CN115855508A - Bearing fault diagnosis method based on arithmetic optimization variational modal decomposition - Google Patents
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Abstract
The invention discloses a bearing fault diagnosis method based on arithmetic optimization variational modal decomposition, which comprises the steps of firstly initializing parameters of an arithmetic optimization algorithm AOA and a variational modal decomposition VMD algorithm; improving the endpoint effect of the variational modal decomposition through a Pearson correlation coefficient theory; selecting the minimum enveloping entropy as a fitness function, optimizing the VMD by AOA to enable the signal to be subjected to adaptive decomposition to obtain a plurality of modal components IMF, selecting the optimal IMF according to the maximum correlation kurtosis value, and finally performing Hilbert enveloping demodulation on the optimal IMF component to obtain the fault frequency. The invention considers the problem that the endpoint effect and the algorithm parameter of the VMD algorithm are difficult to select, proposes to use the Pearson correlation coefficient theory to improve the endpoint effect of the variation modal decomposition, and optimizes the variation modal decomposition parameter by the AOA to realize the signal self-adaptive decomposition. Experiments show that the method can more accurately extract fault characteristic information and avoid serious accidents.
Description
Technical Field
The invention belongs to the technical field of bearing fault diagnosis, and particularly relates to a bearing fault diagnosis method based on arithmetic optimization variational modal decomposition.
Background
The electromechanical device is constructed without the need for rolling bearings, which can greatly affect the safe production of the device. The working environment of the rolling bearing is complex, and according to research, 30% of faults of the rotating machine are caused by the rolling bearing, so that the improvement of the accuracy of bearing fault diagnosis is very important.
In the early stage of the failure of the rolling bearing, a periodic impact signal is generated, but the periodic impact signal is often interfered by strong noise, so that the vibration signal is subjected to pretreatment and noise reduction treatment. In recent years, after the advent of wavelet denoising, a number of adaptive signal denoising methods have been proposed. Huang et al propose a noise reduction method of empirical mode decomposition algorithm, which recursively decomposes a fault signal into a plurality of IMF components, but EMD has problems of mode aliasing, over-decomposition, under-decomposition, and the like. The Variational Modal Decomposition (VMD) adopts a non-recursive modal decomposition method, reduces modal aliasing generated by EMD due to recursive decomposition, and has the characteristic of self-adaptive filtering. VMD decomposition, however, creates end-point effects problems and problems where the selection of algorithm parameters directly affects the accuracy of the decomposition.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems that the early fault of a rolling bearing is weak and the fault characteristics are difficult to extract due to the influence of noise, the invention aims to provide a bearing fault diagnosis method based on the arithmetic optimization VMD (variable Mode Decomposition), so that the influence that the traditional VMD algorithm needs to select parameters manually is avoided, and the fault frequency can be extracted more accurately in the complex noise environment
The technical scheme is as follows: the bearing fault diagnosis method based on the arithmetic optimization variational modal decomposition obtains the fault frequency of a target rolling bearing by executing the following steps based on the vibration signal of the target rolling bearing, and further diagnoses the fault type of the target rolling bearing;
step 1: acquiring a vibration signal of a target rolling bearing;
step 2: improving the endpoint effect of the variation modal decomposition through a Pearson correlation coefficient theory;
and 3, step 3: initializing an arithmetic optimization algorithm and variational modal decomposition parameters; carrying out variational modal decomposition on a vibration signal of the target rolling bearing based on variational modal decomposition to obtain a plurality of IMF components, and optimizing variational modal decomposition parameters by an arithmetic optimization algorithm to obtain a plurality of IMF components in an optimal parameter combination of a fitness value;
and 4, step 4: respectively calculating a correlation kurtosis value for each IMF component in the optimal parameter combination of the fitness values, and screening out the modal component with the maximum correlation kurtosis value;
and 5: and performing Hilbert envelope demodulation by using the modal component obtained by screening to obtain a demodulated spectral diagram, and extracting the fault frequency of the target rolling bearing from the demodulated spectral diagram so as to diagnose the fault of the target rolling bearing.
