CN111272429A - Bearing fault diagnosis method - Google Patents

Bearing fault diagnosis method Download PDF

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CN111272429A
CN111272429A CN202010142396.9A CN202010142396A CN111272429A CN 111272429 A CN111272429 A CN 111272429A CN 202010142396 A CN202010142396 A CN 202010142396A CN 111272429 A CN111272429 A CN 111272429A
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CN111272429B (en
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黄海松
范青松
韩正功
艾彬彬
李玢
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Abstract

The invention discloses a bearing fault diagnosis method, which comprises the following steps: extracting fault characteristics of the vibration signals of the rolling bearing; updating the punishment parameters and the kernel function parameters of the classifier of the SVM according to a training set and an IWOA algorithm: according to the obtained optimal punishment parameter
Figure DEST_PATH_IMAGE001
And optimal kernel function parameters
Figure DEST_PATH_IMAGE002
Constructing a test model of the SVM, and optimizing penalty parameters according to a test set
Figure 230023DEST_PATH_IMAGE001
And optimal kernel function parameters
Figure 147163DEST_PATH_IMAGE002
And determining the fault result of the bearing after ten-fold cross validation by taking the longest optimization time, the shortest optimization time, the average accuracy and the standard deviation as evaluation standards. The bearing fault diagnosis method is strong in bearing fault diagnosis capability and high in identification accuracy.

Description

Bearing fault diagnosis method
Technical Field
The invention belongs to the technical field of machinery, and particularly relates to a bearing fault diagnosis method.
Background
The rolling bearing is one of the most common transmission parts in many parts of mechanical equipment, and belongs to a vulnerable and consumable part. In particular, in machines operating at high speeds, the diagnosis of faults in bearings plays an important role in ensuring their safe and reliable operation. Therefore, the bearing fault diagnosis method has great significance in quickly, accurately and conveniently diagnosing the bearing fault and judging the fault type.
At present, scholars at home and abroad make a great deal of research on relevant theories and technologies of fault diagnosis of rolling bearings. By adopting the rolling bearing fault diagnosis method based on the singular value entropy criterion of the Ensemble Empirical Mode Decomposition (EEMD), the category characteristic intervals of different working states of the rolling bearing can be clearly divided. A Complete integrated Empirical mode decomposition (CEEMDAN) method of self-Adaptive white Noise is adopted to decompose a Noise reduction signal, and weak fault characteristic information of the rolling bearing is effectively extracted. The Fuzzy Entropy (Fuzzy entry ) feature vector is subjected to visual dimensionality reduction through a principal component analysis method and then is used as the input of a clustering algorithm, so that fault diagnosis of the rolling bearing is realized. And by utilizing a rolling bearing slight fault diagnosis method combining Probability Principal Component Analysis (PPCA) with empirical wavelet transform, main fault characteristic components of the bearing are extracted, strong background noise interference is removed, a fault signal is reconstructed, and fault characteristics are extracted. For parameter Optimization of a Support Vector Machine (SVM), the existing Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), and gray Wolf Algorithm (GWO) optimize a parameter C and a penalty factor σ, which have a large influence on classification accuracy in the SVM, all of which have a certain effect, and improve diagnosis accuracy of a bearing.
Whale Optimization Algorithm (WOA) is a novel group meta-heuristic Optimization Algorithm for simulating a hunting behavior of Whale with sitting head, which is proposed in 2016 by mirjarli S and the like, and the WOA Algorithm has the advantages of simple principle, simplicity and convenience in operation, easiness in implementation, few required adjustment parameters, robustness and the like, but the basic WOA Algorithm may have the defects of low convergence speed and stagnation in the later convergence period, and still needs to be further improved.
Disclosure of Invention
The invention aims to overcome the defects and provide the bearing fault diagnosis method which has strong bearing fault diagnosis capability and high identification accuracy.
