non-stable signal, and for the signal, scholars propose various processing methods. In recent years, wavelet denoising, EMD decomposition, EEMD decomposition, and LMD decomposition are often used in the field of fault diagnosis. It should be noted that, although the above methods have achieved certain effects in diagnosing a failure of a rolling bearing, the following problems still remain: (1) wavelet transformation, which is difficult to realize the self-adaptive selection of wavelet basis and decomposition layer number according to actual signals; (2) EMD, EEMD, LMD, etc. all belong to recursive modal decomposition and lack strict mathematical theory. Aiming at the defects of the nonlinear signal processing method, the problem of modal aliasing, endpoint effect and the like generated by signal decomposition such as EMD (empirical mode decomposition) and the like can be effectively avoided by the Variable Mode Decomposition (VMD). MCKD highlights continuous impact pulses submerged by noise through deconvolution operation, improves the correlation kurtosis value of an original signal, and is very suitable for extracting continuous transient impact of weak fault signals. The good accurate-breaking effect is difficult to obtain by singly using the VMD decomposition, and a learner successfully diagnoses the weak fault of the bearing by adopting the MCKD to reduce noise and then adopting the VMD decomposition, but does not discuss how to determine the parameters of the two algorithms. The VMD algorithm and the MCKD algorithm need to be manually set with some parameters, and the values of the parameters have great influence on the algorithms.

Disclosure of Invention

Aiming at the problems that the early-stage generated impact of a rolling bearing is very weak, the bearing is easy to be interfered by system noise, so that the weak fault diagnosis of the bearing is difficult, and the parameters of a VMD algorithm and an MCKD algorithm are difficult to determine; the invention provides a rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD.

The technical method provided by the invention comprises the following steps:

the method comprises the following steps: measuring rotating mechanical equipment by using an acceleration sensor to obtain a vibration acceleration signal;

step two: optimizing in VMD algorithm using PSO algorithmαAndKand then VMD decomposition is carried out on the acquired vibration signals.

Step three: and based on the result of the VMD after the weak fault signal is decomposed, selecting the optimal modal component by utilizing the maximum criterion of the envelope spectrum peak factor.

Step four: determining PSO versus MCKD algorithm according to the prominent frequency range in the envelope spectrum of the optimal modal componentTAnd based on the parameter optimization result, the MCKD analysis further enhances the fault impact component in the optimal component.

Step five: and extracting the fault characteristics of the rolling bearing through the envelope spectrum, and comparing the fault characteristics with the theoretical bearing fault frequency in the transmission system to obtain a diagnosis result.

Preferably, the vibration signal is a transmission shaft radial vibration acceleration signal; and acquiring the vibration acceleration signal through a vibration acceleration sensor.

Preferably, the VMD algorithm is a signal decomposition method in a complete non-recursive mode, and decomposes an actual signal into optimal solutions by iteratively searching in a variational modelKA discrete modeu _k And determining the center frequency of each modal componentω _k And bandwidth. The MCKD algorithm takes the signal correlation kurtosis as an optimization target, deconvolution operation of vibration signals can be completed through iteration, continuous pulses covered by strong noise in the signals are highlighted, and rolling bearing fault characteristic signals are extracted from the signals with low signal-to-noise ratio.

Preferably, the optimization schemes all adopt a PSO algorithm to carry out global optimization on parameters in the VMD and the MCKD.

Preferably, the PSO algorithm is based on inertial weightϖStandard PSO algorithm with varying dishing function. The specific speed updating formula and the position updating formula are as follows:

in the formula:o=1，2，3，…，O；hin order to be able to perform the number of iterations,His the maximum iteration number; are particlesoFirst, thehIn the sub-iterationdThe velocity of the dimension;ϖ _max is the maximum weight of the weight to be given,ϖ _min is the minimum weight;c ₁ andc ₂ is a learning factor;ηis between the interval [0, 1]The random number of (2); is as followshParticles in sub-iterationsoIn the first placedThe position of the individual extreme point of the dimension; is as followshParticles in sub-iterationsoIn thatdThe current position of the dimension; is as followshThe whole population in the second iterationdThe location of the global extremum of the dimension.

