CN111272429B - Bearing fault diagnosis method - Google Patents

Bearing fault diagnosis method Download PDF

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CN111272429B
CN111272429B CN202010142396.9A CN202010142396A CN111272429B CN 111272429 B CN111272429 B CN 111272429B CN 202010142396 A CN202010142396 A CN 202010142396A CN 111272429 B CN111272429 B CN 111272429B
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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. Hair brushThe bearing fault diagnosis capability is strong, and the recognition accuracy is high.

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, 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[σmin,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 GDA0003117230110000021
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 GDA0003117230110000022
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 GDA0003117230110000031
v(t+1)＝w(t)·[v(t)+C·rand()·(Y*(t)-Y(t))]
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 GDA0003117230110000032
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 GDA0003117230110000033
b. calculating a first margin:
Figure GDA0003117230110000034
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 GDA0003117230110000041
d. when K is 1,2.. K, the K-th margin is calculated:
Figure GDA0003117230110000042
e. reuse of EMD for signal rk[n]+δkEk(wi[n]) I1, 2.. I, the decomposition is performed until the first EMD component is solved and the k +1 th CEEMDAN modal component is defined:
Figure GDA0003117230110000043
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 GDA0003117230110000044
where K is the total number of modal components, the original signal can be expressed as:
Figure GDA0003117230110000045
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 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 an original signal is reconstructed:
Figure GDA0003117230110000046
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure GDA0003117230110000047
r is the similarity tolerance, for i, j 1,2., N-m +1, i ≠ j, the calculation:
Figure GDA0003117230110000048
in the formula (I), the compound is shown in the specification,
Figure GDA0003117230110000049
is a vector
Figure GDA00031172301100000410
And
Figure GDA00031172301100000411
the distance between i is averaged for each i and a function is defined as:
Figure GDA00031172301100000412
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 representing the identity matrix,
Figure GDA0003117230110000051
is a sample mean value, and W is a d × q parameter matrix;
the likelihood function for the observed data is:
Figure GDA0003117230110000052
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 GDA0003117230110000053
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,...,λq)；λkCorresponding feature vector as UqQ, 1,2.
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 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 data can not be separated linearly, relaxation variable xi 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 GDA0003117230110000054
Figure GDA0003117230110000055
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure GDA0003117230110000056
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]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 GDA0003117230110000071
b. calculating a first margin:
Figure GDA0003117230110000072
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 GDA0003117230110000073
d. when K is 1,2.. K, the K-th margin is calculated:
Figure GDA0003117230110000074
e. reuse of EMD for signal rk[n]+δkEk(wi[n]) I1, 2.. I, the decomposition is performed until the first EMD component is solved and the k +1 th CEEMDAN modal component is defined:
Figure GDA0003117230110000075
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 GDA0003117230110000076
where K is the total number of modal components, the original signal can be expressed as:
Figure GDA0003117230110000081
delta can be adjusted at each stageiSelecting noises with different signal-to-noise ratios, and finally extracting IMF modal components of the vibration signals through a CEEMDAN algorithm;
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 GDA0003117230110000082
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure GDA0003117230110000083
r is the similarity tolerance, for i, j 1,2., N-m +1, i ≠ j, the calculation:
Figure GDA0003117230110000084
in the formula (I), the compound is shown in the specification,
Figure GDA0003117230110000085
is a vector
Figure GDA0003117230110000086
And
Figure GDA0003117230110000087
the distance between i is averaged for each i and a function is defined as:
Figure GDA0003117230110000088
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)
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 GDA0003117230110000089
is a sample mean value, and W is a d × q parameter matrix;
the likelihood function for the observed data is:
Figure GDA00031172301100000810
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 GDA0003117230110000091
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,...,λq)；λkCorresponding feature vector as UqThe kth column vector (k ═ 1,2.. 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 data can not be separated linearly, relaxation variable xi 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 GDA0003117230110000092
Figure GDA0003117230110000093
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure GDA0003117230110000094
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 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 GDA0003117230110000101
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 GDA0003117230110000102
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 GDA0003117230110000103
v(t+1)＝w(t)·[v(t)+C·rand()·(Y*(t)-Y(t))]
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 GDA0003117230110000104
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 GDA0003117230110000111
Figure GDA0003117230110000121
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 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, and the convergence factor is linearly decreased from 2 to 0 along with the increase of the iteration number;
w is the inertial weight w ═ 1-rand ()/2 introduced from the PSO algorithm, rand () represents the random number between [0,1], v is the introduced "flight" speed, 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 FDA0003138437850000011
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:
D＝|C·Y*(t)-w(t)·Y(t)|
Y(t+1)＝Y(t)+v(t) (19)
v(t+1)＝w(t)·[v(t)+C·rand()·(Y*(t)-Y(t))]
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 FDA0003138437850000021
v(t+1)＝w(t)·[v(t)+C·rand()·(Y*(t)-Y(t))]
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):
D＝|C·Yr(t)-w(t)·Y(t)|
Y(t+1)＝Y(t)+v(t) (21)
v(t+1)＝w(t)·[v(t)+C·rand()·(Y*(t)-Y(t))]
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.
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 s [ n ] is decomposed by empirical mode]+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 FDA0003138437850000022
b. calculating a first margin:
Figure FDA0003138437850000031
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 solvedkK-1 may select the signal-to-noise ratio at each stage, while defining a second CEEMDAN modal component:
Figure FDA0003138437850000032
d. when K is 1,2.. K, the K-th margin is calculated:
Figure FDA0003138437850000033
e. reuse of EMD for signal rk[n]+δkEk(wi[n]) I1, 2.. I, the decomposition is performed until the first EMD component is solved and the k +1 th CEEMDAN modal component is defined:
Figure FDA0003138437850000034
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 FDA0003138437850000035
where K is the total number of modal components, the original signal can be expressed as:
Figure FDA0003138437850000036
can be at each stepSegment adjustment deltaiSelecting noises with different signal-to-noise ratios, and finally extracting IMF modal components of the vibration signals through a CEEMDAN algorithm;
in the 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 an original signal is reconstructed:
Figure FDA0003138437850000037
in the formula, fuzzy membership function algorithm introduced by FuzzyEn is as follows:
Figure FDA0003138437850000038
r is the similarity tolerance, for i, j 1,2., N-m +1, i ≠ j, the calculation:
Figure FDA0003138437850000039
in the formula (I), the compound is shown in the specification,
Figure FDA00031384378500000310
is a vector
Figure FDA00031384378500000311
And
Figure FDA00031384378500000312
the distance between i is averaged for each i and a function is defined as:
Figure FDA00031384378500000313
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 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 representing the identity matrix,
Figure FDA0003138437850000041
is a sample mean value, and W is a d × q parameter matrix;
the likelihood function for the observed data is:
Figure FDA0003138437850000042
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 FDA0003138437850000043
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，…，λq)；λkCorresponding feature vector as UqQ, 1,2.
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 { (x)i，yi)}，i＝1，2，..N, where the input vector xi∈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 data cannot be linearly separated, a relaxation variable ζ 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 FDA0003138437850000044
Figure FDA0003138437850000045
b. constructing a Radial Basis (RBF) kernel function for the SVM, which is defined as:
Figure FDA0003138437850000046
wherein, the sigma is an RBF kernel function parameter.
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