Further, in step 2, adjusting the endpoint effect of the variational modal decomposition by the pearson correlation coefficient theory specifically includes the following steps:
step 2.1: starting from the left end point to the second extreme point N of the vibration signal 1 The length of vibration signal W 1 Searching the waveform M with the maximum Pearson correlation coefficient in a signal interval for a reference signal i The calculation formula of the pearson correlation coefficient is as follows:
wherein Cov (X, Y) represents the covariance of X and Y, var [ X ] is the variance of X, and Var [ Y ] is the variance of Y, and the closer the absolute value of r (X, Y) is to 1, the higher the degree of correlation between X and Y is;
step 2.2: taking the right end point as an end point to the left penultimate point N of the vibration signal 2 The length of vibration signal W 2 Searching the waveform S with the maximum Pearson correlation coefficient in the signal interval as a reference signal i ；
Step 2.3: will M i The appropriate length of the left side is translated to the left of the left end point, S i The appropriate length of the right side translates to the right of the right endpoint.
Further, step 3 specifically includes the following steps:
step 3.1: setting initialization parameters of an arithmetic optimization algorithm; the control parameter mu is fixed to 0.499, the sensitive parameter alpha =5, the population size is set to 5, and the iteration number is 20;
step 3.2: initializing ranges of VMD algorithm parameters k and α, wherein k = [2,20], α = [200,10000];
step 3.3: obtaining K modal components and a penalty factor alpha by utilizing the initialized variational modal decomposition parameters to carry out variational modal decomposition on the vibration signal of the target rolling bearing;
step 3.4: calculating the sum of the envelope entropy values of the K modal components to be the fitness value of the parameter [ K, alpha ] in the group;
step 3.5: judging whether the local search or the global search is carried out according to the calculation of an accelerated optimization function MOA of an arithmetic optimization algorithm, and iterating the step 3.3 and the step 3.4 to update and store the parameter combination with the optimal fitness value; if the terminal condition is met, the calculation is finished to obtain the global optimal fitness value, and the corresponding decomposition layer number k and the penalty factor alpha are the optimal parameters of the variational modal decomposition.
Further, the specific process of step 3.3 is as follows:
the variational modal decomposition algorithm is composed of construction and solution of variational problems, and by constructing the variational problems, bandwidth and frequency are updated, and the sum of all modal components is minimized, and the variational problems are shown in formula (2)
In the formula u k Representing the intrinsic mode function, w k Representing the central frequency of each modal component, converting the constraint variation problem into an unconstrained problem through a Lagrange multiplier and a quadratic penalty term, updating each modal component by using an alternative direction multiplier, and solving the saddle point u of a Lagrange function k ，w k The iterative formula of (a) is as follows:
converting time domain and frequency to obtain modal by using Parseval/Plancherel Fourier equidistant transformation principleComponent u k ：
Center frequency w k ：
Lagrange multiplier:
the above steps are circulated until the condition (8) is satisfied
Further, in step 3.4, the envelope entropy is calculated as follows:
in the formula, E p Representing the envelope entropy, H represents the hilbert transform of the signal;
is the envelope sequence signal of the signal x (j) after hilbert transform.
