Flexible thin-wall bearing fault diagnosis method based on FFT and SABO-KELM

Abstract

The invention aims to provide a flexible thin-wall bearing fault diagnosis method based on FFT and SABO-KELM, and the method comprises the following steps: A, collecting a plurality of groups of original vibration signals of a normal flexible thin-wall bearing and a faulted flexible thin-wall bearing, obtaining the time domain features of the vibration signals, obtaining the frequency domain features through fast Fourier transform, and forming a training set of feature signals; b, taking the error rate of the training set as a fitness function, optimizing a regularization parameter and a kernel function parameter of the KELM model by adopting an SABO algorithm, and inputting the training set for training to obtain an optimized SABO-KELM model; c, original vibration signals of the flexible thin-wall bearing to be detected are collected, time domain features of the vibration signals are obtained, frequency domain features are obtained through fast Fourier transform, and a feature set is constructed; and D, inputting the feature set into the trained SABO-KELM model for processing, so as to identify the fault type. According to the method, the diagnosis performance and reliability can be improved, so that fault type identification and classification can be quickly and accurately completed.

Description

Technical Field

[0001] The invention relates to the technical field of flexible thin-walled bearing fault diagnosis, and in particular to a flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM. Background Art

[0002] As a basic component of industrial robots, the operating state of flexible thin-walled bearings directly affects the performance, operating efficiency and equipment life of industrial robots. Rapid and accurate diagnosis of the vibration signals generated during the operation of flexible thin-walled bearings can greatly reduce the probability of equipment accidents and even reduce casualties, which has high practical significance. However, due to its special structure, the inner and outer rings of flexible thin-walled bearings are deformed into ellipses during operation, which leads to periodic impacts in the vibration signals of flexible thin-walled bearings. Such impacts make it more challenging to extract the fault characteristics of flexible thin-walled bearings from the vibration signals compared with traditional rolling bearings. At present, most of the existing bearing fault diagnosis technologies focus on rolling bearings, while there are relatively few studies on the diagnosis of flexible thin-walled bearings. In summary, it is crucial to use efficient and accurate signal extraction technology and precise and fast fault diagnosis methods for flexible thin-walled bearings. Among them, the appropriateness of parameter settings will significantly affect the effect of signal decomposition and diagnostic classification. The quality of parameter selection is directly related to the stability of the diagnostic model and the accuracy of the diagnostic results. Summary of the invention

[0003] The present invention aims to provide a flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM, which can improve the performance and reliability of diagnosis, thereby quickly and accurately completing fault type identification and classification.

[0004] The technical solution of the present invention is as follows:

[0005] The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM comprises the following steps:

[0006] A. Collect multiple groups of original vibration signals of normal flexible thin-walled bearings and faulty flexible thin-walled bearings respectively, calculate the time domain features of these original vibration signals, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the spectral features corresponding to these time domain features to form a training set of feature signals;

[0007] B. Taking the error rate of the training set as the fitness function, the SABO algorithm is used to optimize the regularization parameters and kernel function parameters of the KELM model. The training set is input for training to obtain the optimal solution of the above parameters, which is then brought into the KELM model to obtain the optimized SABO-KELM model.

[0008] C. Collect the original vibration signal of the flexible thin-walled bearing to be tested, calculate the time domain characteristics of the original vibration signal of the flexible thin-walled bearing to be tested, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the frequency spectrum characteristics corresponding to these time domain characteristics, and construct a feature set;

[0009] D. Input the feature set into the trained SABO-KELM model to identify the fault type.

[0010] The faulty flexible thin-walled bearings include outer ring crack bearings, inner ring crack bearings, and inner and outer ring composite fault bearings.

[0011] In step A, the calculation formula of the Hanning window interpolation fast Fourier transform is:

[0012]

[0013] Where: ω is a complex unit: In ω, i is used as an imaginary unit, p and j as indices from 0 to k-1; the absolute value of y at index k-1 measures the number of occurrences of frequency f=p(fs / k) in the data.

[0014] In step B, the formula of the fitness function is:

[0015]

[0016] Among them, f(xi) represents the result predicted by the model, and yi represents the actual result; ∏(f(xi)=yi) means that if f(xi)=yi, it is equal to 1, otherwise it is 0.

[0017] In step B, the specific optimization process of the SABO algorithm is as follows:

[0018] a. Randomly update the population position: randomly initialize the population in the j-dimensional space, and its expression is:

[0019]

[0020] x i,j =lb j +r i,j ·(ub j -lb j ) (4)

[0021] In the formula, i = 1, L, N, j = 1, L, M; x i,j For individuals; lb j andub j are the upper and lower boundaries of optimization respectively; r is a random number in [0,1];

[0022] Find each search agent X i The following are the evaluation questions:

[0023]

[0024] In the formula, is the vector representation of the evaluation value, F(X i ) is the X for calculating the objective function i .