Preferably, the specific parameters of the standard PSO algorithm are set as follows: learning factor c ₁ =c ₂ =2, population sizeO=30, maximum number of iterationsH=20, maximum weightϖ _max =0.9, minimum weightϖ _min =0.4。

Preferably, the optimization range of the parameters in the VMD algorithm; wherein a penalty factorαHas an optimization range of [100, 2000 ]]Number of componentsKHas an optimization range of [3, 10 ]]。

Preferably, the PSO algorithm optimizes fitness functions of the VMD and the MCKD to be envelope spectrum peak factors, and after the VMD is decomposed, the size of the envelope spectrum peak factor of the component is calculated, so that the optimal component is compared;

wherein the envelope spectrum crest factor defines:

in the formula:X(z) (z=1, 2, …, Z) Is an envelope spectrum off _r ^′ , γf _i ^′ ]Amplitude of the frequency range，f _r ^′ The value is greater than the rotating frequency of the shaft where the fault bearing is located;f _i ^′ in order to transmit the maximum bearing failure frequency of the system,γtaking 4-8.

It is preferable thatAfter the optimal component is subjected to envelope spectrum analysis, determining subsequent MCKD parameters according to the prominent frequency range in the spectrogramTThe optimization range of (1).

Preferably, the optimizing range of the MCKD parameter T is represented by the formulaT=f _s /f _i Determining the number of the first and second groups, wherein,f _s in order to be able to sample the frequency,f _i for the failure frequency, the unknown failure frequency is replaced by the prominent frequency; filter length parameter in the MCKD algorithmLHas an optimization range of [100, 1000%]。

Preferably, the failure frequency specifically includes an outer ring failure frequency, an inner ring failure frequency, a rolling body failure frequency or a cage failure frequency.

Preferably, the comparison between the envelope spectrum of the optimal component after the MCKD analysis and the fault frequency is performed to obtain a fault diagnosis result of the rolling bearing, specifically:

obtaining an envelope spectrogram by using the signal;

judging whether the frequency range in the spectrogram contains the outer ring fault frequency, the inner ring fault frequency, the rolling body fault frequency, the retainer fault frequency and respective integral multiple frequencies;

if yes, outputting fault prompt information;

if not, outputting normal prompt information;

and the fault diagnosis result comprises the fault prompt information and the normal prompt information.

Compared with the prior art, the invention has the advantages and positive effects that:

(1) the advantages of VMD in noise reduction and MCKD in noise covered continuous pulse are fully exerted, and the difficulty of the traditional method in weak fault signal feature extraction is improved; overcomes the defect that weak fault diagnosis is difficult to realize by using MCKD or VMD only

(2) The intelligent optimization algorithm, namely the PSO algorithm is introduced to realize the self-adaptive selection of the parameters of the VMD and the MCKD, so that the wrong diagnosis result caused by artificial parameter selection is avoided, and the PSO algorithm has higher efficiency than a test method and a grid optimization method.

(3) Optimal component after VMD algorithm decomposition, and parameters in the MCKD algorithm can be determined based on the prominent frequency range of the envelope spectrum of the componentTThe optimization range of (2) is reduced, and the parameters are reducedTThe optimization range of (1).

(4) In the PSO algorithm, the solution range of the fitness function is limited, and the influence of random synapse frequency on two optimization algorithms is avoided.

Drawings

FIG. 1 is a flow chart of the diagnostic method of the present invention.

Fig. 2 is a time domain waveform of an experimental signal of a faulty rolling bearing.

Fig. 3 is an envelope spectrum of an experimental signal of a faulty rolling bearing.

FIG. 4 is a flow chart of PSO algorithm optimizing VMD and MCKD in the present invention.