The purpose of the invention and the main technical problem of solving the invention are realized by adopting the following technical scheme:
the invention relates to a bearing fault diagnosis method, which comprises the following steps:
(1) extracting fault characteristics:
1) obtaining a vibration signal of a bearing, and extracting an IMF modal component of the vibration signal by a CEEMDAN method of complete integration empirical mode decomposition of self-adaptive white noise;
2) determining the fuzzy entropy FuzzyEn of the IMF modal component extracted by CEEMDAN, reconstructing the original signal:
3) performing main feature extraction on the reconstructed signal through Probability Principal Component Analysis (PPCA) to remove redundant information;
4) taking a data set processed by PPCA as a feature vector, constructing a training set and a test set of a Support Vector Machine (SVM) in equal proportion and adding class labels;
(2) IWOA-SVM fault diagnosis:
1) constructing an SVM classifier model;
2) updating the penalty parameters and kernel function parameters of the classifier of the SVM according to the training set and the IWOA algorithm:
a. initializing parameters: initializing IWOA algorithm parameters a, AC, w, v, l, p, maximum number of iterations tmaxSearch space [ C ] of penalty parameter Cmin,Cmax]Sum kernel function sigma parameter search space [ sigma ]min,σmax]Where A and C are coefficient vectors, they are defined as:
A＝2a·r-a
C＝2·r (18)
wherein r represents a random number between [0,1], a represents a convergence factor which decreases linearly from 2 to 0 with increasing number of iterations, and rand () represents a random number between [0,1 ];
w is the inertial weight w ═ 1-rand ()/2 introduced from the PSO algorithm, v is the "flight" speed introduced, l is the random number in [ -1,1], p represents the random number between [0,1 ];
b. randomly generating the whale individuals with the initial population size N in the search space, and expressing the position of the ith whale in the D-dimensional space as
Figure BDA0002399536280000031
Let t be 1;
c. introducing w and v in PSO algorithm, calculating fitness values of individual whales, comparing, and recording prey position (optimal whale position) Y*The method comprises a prey surrounding stage, a bubble preying stage and a prey searching stage;
surrounding prey stage:
Figure BDA0002399536280000032
wherein t represents the current iteration, Y (t) represents the position of the individual whale in the t generation, Y*(t) represents the position of the optimal whale in the tth generation (prey position) and updates its own position with each iteration;
bubble predation phase (local search):
Figure BDA0002399536280000033
wherein D' ═ Y*(t) -w (t) Y (t) l, representing the ith whale toDistance of prey, b is the helical constant, l is [ -1,1 [ ]]In (1), p represents [0,1]]A random number in between;
hunter finding phase (global search):
Figure BDA0002399536280000034
in the formula, YrThe position of a random whale in the current population is determined;
d. updating the position of the whale at the head in the population: if p is less than 0.5 and | A | is less than 1, the whale head updates the current position of the whale head according to the formula (19), otherwise, the whale head updates according to the formula (21), and if p is more than or equal to 0.5, the whale head updates according to the formula (20);
e. updating IWOA algorithm parameters a, A, C, w, v, l and p;
f. calculating the fitness value of the whale individuals in the updated population, evaluating again, and re-determining new globally optimal whale individuals and the positions of the whale individuals;
g. judging whether the termination condition of the algorithm is met, namely whether the maximum iteration times are reached, and if not, skipping to the step c to continue the iteration; otherwise, ending, and outputting the global optimal Y*Obtaining the optimal punishment parameter CbestAnd an optimal kernel function parameter σbest；
3) According to the obtained optimal punishment parameter CbestAnd an optimal kernel function parameter σbestConstructing a test model of the SVM, and obtaining the optimal penalty parameter C according to the test set in the step (1)4) and the optimal penalty parameter C in the step (2)2)bestAnd an optimal kernel function parameter σbestAnd determining the fault result of the bearing after ten-fold cross validation by taking the longest optimization time, the shortest optimization time, the average accuracy and the standard deviation as evaluation standards.
The bearing fault diagnosis method comprises the following steps that (1) IMF modal components of the vibration signal are extracted through a complete integration empirical mode decomposition method CEEMDAN of self-adaptive white noise in step 1);
a. signal s [ n ] is analyzed by Empirical Mode Decomposition (EMD)]+δ0wi[n]Performing decomposition, wherein I takes a value in 1,2, I; delta0Is the standard deviation of the noise, wi-N (0,1), defining a first CEEMDAN modal component as:
Figure BDA0002399536280000041
b. calculating a first margin:
Figure BDA0002399536280000042
c. definition Ek[·]Continuing to utilize EMD for the signal r for the k-th modal component after EMD decomposition of the given signal1[n]+δ1E1(wi[n]) I1, 2, I, are decomposed until the first EMD component, δ, is solvedk(k ═ 1) the signal-to-noise ratio can be chosen at each stage, while defining a second CEEMDAN modal component:
Figure BDA0002399536280000043
d. when K is 1,2 …, K, the K-th margin is calculated:
Figure BDA0002399536280000044
e. reuse of EMD for signal rk[n]+δkEk(wi[n]) I-1, 2 …, I, until the first EMD component is solved and the k +1 th CEEMDAN modal component is defined:
Figure BDA0002399536280000051
f. turning to step d, the next k repeats steps d-f until the margin cannot be further decomposed, and the final margin can be expressed as:
Figure BDA0002399536280000052
where K is the total number of modal components, the original signal can be expressed as:
Figure BDA0002399536280000053
delta can be adjusted at each stageiAnd selecting noises with different signal-to-noise ratios, and finally extracting IMF modal components of the vibration signals through a CEEMDAN algorithm.
In the above bearing fault diagnosis method, in step (1)2), for the IMF modal component { t (i), i ═ 1,2 …, N } extracted by the CEEMDAN, FuzzyEn is calculated and the original signal is reconstructed:
Figure BDA0002399536280000054
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure BDA0002399536280000055
r is the similarity tolerance, for i, j ≠ 1,2, …, N-m +1, i ≠ j, calculates:
Figure BDA0002399536280000056
in the formula (I), the compound is shown in the specification,
Figure BDA0002399536280000057
is a vector
Figure BDA0002399536280000058
And
Figure BDA0002399536280000059
the distance between i is averaged for each i and a function is defined as:
Figure BDA00023995362800000510
according to the bearing fault diagnosis method, the main features are extracted and the redundant information is eliminated in the step (1)3), and the method specifically comprises the following steps:
for a data vector set x consisting of N d-dimensional vectors, q-dimensional hidden variables y are introduced to be related to the q-dimensional hidden variables x:
x＝Wy+u+ε (12)
wherein ε represents the observation noise vector ε -N (0, σ I)2) Hidden variables y to N (0, I) (I represents an identity matrix),
Figure BDA0002399536280000061
is a sample mean value, and W is a d × q parameter matrix;
the likelihood function for the observed data is:
Figure BDA0002399536280000062
wherein C is WWT+σ2IdS is a covariance matrix of an observation sample;
unknown parameters W, σ2The maximum likelihood method can be used for estimation, and the optimal solution is as follows:
Figure BDA0002399536280000063
W＝Uq(Λq-σ2Iq)1/2R (14)
wherein R is an arbitrary orthogonal matrix; lambda [ alpha ]kIs the kth maximum eigenvalue of the covariance matrix of the sample; lambdaq＝diag(λ1,λ2,K,λq)；λkCorresponding feature vector as UqThe kth column vector (k ═ 1,2K q).