[0025] b. -v search: In each iteration, the position of the search agent is updated based on the position difference between agents, which can effectively avoid falling into the problem of local optimal solution. The specific definition of its position update process is as follows:

[0026]

[0027] In the formula, is a vector of dimension m, a random number generated from [1,2]; F(A) and F(B) are the values ​​of the objective functions of search agent A and search agent B respectively; sign is the signum function, and * is the Hadamard operation;

[0028] c. Search agent updates new position: In the SABO algorithm, any search agent x i The displacement in the search space is done by each search agent x j The arithmetic mean of -v subtraction is used to calculate the new position of the search agent:

[0029]

[0030] Where: is the i-th search agent X i The new suggested position of ; N is the total number of search agents, is a vector of dimension m; r i is a random value that follows a normal distribution.

[0031] d. Generate the optimal solution: Based on the new position obtained by formula (7), the function value of the target is improved, and then the new position X of the corresponding search agent is calculated according to the following particle position replacement formula (8): i , which is the global optimal solution; the replacement formula (8) of the particle position is:

[0032]

[0033] The output of the KELM model is:

[0034]

[0035] Where x is the input vector, n is the dimension of the input vector; Ω ELM is the kernel matrix, and the formula is as follows:

[0036] Ω ELM =HH T =h(x i )h(x j )=K(x i , x j ) (10)

[0037] In the formula, x i 、x j is the input sample, h(x)H represents the hidden layer output matrix;

[0038] K(x i ,y i ) is the Gaussian radial basis kernel function, and its formula is as follows:

[0039]

[0040] In the formula, λ is the kernel function.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] The method of the present invention provides an effective solution strategy for fault diagnosis of flexible thin-walled bearings, fills the gap in this research field, has the characteristics of excellent diagnostic performance, high classification accuracy, etc., and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Time domain waveforms of flexible thin-walled bearings in different states

[0044] Figure 2 The spectrum diagram of flexible thin-walled bearings in different states;

[0045] Figure 3 This is the test result diagram of the unoptimized KELM model;

[0046] Figure 4 Iterative optimization curve diagram for optimizing KELM model for SABO;

[0047] Figure 5 Test result graph of the KELM model optimized for SABO;

[0048] Figure 6 It is an iterative optimization curve diagram of the FFT-SABO-KELM model in the method of Example 1;

[0049] Figure 7 This is a test result diagram of the method in Example 1. DETAILED DESCRIPTION

[0050] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM comprises the following steps:

[0053] A. Collect multiple groups of original vibration signals of normal flexible thin-walled bearings and faulty flexible thin-walled bearings respectively, calculate the time domain features of these original vibration signals, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the spectral features corresponding to these time domain features to construct a training set;

[0054] The faulty flexible thin-walled bearings include outer ring crack bearings, inner ring crack bearings, and inner and outer ring composite fault bearings.

[0055] The calculation formula of Hanning window interpolation fast Fourier transform is:

[0056]

[0057] Where: ω is a complex unit: In ω, i is used as an imaginary unit, p and j as indices from 0 to k-1; the absolute value of y at index k-1 measures the number of occurrences of frequency f=p(fs / k) in the data.

[0058] B. Taking the error rate of the training set as the fitness function, the SABO algorithm is used to optimize the regularization coefficient and kernel parameter of the KELM model, and the obtained regularization coefficient and kernel parameter are substituted into the KELM model to obtain the optimized KELM model;

[0059] The formula of the fitness function is:

[0060]

[0061] Among them, f(xi) represents the result predicted by the model, and yi represents the actual result; ∏(f(xi)=yi) means that if f(xi)=yi, it is equal to 1, otherwise it is 0.

[0062] The specific optimization process of the SABO algorithm is as follows:

[0063] a. Randomly update the population position: randomly initialize the population in the j-dimensional space, and its expression is:

[0064]

[0065] x i,j =lb j +ri,j ·(ub j -lb j ) (4)

[0066] In the formula, i = 1, L, N, j = 1, L, M; x i,j For individuals; lb j andub j are the upper and lower boundaries of optimization respectively; r is a random number in [0,1];

[0067] Find each search agent X i The following are the evaluation questions:

[0068]

[0069] In the formula, is the vector representation of the evaluation value, F(X i ) is the X for calculating the objective function i .