FIG. 5 is a graph showing the PSO algorithm optimizing the VMD and the fitness function varying with the number of iterations.

Fig. 6 is a graph of the peak factor magnitude of the envelope spectrum of each component after VMD decomposition.

Fig. 7 is an envelope spectrum of the optimal component.

FIG. 8 is a graph showing the PSO algorithm optimizing MCKD and the fitness function varying with the iteration number.

Fig. 9 is a time domain waveform after MCKD algorithm analysis.

Fig. 10 is an envelope spectrum after MCKD algorithm analysis.

Detailed Description

In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.

In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the examples of the present invention.

An example of a Wind power generation simulation system (WTS) developed by Spectra Quest company of America is used for carrying out a rolling bearing inner ring fault experiment, wherein sampling frequency is adoptedf _s 12800Hz, and 8192 points as sampling points.

The specific flow of the rolling bearing weak fault diagnosis method based on the PSO-VMD-MCKD is shown in figure 1, and the method specifically comprises the following steps.

The method comprises the following steps: and measuring the rotating mechanical equipment by using an acceleration sensor to obtain a vibration acceleration signal. Furthermore, Gaussian white noise of "-4 db" is added to the vibration signal to simulate the environmental noise under the actual working condition and the vibration signal closer to the early fault rolling bearing to serve as an experimental signal. It should be noted that the step of adding white noise is only for reflecting the diagnostic effect of the present invention, and is not an actual step of the present invention. Fig. 2 and 3 are time domain waveforms and envelope spectrograms of experimental signals, the impact component of the failed bearing in fig. 2 is covered by strong noise, and the impact frequency component cannot be observed in fig. 3.

Step two: optimizing the VMD parameter and determining the optimal influence parameterα ₀ , K ₀ ]. VMD decomposition to obtain a series of modal components and determine the center frequency of the modal componentsω _k And bandwidth. The algorithm model construction and solving steps are as follows:

1) computing each modality from the hilbert transformu _k (t) So as to obtain a single-sided spectrum of the mode:

in the formula:δ(t) Is a pulse function;tis time; j is an imaginary unit; "+" indicates convolution.

2) Adding an exponential term to the single-sided spectrum to perform frequency mixing, and modulating the spectrum of each mode to a corresponding baseband:

。

3) calculating the gradient of the demodulation signal, and estimating the bandwidth of each modal signal by using the square of the two norms of the gradient; all the components are added and equal to the original signal as a constraint condition, and a constraint variation model is described as follows:

in the formula: {u _k }={u ₁ , …, u _K }，{ω _k }={ω ₁ , …, ω _K }；∂ _t (∙) pairs of functionstAnd (5) calculating partial derivatives.

4) For solving the variational model of the above formula, Lagrange multipliers are introducedλ(t) And a secondary penalty factorαThe constrained variation problem is changed to an unconstrained variation problem. Wherein the content of the first and second substances,αthe interference of the Gaussian noise can be effectively reduced,λ(t) Constraint stringency can be enhanced. The extended lagrangian expression is:

5) continuously iteratively updating the retaining pocket by using an alternative Direction multiplier Algorithm (ADMM)u _k ⁿ⁺¹ }、{ω _k ⁿ⁺¹ }、λ ⁿ⁺¹ The "saddle point" of the above formula is sought. The iteration method comprises the following steps:

in the formula:nis the iteration number;g[1, K]；Гis an update factor;εis a positive number greater than 0 and represents precision.

To updateu _k ⁿ⁺¹ }、{ω _k ⁿ⁺¹ }、λ ⁿ⁺¹ The convergence condition of (1).

6) Carrying out equidistant Fourier transform by using Parseval/planar; solving the three formulas in the step 5 to obtain:

；

；

(ii) a In the formula: and each represents,x(t)、λ ⁿ The corresponding fourier transform. The VMD algorithm is to continuously update the frequency domain of each modal component and then transform the frequency domain to the time domain through Fourier inversion.