The bearing fault diagnosis method comprises the following steps of (2)1) constructing an SVM classifier model:
a. given a set of training sets { (x)i,yi)1, 2, …, N, where the input vector xi∈RdD is the dimension of the input, yiE { -1, +1} is a classIdentifying labels, and constructing a classification function by utilizing an SVM through training samples:
y＝ωTΦ(x)+b (15)
wherein, omega represents a high-dimensional normal vector, and b represents an offset;
when the data cannot be linearly separated, a relaxation variable ξ is introducediAllowing error classification, and simultaneously introducing a penalty factor C to punish the error classification, so that the hyperplane problem of the SVM optimal classification is converted into a minimum value:
Figure BDA0002399536280000064
Figure BDA0002399536280000065
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure BDA0002399536280000071
wherein, the sigma is an RBF kernel function parameter.
Compared with the prior art, the invention has obvious advantages and beneficial effects. According to the technical scheme, the vibration signal of the bearing is obtained, and the IMF modal component of the vibration signal is extracted through a CEEMDAN method of complete integration empirical mode decomposition of self-adaptive white noise; determining a fuzzy yEn post-reconstruction signal of the modal component, eliminating noise in the reconstruction signal and reducing feature dimension by using PPCA, and constructing a training set and a test set of a Support Vector Machine (SVM) by using the reconstructed signal as a feature vector; updating the punishment parameters and kernel function parameters of the classifier of the SVM according to the training set and the IWOA algorithm; the SVM determines the fault result of the bearing according to the test set, the punishment parameter and the kernel function parameter, so that the problems of low efficiency and low precision of bearing fault diagnosis are solved, and the efficiency and the precision of fault identification of the rolling bearing are improved.
The CEEMDAN algorithm is based on EEMD and it enables an accurate reconstruction of the original signal and it requires less than half of the screening iterations compared to EEMD, thus reducing the computational cost. The method adds a de-equalization algorithm in vector reconstruction by using the fuzzy entropy FuzzyEn, and replaces a hard threshold criterion by using a fuzzy membership function, so that the method is less dependent on parameter selection and data length, is more robust to noise, has more stable entropy value, and has been successfully used in the field of rolling bearing fault diagnosis. In the signal feature extraction step, the complexity of signals of different fault types is different, and the fuzzy En values of the signals are also different. Therefore, the mean value of the fuzzy is selected as the characteristic of the original signal, and a foundation is laid for the next step of constructing a training set and a testing set.
The method is characterized in that Probability Principal Component Analysis (PPCA) is utilized, which is a popularization of PCA in probability, non-principal component factors discarded in the traditional PCA are introduced into an implicit variable model in a noise variance mode to be solved, and after probability functions of principal components and errors are determined, parameters are estimated through an Expectation Maximization (EM) algorithm, so that an optimal probability model is established.
The PPCA adopted can eliminate noise, simultaneously retain original signal characteristics, even enhance the capability, has higher running speed than PCA and better characteristic extraction effect than PCA, can avoid information redundancy, reduces the dimension, and is applied to the fields of characteristic extraction, modal identification and the like.
An SVM with good performance is constructed, and the punishment factor C and the RBF kernel function parameter sigma are reasonably selected, so that the precision of the SVM classifier can be effectively improved.
Inertia weight w and flight speed v in PSO algorithm are introduced to update the position of whale in WOA algorithm, so that search space can be explored randomly and the optimal penalty parameter C of SVM can be searched more efficientlybestAnd an optimal kernel function parameter σbest。
In conclusion, in order to effectively improve the accuracy of bearing fault diagnosis, the method adopts a CEEMDAN-fuzzy En-PPCA-based feature extraction method and an IWOA-SVM bearing fault diagnosis model for optimizing vector machine parameters by improving a whale optimization algorithm aiming at nonlinear and non-stable bearing fault signals. CEEMDAN is applied to reconstruction of fault vibration signals, fuzzy En entropy values are applied to distinguishing characteristic parameters of different fault states of the bearing, PPCA is adopted to extract main characteristics of the bearing fault, and experiments prove that a better early-stage preprocessing effect is obtained. Meanwhile, four fault diagnosis methods are also compared through experiments: GA. The PSO, WOA and IWOA-SVM, and experimental results prove that the method has the advantages of strong optimizing capability and high convergence rate, solves the problems of low convergence rate and easiness in falling into local optimization of the traditional optimization algorithm, and has stronger bearing fault diagnosis capability and higher identification accuracy. The feasibility and the superiority of the IWOA algorithm on SVM parameter optimization in bearing fault diagnosis are verified, the popularization on engineering application is facilitated, and the practicability is high.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2(a) is a diagram of the spatial distribution test set of principal components after CEEMDAN-FuzzyEn treatment;
FIG. 2(b) is a diagram of the principal component spatial distribution training set after CEEMDAN-fuzzy En treatment;
FIG. 3(a) is a PPCA main feature extraction result test set diagram;
FIG. 3(b) is a PPCA dominant feature extraction result training set diagram.