Further, the arithmetic optimization algorithm comprises the following specific steps:
step 6.1: initializing a population, wherein the number of the preset population is m, the dimension of the population is n, an m multiplied by n search space is formed, and a mathematical formula model is shown as a formula (11)
Before iterative search, an arithmetic optimization algorithm judges whether local search or global search is carried out according to the calculation of a mathematical accelerated optimization function (MOA) of a formula (12), a random number m between 0 and 1 is taken, if m is smaller than the MOA, global search is carried out, namely an exploration phase, and when m is not smaller than the MOA, local search is carried out, namely a development phase;
in the formula I max Representing the maximum algebra of population iteration; i represents the current number of iterations; m _ max and m _ min respectively represent the maximum value and the minimum value which can be taken by the mathematical acceleration optimization function, and respectively take the values of 1 and 0.2;
step 6.2, a surveying phase; by using two operators of multiplication and division, the mathematical model is shown in equations (13) and (14):
in the formula x m,n (i + 1) indicates that when the iteration number is i +1, the position of the mth solution is the nth dimension, best (x) n ) The optimal solution is shown to be positioned at the nth dimension, epsilon is a minimum value, the condition that the denominator is invalid is prevented, and r 2 Is a random number, UB, between 0 and 1 n And LB n Respectively representing the maximum value and the minimum value which can be taken by the population in the jth dimension, avoiding the occurrence of boundary crossing after population iteration, and generally setting the value of u to be 0.499; MOP is the probability of the numerical optimizer, and the formula of the calculation is shown as (15)
Wherein alpha is a sensitive parameter and represents the global search precision in the iterative process of the algorithm;
and 6.3, in the development stage, searching in small step by using an addition operator and a subtraction operator, wherein mathematical models are shown as formulas (16) and (17)
In the formula best (x) n ) Indicates that the optimal solution is at the nth dimension position, r 3 Is a random number between 0 and 1.
Further, in step 4, the calculating of the correlation kurtosis value is specifically as follows:
x represents the sensor passing noise e n Then, the received noise-containing signal, y represents the original fault signal without noise interference, h represents the response of the original fault signal after noise interference, and x represents the formula (18):
not counting e n The maximum correlation kurtosis deconvolution algorithm is considered to find the best non-recursive filter, and the impulse signal y is expressed as:
wherein the filter coefficient of L; an objective function maximizing the correlation kurtosis value is expressed as equation (20);
has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the method adopts the Pearson coefficient to improve the VMD endpoint effect, and effectively reduces the waveform divergence at the IMF component endpoint; the AOA-VMD algorithm is used for effectively solving the problems of over-decomposition and under-decomposition caused by the fact that parameters need to be manually selected in the traditional VMD algorithm. The AOA algorithm utilizes addition, subtraction, multiplication and division in mathematics to perform local search and global search, and has the advantages of high convergence speed, high precision and the like. The maximum correlation kurtosis value is used as the selection standard of the IMF, so that the situation that the change characteristics of impact components cannot be fully represented by the traditional kurtosis index is avoided, and the correlation kurtosis well keeps the characteristic information of signals and can reflect the periodic impact characteristics.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a time domain waveform diagram of an outer ring fault signal;
FIG. 3 time domain diagrams of two IMF components resulting from VMD decomposition before and after improving the end-point effect;
FIG. 4 shows two frequency domain plots of IMF components from VMD decomposition before and after improving the end-point effect;
FIG. 5 an iterative graph of AOA optimized VMD;
FIG. 6 is an optimized VMD decomposition time domain diagram;
figure 7 is a graph of the demodulated spectrum of the optimal IMF component.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
Examples
The experimental data adopts the experimental data of the bearing vibration center of the university of Kaesichu, USA, the bearing model is SKF-6205, the rotating speed is 1797r/min, the load is 0HP, the sampling frequency is 12Khz, and the fault size is 0.007inch. The data comprises normal data, inner ring faults, outer ring faults and rolling body faults. The frequency of failure of the outer ring bearing can be calculated to be 107.36Hz, and the frequency of failure of the inner ring bearing can be calculated to be 162.19Hz. Considering that the noise-containing ratio of the Kaiseku data set is relatively small and is inevitably interfered by noise in the actual working condition, 5db of Gaussian white noise is added on the basis of the Kaiseku data set as experimental data. The time domain of the outer circle noisy signal is shown in fig. 2;
the invention relates to a bearing fault diagnosis algorithm based on an arithmetic optimization VMD, which comprises the following steps:
the method comprises the following steps: initializing parameters of an arithmetic optimization algorithm and a variational modal decomposition.