7) In summary, the specific implementation flow of the VMD can be formulated as follows:

7.1) initializationu _k ¹ }、{ω _k ¹ }、λ ¹ ，n=0；

7.2)n=n+1, start the loop of the whole algorithm;

7.3)k=k+1, up tok=KUpdateu _k 、ω _k ；

7.4) updateλ；

7.5) judging whether the convergence condition is met, if so, stopping iteration, and if not, returning to the step 7.2.

FIG. 4 is a flowchart showing the steps of particle swarm optimization for optimizing the VMD and MCKD parameters. In the PSO algorithm, the specific velocity update formula and the position update formula are:

in the formula:o=1，2，3，…，O；his the iteration number; are particlesoFirst, thehIn the sub-iterationdThe velocity of the dimension;ϖ _max is the maximum weight of the weight to be given,ϖ _min is the minimum weight;c ₁ andc ₂ is a learning factor;ηis between the interval [0, 1]The random number of (2); is as followshParticles in sub-iterationsoIn the first placedThe position of the individual extreme points of the dimension; is as followshParticles in sub-iterationsoIn thatdThe current position of the dimension; is as followshThe whole population in the second iterationdThe location of the global extremum of the dimension.

The fitness function in the PSO algorithm is an envelope spectrum peak factor E _c The definition is as follows:

in the formula:X(z) (z=1, 2, …, Z) Is [ 2 ]f _r ^′ , γf _i ^′ ]Envelope spectrum amplitude of frequency range，f _r ^′ The value is greater than the rotating frequency of the shaft where the fault bearing is located;f _i ^′ in order to transmit the maximum bearing failure frequency of the system,γtaking 4-8. The larger the envelope spectrum peak factor, the more significant the fault signature.

The parameters set in the particle swarm optimization are as follows: learning factorc ₁ =c ₂ =2, population sizeO=30, maximum number of iterationsH=20, maximum weightϖ _max =0.9, minimum weightϖ _min = 0.4. Particle swarm algorithm for VMD parameter combinationα, K]The optimization is carried out, and the optimization is carried out,αhas an optimization range of [100, 2000 ]]，KHas an optimization range of [3, 10 ]]. Setting a fitness function solving frequency range of [15, 300 ] according to the maximum possible bearing fault frequency of the transmission system]. FIG. 5 is a graph of a particle swarm algorithm optimizing VMD with a fitness function varying with iteration number, showing PSO algorithm convergence in generation 6; the optimization result obtained isα ₀ =10，K ₀ = 1090. Then, a penalty factor in the VMD algorithm is setα ₀ Number of components =10K ₀ = 1090; VMD decomposition of experimental signals was performed.

Step three: after VMD decomposition, calculating envelope spectrum peak value factor of each component, selecting E _c The component with the largest index is the optimal component. The amplitude map of each component is shown in fig. 6, thereby judging the component 9 as the optimum component.

Step four: the component 9 is subjected to envelope spectrum analysis, and fig. 7 shows the envelope spectrum of the component 9. From which a prominent frequency of 45.33Hz is selected, a frequency band [30, 70 ]]. By the formulaT=f _s /f _i (ii) a Wherein, the first and the second end of the pipe are connected with each other,f _s in order to be able to sample the frequency,f _i for the fault frequency, the unknown fault frequency is replaced by the prominent frequency as the solutionTThe frequency range of (c). Thereby calculating the parametersTHas an optimization range of [182, 427 ]]. Setting parametersLHas an optimization range of [100, 1000%]. And in the optimization process of the PSO algorithm on the MCKD algorithm parameters, setting the parameters in the same step two. The MCKD algorithm steps are as follows:

1) periodic impulse signaly _i (i=1, 2, …, N) The relative kurtosis of (a) is defined as:

in the formula:Tis the impulse signal period;Mis the shift number;m[0, M](ii) a Increase ofMThe number of algorithm sequence pulses is increased, taking into accountMToo large of an influence on the precision, the invention selectsM=7。