Detailed Description
Referring to fig. 1, the bearing fault diagnosis method of the present invention includes the steps of:
(1) extracting fault characteristics:
1) obtaining a vibration signal of a bearing, and extracting an IMF modal component of the vibration signal by a CEEMDAN method of complete integration empirical mode decomposition of self-adaptive white noise, wherein the method comprises the following steps;
a. EMD pair signal s [ n ] is decomposed by empirical mode]+δ0wi[n]Carrying out decomposition, wherein I takes a value in 1,2 …, I; delta0Is the standard deviation of the noise, wi-N (0,1), defining a first CEEMDAN modal component as:
Figure BDA0002399536280000091
b. calculating a first margin:
Figure BDA0002399536280000092
c. definition Ek[·]Continuing to utilize EMD for the signal r for the k-th modal component after EMD decomposition of the given signal1[n]+δ1E1(wi[n]) I1, 2 …, I, until the first EMD component, δ, is solvedk(k ═ 1) the signal-to-noise ratio can be chosen at each stage, while defining a second CEEMDAN modal component:
Figure BDA0002399536280000093
d. when K is 1,2 …, K, the K-th margin is calculated:
Figure BDA0002399536280000094
e. reuse of EMD for signal rk[n]+δkEk(wi[n]) I-1, 2 …, I, until the first EMD component is solved and the k +1 th CEEMDAN modal component is defined:
Figure BDA0002399536280000095
f. turning to step d, the next k repeats steps d-f until the margin cannot be further decomposed, and the final margin can be expressed as:
Figure BDA0002399536280000096
where K is the total number of modal components, the original signal can be expressed as:
Figure BDA0002399536280000097
delta can be adjusted at each stageiSelecting noises with different signal-to-noise ratios, and finally extracting vibration information through a CEEMDAN algorithmThe IMF modal component of the number;
2) determining the fuzzy entropy FuzzyEn of the IMF modal component extracted by CEEMDAN, reconstructing the original signal:
wherein for the imef modal components { t (i), i ═ 1,2.., N } extracted by CEEMDAN, FuzzyEn is calculated and the original signal is reconstructed:
Figure BDA0002399536280000101
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure BDA0002399536280000102
r is the similarity tolerance, for i, j 1,2., N-m +1, i ≠ j, the calculation:
Figure BDA0002399536280000103
in the formula (I), the compound is shown in the specification,
Figure BDA0002399536280000104
is a vector
Figure BDA0002399536280000105
And
Figure BDA0002399536280000106
the distance between i is averaged for each i and a function is defined as:
Figure BDA0002399536280000107
3) main feature extraction is carried out on the reconstructed signal through Probability Principal Component Analysis (PPCA), redundant information is eliminated, and the method specifically comprises the following steps:
for a data vector set x consisting of N d-dimensional vectors, q-dimensional hidden variables y are introduced to be related to the q-dimensional hidden variables x:
x＝Wy+u+ε (12)
in the formula (I), the compound is shown in the specification,ε is the observation noise vector ε -N (0, σ I)2) Hidden variables y to N (0, I) (I represents an identity matrix),
Figure BDA0002399536280000108
is a sample mean value, and W is a d × q parameter matrix;
the likelihood function for the observed data is:
Figure BDA0002399536280000109
wherein C is WWT+σ2IdS is a covariance matrix of an observation sample;
unknown parameters W, σ2The maximum likelihood method can be used for estimation, and the optimal solution is as follows:
Figure BDA0002399536280000111
W＝Uq(Λq-σ2Iq)1/2R (14)
wherein R is an arbitrary orthogonal matrix; lambda [ alpha ]kIs the kth maximum eigenvalue of the covariance matrix of the sample; lambdaq＝diag(λ1,λ2,K,λq)；λkCorresponding feature vector as UqThe kth column vector (k ═ 1,2K q);
4) taking a data set processed by PPCA as a feature vector, constructing a training set and a test set of a Support Vector Machine (SVM) in equal proportion and adding class labels;
(2) IWOA-SVM fault diagnosis:
1) constructing an SVM classifier model:
a. given a set of training sets { (x)i,yi)1, 2, N, where the input vector x is inputi∈RdD is the dimension of the input, yiE { -1, +1} is a class label, and a classification function is constructed by training samples by using the SVM:
y＝ωTΦ(x)+b (15)
wherein, omega represents a high-dimensional normal vector, and b represents an offset;
when the data cannot be linearly separated, a relaxation variable ξ is introducediAllowing error classification, and simultaneously introducing a penalty factor C to punish the error classification, so that the hyperplane problem of the SVM optimal classification is converted into a minimum value:
Figure BDA0002399536280000112
Figure BDA0002399536280000113
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure BDA0002399536280000114
wherein, σ is RBF kernel function parameter, which affects the complexity of the sample in the characteristic space distribution;
2) updating the penalty parameters and kernel function parameters of the classifier of the SVM according to the training set and the IWOA algorithm:
a. initializing parameters: initializing IWOA algorithm parameters a, A, C, w, v, l, p and maximum iteration number tmaxSearch space [ C ] of penalty parameter Cmin,Cmax]Sum kernel function sigma parameter search space [ sigma ]min,σmax]Where A and C are coefficient vectors, they are defined as:
A＝2a·r-a
C＝2·r (18)
wherein r represents a random number between [0,1], a represents a convergence factor which decreases linearly from 2 to 0 with increasing number of iterations, and rand () represents a random number between [0,1 ];