[0070] b. -v search: In each iteration, the position of the search agent is updated based on the position difference between agents, which can effectively avoid falling into the problem of local optimal solution. The specific definition of its position update process is as follows:

[0071]

[0072] In the formula, is a vector of dimension m, a random number generated from [1,2]; F(A) and F(B) are the values ​​of the objective functions of search agent A and search agent B respectively; sign is the signum function, and * is the Hadamard operation;

[0073] c. Search agent updates new position: In the SABO algorithm, any search agent x i The displacement in the search space is done by each search agent x j The arithmetic mean of -v subtraction is used to calculate the new position of the search agent:

[0074]

[0075] Where: is the i-th search agent X i The new suggested position of ; N is the total number of search agents, is a vector of dimension m; r i is a random value that follows a normal distribution.

[0076] d. Generate the optimal solution: Based on the new position obtained by formula (7), the function value of the target is improved, and then the new position X of the corresponding search agent is calculated according to the following particle position replacement formula (8): i , which is the global optimal solution; the replacement formula (8) of the particle position is:

[0077]

[0078] The output of the KELM model is:

[0079]

[0080] Where x is the input vector, n is the dimension of the input vector; Ω ELM is the kernel matrix, and the formula is as follows:

[0081] Ω ELM =HH T =h(x i )h(x j )=K(x i , x j ) (10)

[0082] In the formula, x i 、x j is the input sample, h(x) and H represent the hidden layer output matrix;

[0083] K(x i ,x j ) is the Gaussian radial basis kernel function, and its formula is as follows:

[0084]

[0085] In the formula, λ is the kernel function.

[0086] C. Collect the original vibration signal of the flexible thin-walled bearing to be tested, calculate the time domain characteristics of the original vibration signal of the flexible thin-walled bearing to be tested, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the frequency spectrum characteristics corresponding to these time domain characteristics, and construct a feature set;

[0087] D. Input the feature set into the trained SABO-KELM model to identify the fault type.

[0088] Example 2

[0089] Comparative experiment on fault diagnosis of flexible thin-walled bearings

[0090] 1 Test conditions

[0091] The test data comes from the acceleration sensor detection. The outer ring fault of the tested flexible thin-walled bearing is simulated by electrospark machining a rectangular pit with a length and width of 1 mm. The specific parameters are shown in Table 1.

[0092] Table 1 Basic test parameters

[0093]

[0094] 2. Vibration signal analysis

[0095] In the test, the motor speed was set to 1050r / min (i.e., the rotation frequency fn = 17.5Hz), the sampling frequency was set to 12800Hz, and the time domain waveforms of the original vibration signals of the flexible thin-walled bearing were measured as follows: Figure 1 As shown, its spectrum is as follows Figure 2 shown.

[0096] Depend on Figure 1 It is not difficult to find that compared with the vibration signal of a normal flexible thin-walled bearing, the vibration signal amplitude of the flexible thin-walled bearing with inner ring, outer ring, and inner and outer ring combined faults is significantly increased. Although the periodic impact phenomenon can be roughly seen from the figure, the regularity of these impacts cannot be observed. Figure 2 Although frequency changes can be seen in the image, these changes are most likely caused by signal instability, and these frequencies cannot reflect the true fault information of the bearing.

[0097] 3 Fault diagnosis of flexible thin-walled bearing outer ring

[0098] (1) Figure 1 The time domain signals of multiple groups of flexible thin-walled bearings represented in the figure are used as input, divided into a training set and a test set, and the KELM model with the Gaussian radial kernel function of Example 1 as the kernel function is used for diagnosis. The results are shown in FIG. Figure 3 shown.

[0099] Depend on Figure 3 It can be seen that when the time domain signal of the flexible thin-walled bearing is collected as input and the KELM model without any optimization is used for diagnosis, the diagnostic accuracy of the training set reaches 100%, but the diagnostic accuracy of the test set is only 22.5%, which indicates that the model has a serious overfitting phenomenon.

[0100] (2) The SABO algorithm is used to optimize the regularization coefficient and kernel parameter of the KELM model to explore the impact of key parameters in the model on the classification accuracy, and the time domain signal is input into the optimized model for diagnosis. Figure 4 The iteration curve when SABO optimizes the KELM model, and the test results are as follows Figure 5 shown.

[0101] contrast Figure 3 and Figure 5 It can be seen that although the classification performance of the KELM model has improved after the SABO algorithm optimizes the parameters, the classification effect is still very poor. And from the iteration graph, it can be seen that the SABO algorithm needs a total of 5 iterations to find the global optimal solution, and there is still room for improvement in the optimization speed.

[0102] (3) The test set is diagnosed using the method of Example 1, and the iterative optimization curve is as follows: Figure 6 The test results are shown in Figure 7 shown.