Step two: the endpoint effect of Variational Modal Decomposition (VMD) is improved by pearson's correlation coefficient theory.
Taking the simulation signal y = sin (2 × pi × 24 × t) +0.3sin (2 × pi × 30 × t) as a research object, and directly performing VMD decomposition on the simulation signal to obtain two modal components IMF1 and IMF2, as shown in the upper and lower parts of (a) in fig. 3, respectively, it can be seen that amplitude oscillation occurs at the left and right end points of the components IMF1 and IMF 2; the frequency domain diagrams of the two modal components IMF1 and IMF2 obtained by directly performing VMD decomposition on the simulation signal are respectively shown in the upper part and the lower part of (a) in fig. 4, and it can be seen from the diagrams that the frequency domain diagram corresponding to the IMF1 component has a central frequency of 30Hz, aliasing of a frequency of 24Hz occurs, and the frequency domain diagram corresponding to the IMF2 component has a central frequency of 24Hz. Performing VMD decomposition on the simulation signal after the endpoint effect improvement to obtain IMF1 and IMF2 components, wherein the IMF1 and IMF2 components are respectively shown as an upper part and a lower part in (b) in fig. 3, and the IMF1 and IMF2 components can be seen from the figure that amplitude oscillation at the endpoint does not occur; the frequency domain diagrams of the IMF1 component and the IMF2 component obtained by VMD decomposition after the endpoint effect is improved are respectively shown as an upper part and a lower part in (b) in fig. 4, and it can be seen that the frequency domain diagram central frequency corresponding to the IMF1 component is 30Hz, the frequency domain diagram central frequency corresponding to the IMF2 component is 24Hz, and modal aliasing does not occur.
In the second step, the pearson correlation coefficient theory improves the endpoint effect of the VMD by the following specific process:
step 2.1, using the signal W1 with the length from the left end point as the starting point to the second extreme point N1 of the signal as the reference signal, searching the waveform Mi with the maximum pearson correlation coefficient in the signal interval, wherein the calculation formula of the pearson correlation coefficient is as follows:
wherein Cov (X, Y) represents the covariance of X and Y, var [ X ] is the variance of X, and Var [ Y ] is the variance of Y. The closer the absolute value of r (X, Y) is to 1, the higher the degree of correlation between X and Y.
And 2.2, taking the signal W2 from the right end point as an end point to the last extreme point N2 on the left side of the signal as a reference signal, and searching for the waveform Si with the maximum Pearson correlation coefficient in a signal interval.
Step 2.3, translate the appropriate length on the left side of Mi to the left side of the left endpoint, translate the appropriate length on the right side of Si to the right side of the right endpoint.
Step three: and carrying out variation modal decomposition on the vibration signal of the target rolling bearing to obtain a plurality of IMF components. And optimizing the variation modal decomposition parameters based on an arithmetic optimization algorithm to obtain a parameter combination with the optimal fitness value. The specific process is as follows:
step 3.1: setting initialization parameters of an arithmetic optimization algorithm; the control parameter mu is fixed to 0.499, the sensitive parameter alpha =5, the population size is set to 5, and the iteration number is 20;
step 3.2: initializing ranges of VMD algorithm parameters k and α, where k = [2,20], α = [200,10000] to avoid under-decomposition of the signal;
step 3.3: k IMF components and a penalty factor alpha are obtained after the variation modal decomposition parameters are initialized, and variation modal decomposition is carried out on the vibration signals of the target rolling bearing; the variation modal decomposition comprises the following specific processes:
the VMD algorithm is composed of construction and solution of variation problems. Updating bandwidth and frequency and minimizing the sum of all modal components by constructing a variation problem as shown in the following formula:
where uk denotes the eigenmode function and wk denotes the center frequency of the respective modal component. The constraint variational problem is converted into an unconstrained problem through Lagrange multipliers and quadratic penalty terms, as shown in the following formula:
updating respective modal classifications with alternating direction multipliers
Updating the center frequency wk
Updating lagrange multipliers
The above steps are circulated until the condition (6) is satisfied
Step 3.4: and calculating the sum of the envelope entropy values of the K modal components to obtain the fitness value of the parameter [ K, alpha ] in the group.