w is the inertial weight w ═ 1-rand ()/2 introduced from the PSO algorithm, v is the "flight" speed introduced, l is the random number in [ -1,1], p represents the random number between [0,1 ];
b. randomly generating an Ottea individual with an initial population size of N in a search space, and then listing the position of the ith whale in a D-dimensional spaceIs shown as
Figure BDA0002399536280000121
Let t be 1;
c. introducing w and v in PSO algorithm, calculating fitness values of individual whales, comparing, and recording prey position (optimal whale position) Y*The method comprises a prey surrounding stage, a bubble preying stage and a prey searching stage;
surrounding prey stage:
Figure BDA0002399536280000122
wherein t represents the current iteration, Y (t) represents the position of the individual whale in the t generation, Y*(t) represents the position of the optimal whale in the tth generation (prey position) and updates its own position with each iteration;
bubble predation phase (local search):
Figure BDA0002399536280000123
wherein D' ═ Y*(t) -w (t) Y (t) l, representing the distance of the ith whale to the prey, b being the helical constant, l being [ -1,1 [ ]]In (1), p represents [0,1]]A random number in between;
hunter finding phase (global search):
Figure BDA0002399536280000131
in the formula, YrThe position of a random whale in the current population is determined;
d. updating the position of the whale at the head in the population: if p is less than 0.5 and | A | is less than 1, the whale head updates the current position of the whale head according to the formula (19), otherwise, the whale head updates according to the formula (21), and if p is more than or equal to 0.5, the whale head updates according to the formula (20);
e. updating IWOA algorithm parameters a, A, C, w, v, l and p;
f. calculating the fitness value of the whale individuals in the updated population, evaluating again, and re-determining new globally optimal whale individuals and the positions of the whale individuals;
g. judging whether the termination condition of the algorithm is met, namely whether the maximum iteration times are reached, and if not, skipping to the step c to continue the iteration; otherwise, ending, and outputting the global optimal Y*Obtaining the optimal punishment parameter CbestAnd an optimal kernel function parameter σbest；
3) According to the obtained optimal punishment parameter CbestAnd an optimal kernel function parameter σbestConstructing a test model of the SVM, and obtaining the optimal penalty parameter C according to the test set in the step (1)4) and the optimal penalty parameter C in the step (2)2)bestAnd an optimal kernel function parameter σbestAnd determining the fault result of the bearing after ten-fold cross validation by taking the longest optimization time, the shortest optimization time, the average accuracy and the standard deviation as evaluation standards.
Experimental example:
the invention relates to a CEEMDAN-fuzzy En-PPCA-based feature extraction method and an IWOA-SVM bearing fault diagnosis model for optimizing vector machine parameters by improving a whale optimization algorithm, which are used for improving the fault identification accuracy and efficiency of a rolling bearing. The rolling bearing with the fault due to abrasion can generate vibration and noise in the operation process, so that vibration data are collected through a sensor.
In order to verify the feasibility and the effectiveness of the feature extraction method and the fault diagnosis model provided by the invention, SKF6205 rolling bearing data collected by a fault simulation experiment table of a Kaiser university of Ussum (CWRU) electrical engineering laboratory is used for verifying the feature extraction method and the fault diagnosis model, and the superiority of the method is emphasized by comparing optimization methods such as GA-SVM, PSO-SVM, WOA-SVM and the like.
The vibration data of the experiment are collected under the working conditions that the motor is in no-load, the rotating speed is 1797r/min and the sampling frequency is 12000Hz, the experiment uses an electric spark machining technology to arrange single-point faults on the bearing, the fault width diameter is 0.1778mm and the fault depth is 0.2794mm, and vibration signals of normal states, inner ring faults, outer ring faults and rolling body faults are collected.
Decomposing sample data of the four vibration signals by using a CEEMDAN algorithm to obtain respective IMF modal components, respectively calculating fuzzy En entropy values of the first three IMF components of the four vibration signals, extracting PPCA main characteristics, and after preprocessing, taking 200 groups of samples of each type, wherein the test set and the training set are half of the samples. The spatial distribution of the principal components after the CEEMDAN-fuzzy en processing is shown in fig. 2(a) and 2(b), and the results after the PPCA feature extraction processing are shown in fig. 3(a) and 3 (b).
According to the method, GA-SVM, PSO-SVM, WOA-SVM and IWOA-SVM models are respectively selected for carrying out experiments on bearing data samples of normal, inner ring faults, outer ring faults and rolling body faults which are preprocessed in the early stage, namely GA, PSO, WOA and IWOA algorithms are adopted for optimizing SVM classifier parameters C and sigma respectively, each algorithm is tested for 20 times, other experimental conditions are carried out under the same condition, and for example, initial population N and iteration times t are respectively set to be 20 and 100.