2) The actual signal is filtered so that the correlation kurtosis is maximized:

in the formula:y、xare respectively periodic signalsy _i Actual signalx _i The vector form of (1);f=[f ₁ , …, f _L ] ^T ；Lis a filter length parameter;l[0, L]。

3) solving the above equation is equivalent to solving

Finally, the result of the obtained filter coefficients is expressed by using a matrix form:

；

in the formula:

；

，r=[0, T, ∙∙∙, mT]；

。

4) the specific implementation process of the MCKD algorithm is as follows:

4.1) initializing the deconvolution periodTNumber of displacementsMAnd filter lengthLThe like;

4.2) calculating the input signalxIs/are as followsX _T ，X ₀ ^T ，(X ₀ X ₀ ^T ) ^-1 ；

4.3) calculating the filtered output signaly；

4.4) according toyCalculating outψAndβ；

4.5) update the FilterfThe coefficient of (a);

4.6) correlation kurtosis value delta of the filtered signal before and after filteringCK _M (T) If the value is less than the threshold value, ending the iteration; otherwise, returning to the step 4.3.

FIG. 8 is a graph showing PSO algorithm optimized MCKD parameter iteration, the particle swarm optimization converges in the 17 th generation, and the obtained optimal parameter combinations are [820, 267]. Setting the filter length parameter of the MCKD algorithm to 820 and the deconvolution periodTAt 267, MCKD analysis was performed on fraction 9.

Step five: according to a theoretical formula for calculating the fault characteristic frequency of the rolling bearing given in the precision diagnosis technology of the rolling bearing fault and the specific bearing parameters of the fault bearing ER-12K shown in the table 1, the multiple relation between the fault characteristic frequency and the rotating frequency of the used fault bearing is calculated and obtained and is shown in the table 2.

TABLE 1 Fault bearing concrete parameter Table

TABLE 2 conversion multiple of fault frequency

According to the rotation frequency of the shaft where the fault bearing is located, the calculated fault frequency of the inner ring is 48.44 Hz. Fig. 9 is a time domain waveform after MCKD analysis, from which it is obvious that a fault impact component can be observed, in the figure, a total of 8 impact periods is 0.165s, and the reciprocal of a single period is just the fault frequency. Fig. 10 is an envelope spectrum after MCKD analysis, in which a fault frequency of 48.44Hz and its frequency multiplication are clearly visible, so that it is determined that the rolling bearing is an inner ring fault.

In conclusion, the rolling bearing weak fault diagnosis method based on the PSO-VMD-MCKD can successfully extract the bearing weak fault characteristics covered by strong background noise. Due to the combination of the VMD and the MCKD, the weak fault diagnosis of the bearing can be realized more accurately; the PSO algorithm can realize the selection of VMD \ MCKD parameters.

The above description is only for the best mode of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (10)

1. A rolling bearing weak fault diagnosis method based on PSO-VMD-MCKD is characterized by comprising the following steps: the method comprises the following steps:

the method comprises the following steps: measuring rotating mechanical equipment by using an acceleration sensor to obtain a vibration acceleration signal;

step two: optimizing in VMD algorithm using PSO algorithmαAndKthen VMD decomposition is carried out on the collected vibration signals;

step three: based on the result of the VMD after the weak fault signal is decomposed, selecting the optimal modal component by utilizing the maximum criterion of the envelope spectrum peak factor;

step four: determining PSO versus MCKD algorithm according to the prominent frequency range in the envelope spectrum of the optimal modal componentTBased on the parameter optimization result, the MCKD further enhances the fault impact component in the optimal component;

step five: and extracting the fault characteristics of the rolling bearing through the envelope spectrum, and comparing the fault characteristics with the theoretical bearing fault frequency in the transmission system to obtain a diagnosis result.

2. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 1, characterized in that: the vibration signal is a radial vibration acceleration signal of the transmission shaft.

3. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 1, characterized in that: the VMD algorithm decomposes an actual signal into optimal solutions by iteratively searching in a variational modelKA discrete modeu _k And determining the center frequency of each modal componentω _k And a bandwidth; the MCKD algorithm takes the signal correlation kurtosis as an optimization target, completes the deconvolution operation of the vibration signal through iteration, highlights continuous pulses covered by strong noise in the signal, and extracts a characteristic signal representing the vibration characteristic of the rolling bearing from the signal with low signal-to-noise ratio.

4. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 1, characterized in that the optimization schemes all adopt a PSO algorithm to globally optimize parameters in the VMD and the MCKD; the PSO algorithm adopts inertiaWeight ofϖA standard PSO algorithm with a concave function variation; the specific speed updating formula and the position updating formula are as follows:

in the formula:o=1，2，3，…，O(ii) a O is the population scale;hin order to be able to perform the number of iterations,His the maximum iteration number; are particlesoFirst, thehIn the sub-iterationdThe velocity of the dimension;ϖ _max is the maximum weight of the weight to be given,ϖ _min is the minimum weight;c ₁ andc ₂ is a learning factor;ηis between the interval [0, 1]The random number of (2); is as followshParticles in sub-iterationsoIn the first placedThe position of the individual extreme point of the dimension; is as followshParticles in sub-iterationsoIn thatdThe current position of the dimension; is as followshThe whole population in the second iterationdThe location of the global extremum of the dimension.

5. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 4, characterized in that: setting specific parameters of the standard PSO algorithm: learning factor c ₁ =c ₂ =2, population sizeO=30, maximum number of iterationsH=20, maximum weightϖ _max =0.9, minimum weightϖ _min =0.4。

6. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 4, characterized in that: penalty factor in optimization range of parameter in VMD algorithmαHas an optimization range of [100, 2000 ]]Number of componentsKHas an optimization range of [3, 10 ]]。

7. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 6, characterized in that: the PSO algorithm optimizes fitness functions of the VMD and the MCKD to be envelope spectrum peak value factors, and after the VMD is decomposed, the size of the envelope spectrum peak value factor of the component is calculated, so that the optimal component is compared;

wherein the envelope spectrum crest factor defines:

in the formula:X(z) Is an envelope spectrum inf _r ^′ , γf _i ^′ ]Amplitude of the frequency range，f _r ^′ The value is greater than the rotating frequency of the shaft where the fault bearing is located;f _i ^′ the failure frequency of the maximum bearing of the traditional system is obtained; z=1, 2, …, Z；γtaking 4-8.

8. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 7, characterized in that: after the optimal component is subjected to envelope spectrum analysis, determining subsequent MCKD parameters according to the prominent frequency range in the spectrogramTThe optimization range of (1); the MCKD parameterTIs given by the formulaT=f _s /f _i Determining, wherein,f _s in order to be able to sample the frequency,f _i for the fault frequency, the unknown fault frequency is replaced by the prominent frequency; filter length parameter in the MCKD algorithmLHas an optimization range of [100, 1000%]。

9. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 8, characterized in that: the fault frequency specifically comprises an outer ring fault frequency, an inner ring fault frequency, a rolling body fault frequency or a retainer fault frequency.

10. The PSO-VMD-MCKD-based rolling bearing weak fault diagnosis method according to claim 9, characterized in that: the method comprises the following steps of comparing the envelope spectrum of the optimal component analyzed by the MCKD with the fault frequency to obtain a fault diagnosis result of the rolling bearing, and specifically comprises the following steps:

obtaining an envelope spectrogram by using the signal;

judging whether the frequency range in the spectrogram contains the outer ring fault frequency, the inner ring fault frequency, the rolling body fault frequency, the retainer fault frequency and respective integral multiple frequencies;

if yes, outputting fault prompt information;

if not, outputting normal prompt information;

and the fault diagnosis result comprises the fault prompt information and the normal prompt information.

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