The envelope entropy is calculated as follows:
in the formula, E p Representing the entropy of the envelope, H representing the hilbert transform of the signal;
is the envelope sequence signal of the signal x (j) after hilbert transform.
Step 3.5: judging whether the local search or the global search is carried out according to the calculation of an accelerated optimization function MOA of an arithmetic optimization algorithm, and iteratively carrying out the step 3.1.3 and the step 3.1.4 to update and store the parameter combination with the optimal fitness value; if the terminal conditions are met, the calculation is finished to obtain the global optimal fitness value, and the corresponding decomposition layer number k and the punishment factor alpha are the optimal parameters of the variational modal decomposition. The decomposition mode number and the penalty parameter alpha of the VMD are optimized by using the AOA, the flow chart is shown as figure 1, the iteration of the fitness value is shown as figure 5, and the fitness value is shown as figure 5 when the iteration number is 6Convergence is achieved. The IMF component obtained by the optimal parameter decomposition is shown in FIG. 6, and the optimal modal component u can be seen from FIG. 6 k The number of (t) is 3.
In step 3.5, the specific steps of the AOA algorithm are as follows:
step 3.5.1-initialize the population. The number of the preset population is m, the dimension of the population is n, an m multiplied by n search space is formed, and a mathematical formula model is shown as follows.
The arithmetic optimization algorithm judges whether to search locally or globally according to the calculation of a mathematical accelerated optimization function (MOA) as shown in the following formula before iterative search. And taking a random number m between 0 and 1, if m is smaller than the MOA, carrying out global search, namely an exploration phase, and when m is not smaller than the MOA, carrying out local search, namely a development phase.
In the formula, imax represents the maximum algebra of population iteration; i represents the current number of iterations; and m _ max and m _ min respectively represent the maximum value and the minimum value which can be obtained by the mathematical acceleration optimization function, and respectively take the values of 1 and 0.2.
Step 3.5.2-survey phase. The method mainly utilizes two operators of multiplication and division, and is suitable for global search with larger step length due to higher discrete degree of the multiplication operator and the division operator. The mathematical model is shown as follows:
where xm, n (i + 1) indicates that the position of the mth solution is the nth dimension when the iteration number is i + 1. best (xn) indicates that the optimal solution is located at the nth dimension position, and epsilon is a minimum value, so that the condition that the denominator is invalid is prevented. r2 is a random number between 0 and 1. UBn and LBn respectively represent the maximum value and the minimum value which can be obtained by the population in the jth dimension, and the occurrence of boundary crossing after population iteration is avoided. The value of u is typically set to 0.499; MOP is the numerical optimizer probability, and the formula of the calculation is as follows:
where α is a sensitive parameter, which represents the accuracy of global search in the iterative process of the algorithm, and is usually equal to 5.
Step 3.5.3, development phase. The small-step search is mainly carried out by utilizing an addition operator and a subtraction operator, and the small-step search is suitable for the local search with small step length and is easy to approach a target due to the fact that the dispersion degree of the addition operator and the subtraction operator is low. The mathematical model is shown as follows:
in the formula, best (xn) represents that the optimal solution is located at the nth dimension position, and r3 is a random number between 0 and 1.
Step four: and calculating a correlation kurtosis value for each modal component, and screening out the modal component with the maximum correlation kurtosis value.
In step four, the formula for deconvolving the maximum correlation kurtosis is as follows:
let x represent sensor passing noise e n And then receiving a noise-containing signal, wherein y represents an original fault signal which is not subjected to noise interference, and h represents a response of the original fault signal subjected to the noise interference. The noisy signal x is shown as follows:
not counting e n The maximum correlation kurtosis deconvolution algorithm can be regarded as finding the best non-recursive filter. The impact signal y can be expressed as:
wherein, the filter coefficient of L.