In order to evaluate the performance of the SVM classifier, five data such as the longest, shortest and average optimizing time, average accuracy, standard deviation and the like of a test set are counted as judgment standards in an experiment, and classification results are shown in Table 1 after cross validation of the four algorithms by ten folds.
TABLE 1 comparison of four different fault diagnosis model experiments
Figure BDA0002399536280000141
From the analysis of table 1 it can be concluded that: the average optimizing time of the WOA-SVM and IWOA-SVM test sets is 11.64s and 3.96s respectively, compared with GA-SVM (112.87s) and PSO-SVM (88.49s), convergence time is greatly shortened, average accuracy rate reaches 98.45% and 98.63%, compared with GA-SVM (112.87s) and PSO-SVM (88.49s), the convergence time is improved by 3% -4%, fault recognition time and accurate effect are better shown, particularly, compared with WOA, the average optimizing time is reduced by 7.68s, 2/3 is shortened, the average accuracy rate is improved by 0.18%, optimizing speed is higher, accuracy is higher, and the superiority of the improved IWOA algorithm is shown. In addition, compared with the GA, PSO and WOA algorithms, the standard deviation (0.36) of the average optimization time of the IWOA algorithm is about 1/10 of the PSO (3.70) and the WOA (3.40) and about 1/25 of the GA algorithm (8.58), which shows that the IWOA algorithm can be consistent in the optimization time and shows great stability. From the standard deviation value (0.10) of the average IWOA accuracy, the average IWOA accuracy is also the minimum of several algorithms, which shows that the IWOA-SVM model can better solve the problem that the algorithm is easy to fall into local optimization, and the accuracy of the diagnosis result is ensured.
In conclusion, the IWOA-SVM has the advantages of higher convergence speed, higher stability, easier achievement of optimal classification, stronger bearing fault diagnosis capability and higher identification accuracy. Experiments prove the feasibility and superiority of the IWOA algorithm on SVM parameter optimization in bearing fault diagnosis.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are within the scope of the present invention without departing from the technical spirit of the present invention.

Claims (4)

1. A bearing fault diagnosis method comprises the following steps:
(1) extracting fault characteristics:
1) obtaining a vibration signal of a bearing, and extracting an IMF modal component of the vibration signal by a CEEMDAN method of complete integration empirical mode decomposition of self-adaptive white noise;
2) determining the fuzzy entropy FuzzyEn of the IMF modal component extracted by CEEMDAN, reconstructing the original signal:
3) performing main feature extraction on the reconstructed signal through Probability Principal Component Analysis (PPCA) to remove redundant information;
4) taking a data set processed by PPCA as a feature vector, constructing a training set and a test set of a Support Vector Machine (SVM) in equal proportion and adding class labels;
(2) IWOA-SVM fault diagnosis:
1) constructing an SVM classifier model;
2) updating the penalty parameters and kernel function parameters of the classifier of the SVM according to the training set and the IWOA algorithm:
a. initializing parameters: initializing IWOAAlgorithm parameters
Figure 99212DEST_PATH_IMAGE001
Maximum number of iterations
Figure 169936DEST_PATH_IMAGE002
Penalty parameter
Figure 410293DEST_PATH_IMAGE003
Search space of
Figure 250073DEST_PATH_IMAGE004
And kernel function
Figure 668416DEST_PATH_IMAGE005
Parameter search space
Figure 960857DEST_PATH_IMAGE006
Wherein
Figure 4906DEST_PATH_IMAGE007
And
Figure 699192DEST_PATH_IMAGE008
are coefficient vectors, which are defined as:
Figure 350753DEST_PATH_IMAGE009
in the formula
Figure 333753DEST_PATH_IMAGE010
Represents [0,1]]A random number in between, and a random number,
Figure 728962DEST_PATH_IMAGE011
representing a convergence factor, decreases linearly from 2 to 0 as the number of iterations increases,
Figure 464706DEST_PATH_IMAGE012
represents [0,1]]A random number in between;
Figure 552748DEST_PATH_IMAGE013
is the inertial weight introduced from the PSO algorithm
Figure 819781DEST_PATH_IMAGE014
，
Figure 690785DEST_PATH_IMAGE015
Is the introduced "flying" speed of the aircraft,
Figure 359664DEST_PATH_IMAGE016
is [ -1,1 [ ]]The random number in (1) is selected,
Figure 799698DEST_PATH_IMAGE017
represents [0,1]]A random number in between;
b. randomly generating an initial population size in a search space of
Figure 288448DEST_PATH_IMAGE018
The individual of Otacea, the first
Figure 291039DEST_PATH_IMAGE019
Is only whale in
Figure 752108DEST_PATH_IMAGE020
The position in dimensional space can be expressed as
Figure 916373DEST_PATH_IMAGE021
，
Figure 344949DEST_PATH_IMAGE022
Let us order
Figure 885652DEST_PATH_IMAGE023
；
c. Introduced into PSO algorithm
Figure 201226DEST_PATH_IMAGE024