[0103] Depend on Figure 7 It can be seen that after the original time domain signal of the flexible thin-walled bearing is converted into spectral features by FFT and input into the SABO-KELM model in combination with the time domain features of the original signal, its classification accuracy reaches 100%, indicating that the classification accuracy and generalization performance of the FFT-SABO-KELM model of Example 1 are very good.

[0104] Example 3

[0105] The training set accuracy and test set accuracy of the FFT-SABO-KELM model, SABO-KELM model, FFT-KELM model, and KELM model of Example 1 are compared, and the results are listed in Table 1. As can be seen from Table 1, the training set and test set accuracy of the FFT-SABO-KELM model of Example 1 reached 100%, which is much higher than the other models.

[0106] Table 1 Diagnostic results of different models

[0107]

Claims

1. A flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM, characterized in that: The following steps are involved: A. Collect multiple groups of original vibration signals of normal flexible thin-walled bearings and faulty flexible thin-walled bearings respectively, calculate the time domain features of these original vibration signals, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the spectral features corresponding to these time domain features to form a training set of feature signals; B. Taking the error rate of the training set as the fitness function, the SABO algorithm is used to optimize the regularization parameters and kernel function parameters of the KELM model. The training set is input for training to obtain the optimal solution of the above parameters, which is then brought into the KELM model to obtain the optimized SABO-KELM model. C. Collect the original vibration signal of the flexible thin-walled bearing to be tested, calculate the time domain characteristics of the original vibration signal of the flexible thin-walled bearing to be tested, and use the RMS feature extraction method based on Hanning window interpolation fast Fourier transform to obtain the frequency spectrum characteristics corresponding to these time domain characteristics, and construct a feature set; D. Input the feature set into the trained SABO-KELM model to identify the fault type.

2. The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM as claimed in claim 1, characterized in that: In the step A, the faulty flexible thin-walled bearing includes a bearing with an outer ring crack, a bearing with an inner ring crack, and a bearing with composite inner and outer ring faults.

3. The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM as claimed in claim 1, characterized in that: In step A, the calculation formula of the Hanning window interpolation fast Fourier transform is: Where: ω is a complex unit: In ω, i is used as an imaginary unit, p and j as indices from 0 to k-1; the absolute value of y at index k-1 measures the number of occurrences of frequency f=p(fs / k) in the data.

4. The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM as claimed in claim 1, characterized in that: In step B, the formula of the fitness function is: Among them, f(xi) represents the result predicted by the model, and yi represents the actual result; ∏(f(xi)=yi) means that if f(xi)=yi, it is equal to 1, otherwise it is 0.

5. The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM as claimed in claim 1, characterized in that: In step B, the specific optimization process of the SABO algorithm is as follows: a. Randomly update the population position: Randomly initialize the population in the j-dimensional space, and its expression is: x i,j =lb j +r i,j ·(ub j -lb j ) (4) Where, i = 1, ..., N, j = 1, ..., M; x i,j For individuals; lb j andub j are the upper and lower boundaries of optimization respectively; r is a random number in [0,1]; Find each search agent X i The following are the evaluation questions: In the formula, is the vector representation of the evaluation value, F(X i ) is the X for calculating the objective function i . b. -v search: In each iteration, the position of the search agent is updated based on the position difference between agents, which can effectively avoid falling into the problem of local optimal solution. The specific definition of its position update process is as follows: In the formula, is a vector of dimension m, a random number generated from [1,2]; F(A) and F(B) are the values ​​of the objective functions of search agent A and search agent B respectively; sign is the signum function, and * is the Hadamard operation; c. Search agent updates new position: In the SABO algorithm, any search agent x i The displacement in the search space is done by each search agent x j The arithmetic mean of -v subtraction is used to calculate the new position of the search agent: Where: is the i-th search agent X i The new suggested position of ; N is the total number of search agents, is a vector of dimension m; r i is a random value that follows a normal distribution. d. Generate the optimal solution: Based on the new position obtained by formula (7), the function value of the target is improved, and then the new position X of the corresponding search agent is calculated according to the following particle position replacement formula (8): i , which is the global optimal solution; the replacement formula (8) of the particle position is:

6. The flexible thin-walled bearing fault diagnosis method based on FFT and SABO-KELM as claimed in claim 1, characterized in that: The output of the KELM model is: Where x is the input vector, n is the dimension of the input vector; Ω ELM is the kernel matrix, and the formula is as follows: Ω ELM =HH T =h(x i )h(x j )=K(x i ,x j ) (10) In the formula, x i 、x j is the input sample, h(x)H represents the hidden layer output matrix; K(x i , x j ) is the Gaussian radial basis kernel function, and its formula is as follows: In the formula, λ is the kernel function.

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