Then the objective function that maximizes the correlation kurtosis value can be expressed as:
step five: and performing Hilbert envelope demodulation by using the modal components obtained by screening to obtain a frequency domain diagram. Fig. 7 shows the frequency of rotation F of the rolling bearing r Bearing failure frequency F 0 And 2 frequency multiplication F 1 3 frequency multiplication F 2 And 4 frequency multiplication F 3 The method is obvious, and the actual condition of the bearing outer ring fault is verified to be the same.
Claims (7)
1. A bearing fault diagnosis method based on arithmetic optimization variational modal decomposition is characterized in that based on vibration signals of a target rolling bearing, the following steps are executed to obtain the fault frequency of the target rolling bearing, and then the fault of the target rolling bearing is diagnosed;
step 1: acquiring a vibration signal of a target rolling bearing;
and 2, step: improving the endpoint effect of the variational modal decomposition through a Pearson correlation coefficient theory;
and step 3: initializing an arithmetic optimization algorithm and a variation modal decomposition parameter; carrying out variational modal decomposition on a vibration signal of the target rolling bearing based on variational modal decomposition to obtain a plurality of IMF components, and optimizing variational modal decomposition parameters by an arithmetic optimization algorithm to obtain a plurality of IMF components in an optimal parameter combination of fitness values;
and 4, step 4: respectively calculating a correlation kurtosis value for each IMF component in the optimal parameter combination of the fitness values, and screening out the modal component with the maximum correlation kurtosis value;
and 5: and performing Hilbert envelope demodulation by using the modal component obtained by screening to obtain a demodulated spectral diagram, and extracting the fault frequency of the target rolling bearing from the demodulated spectral diagram so as to diagnose the fault of the target rolling bearing.
2. The method for diagnosing the bearing fault based on the arithmetically optimized variational modal decomposition according to claim 1, wherein in the step 2, the step of adjusting the end point effect of the variational modal decomposition through the Pearson's correlation coefficient theory specifically comprises the following steps:
step 2.1: starting from the left end point to the second extreme point N of the vibration signal 1 The length of vibration signal W 1 Searching the waveform M with the maximum Pearson correlation coefficient in a signal interval as a reference signal i The calculation formula of the pearson correlation coefficient is as follows:
wherein Cov (X, Y) represents the covariance of X and Y, var [ X ] is the variance of X, and Var [ Y ] is the variance of Y, and the closer the absolute value of r (X, Y) is to 1, the higher the degree of correlation between X and Y is;
step 2.2: taking the right end point as an end point to the left penultimate point N of the vibration signal 2 The length of vibration signal W 2 Searching the waveform S with the maximum Pearson correlation coefficient in the signal interval as a reference signal i ；
Step 2.3: will M i The appropriate length of the left side is translated to the left of the left end point, S i The appropriate length of the right side translates to the right of the right endpoint.
3. The bearing fault diagnosis method based on the arithmetical optimization variational modal decomposition according to claim 1, wherein the step 3 specifically comprises the following steps:
step 3.1: setting initialization parameters of an arithmetic optimization algorithm; the control parameter mu is fixed to be 0.499, the sensitive parameter alpha =5, the population size is set to be 5, and the iteration number is 20;
step 3.2: initializing ranges of VMD algorithm parameters k and α, wherein k = [2,20], α = [200,10000];
step 3.3: obtaining K modal components and a penalty factor alpha by utilizing the initialized variational modal decomposition parameters to carry out variational modal decomposition on the vibration signal of the target rolling bearing;
step 3.4: calculating the sum of the envelope entropy values of the K modal components to be the fitness value of the parameter [ K, alpha ] in the group;
step 3.5: judging whether the local search or the global search is carried out according to the calculation of an accelerated optimization function MOA of an arithmetic optimization algorithm, and iterating the step 3.3 and the step 3.4 to update and store the parameter combination with the optimal fitness value; if the terminal condition is met, the calculation is finished to obtain the global optimal fitness value, and the corresponding decomposition layer number k and the penalty factor alpha are the optimal parameters of the variational modal decomposition.