Calculating the fitness value of each whale individual, comparing, and recording the prey position (optimal whale position)
Figure 801972DEST_PATH_IMAGE025
The method comprises a prey surrounding stage, a bubble preying stage and a prey searching stage;
surrounding prey stage:
Figure 452265DEST_PATH_IMAGE026
in the formula (I), the compound is shown in the specification,
Figure 796659DEST_PATH_IMAGE027
which is indicative of the current iteration of the process,
Figure 294636DEST_PATH_IMAGE028
is shown as
Figure 738387DEST_PATH_IMAGE029
The location of individual whales in the generations,
Figure 954605DEST_PATH_IMAGE030
is shown as
Figure 24061DEST_PATH_IMAGE031
The position of the optimal whale in the generation (prey position) and updating its own position with each iteration;
bubble predation phase (local search):
Figure 376545DEST_PATH_IMAGE032
in the formula (I), the compound is shown in the specification,
Figure 53514DEST_PATH_IMAGE033
denotes the first
Figure 429131DEST_PATH_IMAGE035
The distance of an individual whale to a prey,
Figure 115328DEST_PATH_IMAGE036
is a constant of the helix and is,
Figure 509269DEST_PATH_IMAGE037
is [ -1,1 [ ]]The random number in (1) is selected,
Figure 622718DEST_PATH_IMAGE038
represents [0,1]]A random number in between;
hunter finding phase (global search):
Figure 547949DEST_PATH_IMAGE039
in the formula (I), the compound is shown in the specification,
Figure 709940DEST_PATH_IMAGE040
the position of a random whale in the current population is determined;
d. updating the position of the whale at the head in the population: if it is
Figure 37016DEST_PATH_IMAGE041
And is
Figure 508318DEST_PATH_IMAGE042
The whale at the head updates the current position of the whale at the head according to (19), otherwise, the whale at the head updates the current position according to (21), and if the whale at the head does not update the current position
Figure 655265DEST_PATH_IMAGE043
Updating according to the formula (20);
e. updating IWOA algorithm parameters
Figure 620947DEST_PATH_IMAGE044
；
f. Calculating the fitness value of the whale individuals in the updated population, evaluating again, and re-determining new globally optimal whale individuals and the positions of the whale individuals;
g. judging whether the termination condition of the algorithm is met, namely whether the maximum iteration times are reached, and if not, skipping to the step c to continue the iteration; otherwise, ending, and outputting the global optimum
Figure 802530DEST_PATH_IMAGE045
Obtaining the optimal punishment parameter
Figure 257782DEST_PATH_IMAGE046
And optimal kernel function parameters
Figure 344555DEST_PATH_IMAGE047
；
3) According to the obtained optimal punishment parameter
Figure 910666DEST_PATH_IMAGE048
And optimal kernel function parameters
Figure 884438DEST_PATH_IMAGE049
Constructing a test model of the SVM, and obtaining the optimal penalty parameter according to the test set in the step (1)4) and the optimal penalty parameter in the step (2)2)
Figure 510592DEST_PATH_IMAGE050
And optimal kernel function parameters
Figure 632131DEST_PATH_IMAGE051
And determining the fault result of the bearing after ten-fold cross validation by taking the longest optimization time, the shortest optimization time, the average accuracy and the standard deviation as evaluation standards.
2. The bearing fault diagnosis method as claimed in claim 1, wherein the step (1)1) of extracting the IMF modal component of the vibration signal by a complete integrated empirical mode decomposition method CEEMDAN of adaptive white noise comprises the steps of;
a. EMD pair signal decomposition using empirical mode
Figure 188884DEST_PATH_IMAGE052
The decomposition is carried out, wherein,
Figure 345058DEST_PATH_IMAGE053
in that
Figure 79796DEST_PATH_IMAGE054
Taking a middle value;
Figure 688632DEST_PATH_IMAGE055
is the standard deviation of the noise, and,
Figure 596545DEST_PATH_IMAGE056
defining the first CEEMDAN modal component as:
Figure 800037DEST_PATH_IMAGE057
b. calculating a first margin:
Figure 767993DEST_PATH_IMAGE058
c. definition of
Figure 801808DEST_PATH_IMAGE059
For the second after EMD decomposition of a given signal
Figure 513412DEST_PATH_IMAGE060
Individual modal component, continuing to use EMD pair signal
Figure 831129DEST_PATH_IMAGE061
，
Figure 907670DEST_PATH_IMAGE062
Performing decomposition until the first EMD component is solved,
Figure 225519DEST_PATH_IMAGE063
the signal-to-noise ratio can be selected at each stage while defining a second CEEMDAN modal component:
Figure 927764DEST_PATH_IMAGE064
d. when in use
Figure 913038DEST_PATH_IMAGE065
When it is calculated
Figure 222797DEST_PATH_IMAGE066
The balance is as follows:
Figure 965625DEST_PATH_IMAGE067
e. reusing EMD pair signals
Figure 19031DEST_PATH_IMAGE068
，
Figure 45762DEST_PATH_IMAGE069
Performing decomposition until the first EMD component is solved, and defining the second EMD component
Figure 526422DEST_PATH_IMAGE070
Individual CEEMDAN modal components:
Figure 22125DEST_PATH_IMAGE071
f. next one is
Figure 613644DEST_PATH_IMAGE072
Go toAnd d, repeating the steps d-f until the margin can not be decomposed continuously, wherein the final margin can be expressed as:
Figure 573509DEST_PATH_IMAGE073
in the formula (I), the compound is shown in the specification,
Figure 412021DEST_PATH_IMAGE074
is the total number of modal components, the original signal can be expressed as:
Figure 191758DEST_PATH_IMAGE075
can be adjusted at each stage
Figure 524651DEST_PATH_IMAGE076
Selecting noises with different signal-to-noise ratios, and finally extracting IMF modal components of the vibration signals through a CEEMDAN algorithm;
in the above bearing fault diagnosis method, step (1)2) is performed on the IMF modal component extracted by the CEEMDAN
Figure 339023DEST_PATH_IMAGE077
Calculate FuzzyEn and reconstruct the original signal:
Figure 348436DEST_PATH_IMAGE078
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure 615470DEST_PATH_IMAGE079
Figure 814370DEST_PATH_IMAGE080
to a similar tolerance, for
Figure 420932DEST_PATH_IMAGE081
And calculating:
Figure 414295DEST_PATH_IMAGE082
in the formula (I), the compound is shown in the specification,
Figure 355575DEST_PATH_IMAGE083
is a vector
Figure 358166DEST_PATH_IMAGE084
And
Figure 819235DEST_PATH_IMAGE085
to each of
Figure 983500DEST_PATH_IMAGE086
The average is found and a function is defined, having:
Figure 412076DEST_PATH_IMAGE087
。
3. the bearing fault diagnosis method according to claim 1 or 2, wherein the main features are extracted and the redundant information is removed in the step (1)3), and the method comprises the following specific steps:
for one is composed of
Figure 952779DEST_PATH_IMAGE088
An
Figure 268354DEST_PATH_IMAGE089
Data vector set composed of dimension vectors
Figure 869099DEST_PATH_IMAGE090
Introduction of
Figure 332442DEST_PATH_IMAGE091
Dimension hidden variable
Figure 881364DEST_PATH_IMAGE092
In connection therewith:
Figure 113762DEST_PATH_IMAGE093
in the formula (I), the compound is shown in the specification,
Figure 823092DEST_PATH_IMAGE094
is observing a noise vector
Figure 773731DEST_PATH_IMAGE095
Hidden variable
Figure 656236DEST_PATH_IMAGE096
（
Figure 195671DEST_PATH_IMAGE097
Representing an identity matrix),
Figure 138219DEST_PATH_IMAGE098
is the average value of the samples and is,
Figure 513837DEST_PATH_IMAGE099
is a parameter matrix;
the likelihood function for the observed data is:
Figure 200033DEST_PATH_IMAGE100
in the formula (I), the compound is shown in the specification,
Figure 593974DEST_PATH_IMAGE101
，
Figure 707424DEST_PATH_IMAGE102
a covariance matrix for the observation sample;
unknown ginsengNumber of
Figure 570337DEST_PATH_IMAGE103
The maximum likelihood method can be used for estimation, and the optimal solution is as follows:
Figure 794645DEST_PATH_IMAGE104
in the formula (I), the compound is shown in the specification,
Figure 121721DEST_PATH_IMAGE105
is an arbitrary orthogonal matrix;
Figure 327444DEST_PATH_IMAGE106
is the first of the covariance matrix of the sample
Figure 739971DEST_PATH_IMAGE107
A maximum eigenvalue;
Figure 705652DEST_PATH_IMAGE108
；
Figure 887235DEST_PATH_IMAGE109
corresponding feature vector as
Figure 342487DEST_PATH_IMAGE110
To (1) a
Figure 163682DEST_PATH_IMAGE111
A column vector
Figure 729792DEST_PATH_IMAGE112
。
4. A bearing fault diagnosis method according to claim 3, wherein the step (2)1) of constructing the SVM classifier model:
a. given a set of training sets
Figure 969144DEST_PATH_IMAGE113
，
Figure 595297DEST_PATH_IMAGE114
In the formula, input vector
Figure 716837DEST_PATH_IMAGE115
，
Figure 273589DEST_PATH_IMAGE116
Is the dimension of the input that is,
Figure 429764DEST_PATH_IMAGE117
the method is a class label, and a classification function is constructed by training samples through an SVM:
Figure 164502DEST_PATH_IMAGE118
wherein the content of the first and second substances,
Figure 773337DEST_PATH_IMAGE119
a high-dimensional normal vector is represented,
Figure 868201DEST_PATH_IMAGE120
represents an offset;
when data can not be separated linearly, relaxation variables are introduced
Figure 878883DEST_PATH_IMAGE121
Allowing error classification while introducing penalty factors
Figure 846839DEST_PATH_IMAGE122
Punishment is carried out on the error classification, and then the hyperplane problem of the SVM optimal classification is converted into the minimum value:
Figure 880654DEST_PATH_IMAGE123
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure DEST_PATH_IMAGE124
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE125
is a RBF kernel function parameter.
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CN114818809B (en) * 2022-04-27 2024-03-22 合肥工业大学 Fault diagnosis method for SCA-SVM motor rolling bearing based on cross wavelet
CN115221930A (en) * 2022-09-20 2022-10-21 苏州鸿哲智能科技有限公司 Fault diagnosis method for rolling bearing
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CN117574057B (en) * 2023-11-24 2024-05-28 昆明理工大学 Intelligent fault diagnosis method for vertical water pump unit

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