4. The bearing fault diagnosis method based on the arithmetical optimization variational modal decomposition according to claim 3, characterized in that the specific process of step 3.3 is as follows:
the variational modal decomposition algorithm is composed of construction and solution of variational problems, and by constructing the variational problems, bandwidth and frequency are updated, and the sum of all modal components is minimized, and the variational problems are shown in formula (2)
In the formula u k Representing the intrinsic mode function, w k Representing the central frequency of each modal component, converting the constraint variation problem into an unconstrained problem through a Lagrange multiplier and a quadratic penalty term, updating each modal component by using an alternative direction multiplier, and solving the saddle point u of a Lagrange function k ，w k The iterative formula of (a) is as follows:
converting time domain and frequency to obtain modal component u by using Parseval/Plancherel Fourier equidistant transformation principle k ：
Center frequency w k ：
Lagrange multiplier:
the above steps are circulated until the condition (8) is satisfied
5. The bearing fault diagnosis method based on the arithmetically optimized variational modal decomposition according to claim 3, wherein in step 3.4, the envelope entropy is calculated as follows:
in the formula, E p Representing the envelope entropy, H represents the hilbert transform of the signal;
is the envelope sequence signal of the signal x (j) after hilbert transform.
6. The bearing fault diagnosis method based on the arithmetical optimization variational modal decomposition according to claim 3, wherein the arithmetical optimization algorithm comprises the following specific steps:
step 6.1: initializing a population, wherein the number of the preset population is m, the dimension of the population is n, an m multiplied by n search space is formed, and a mathematical formula model is shown as a formula (11)
Before iterative search, an arithmetic optimization algorithm judges whether local search or global search is carried out according to the calculation of a mathematical accelerated optimization function (MOA) of a formula (12), a random number m between 0 and 1 is taken, if m is smaller than the MOA, global search is carried out, namely an exploration phase, and when m is not smaller than the MOA, local search is carried out, namely a development phase;
in the formula I max Representing the maximum algebra of population iteration; i represents the current number of iterations; m _ max and m _ min respectively represent the maximum value and the minimum value which can be taken by the mathematical acceleration optimization function, and respectively take the values of 1 and 0.2;
step 6.2, a surveying phase; by using two operators of multiplication and division, the mathematical model is shown in equations (13) and (14):
in the formula x m,n (i + 1) indicates that when the iteration number is i +1, the position of the mth solution is the nth dimension, best (x) n ) Showing the position of the optimal solution in the nth dimension, and epsilon is a minimum value to prevent the condition that the denominator fails, r 2 Is a random number, UB, between 0 and 1 n And LB n Respectively representing the maximum value and the minimum value which can be taken by the population in the jth dimension, avoiding the occurrence of boundary crossing after population iteration, and generally setting the value of u to be 0.499; MOP is the probability of the numerical optimizer, and the formula of the calculation is shown as (15)
Wherein alpha is a sensitive parameter and represents the global search precision in the iterative process of the algorithm;
and 6.3, in the development stage, searching in small step by using an addition operator and a subtraction operator, wherein mathematical models are shown as formulas (16) and (17)
In the formula best (x) n ) Indicates that the optimal solution is at the nth dimension position, r 3 Is a random number between 0 and 1.
7. The method for diagnosing the bearing fault based on the arithmetically optimized variational modal decomposition according to claim 1, wherein in the step 4, the calculated correlation kurtosis value is specifically as follows:
x represents the sensor passing noise e n Then, the received noise-containing signal, y represents the original fault signal without noise interference, h represents the response of the original fault signal after noise interference, and x represents the formula (18):
not counting e n The maximum correlation kurtosis deconvolution algorithm is considered to find the best non-recursive filter, and the impulse signal y is expressed as:
wherein the filter coefficient of L; an objective function maximizing the correlation kurtosis value is expressed as equation (20);
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