A Bearing Fault Diagnosis Method Based on Legendre Multi-Wavelet Transform

Abstract

The present invention relates to the technical field of bearing fault diagnosis, and particularly to a bearing fault diagnosis method based on Legendre multi-wavelet transform. The method includes obtaining original signal data; dividing the sample set into a training set and a test set; performing 3-level Legendre wavelet decomposition to obtain corresponding low-frequency signal components and high-frequency signal components; calculating the RMS and SD values; inputting the RMS and SD of the training set into a BPNN classifier; verifying the accuracy through the test set; and diagnosing bearing faults. The present invention proposes to extract the fault essential features of the bearing signal characteristics through multi-scale by Legendre multi-wavelet, and identify them through a BPNN classifier, constructing an LW-BPNN bearing fault diagnosis method; when used for bearing fault diagnosis, only two statistical parameters, RMS and SD, and a BPNN classifier are needed to complete the fault identification with a relatively high diagnosis rate, effectively reducing the complexity of the framework, and also being simpler and more convenient in terms of feature extraction and parameter optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault diagnosis, and designs a bearing fault diagnosis method based on Legendre multi-wavelet transform. Background Art

[0002] Rolling bearings are the core components of rotating mechanisms, and their health conditions will have a huge impact on the performance, stability and life of the mechanisms. However, the working environment of rolling bearings is very harsh. Different forms of damage such as abrasive wear, cracks, fatigue spalling, electro-erosion and corrosion are likely to occur on the bearing surface due to high temperature, high pressure, variable speed and variable load, etc., and then successively cause fault problems such as inner ring faults, outer ring faults, roller faults, etc. Therefore, researching effective intelligent fault diagnosis technologies is of great significance for accurately evaluating the health conditions of rolling bearings.

[0003] Traditional intelligent fault diagnosis methods based on machine learning, such as improved algorithms like artificial neural networks, random forests, support vector machines, fuzzy inference, etc., almost all rely on manual experience to extract the features of raw data and lack adaptability. To address this problem, various signal processing methods such as Fourier transform, variational mode decomposition, empirical mode decomposition, wavelet decomposition, wavelet packet transform, etc. are adopted, and feature vectors are artificially selected as the input of intelligent classifiers to achieve fault identification and classification. For example, Yan et al. (X. Yan, M. Jia, Intelligent fault diagnosis of rotating machinery using improved multiscale dispersion entropy and mRMR feature selection, Knowl. Based Syst. 163 (2018) 450-470.) proposed a fault diagnosis method based on improved multiscale dispersion entropy and maximum correlation minimum redundancy, and used the extreme learning machine as a classifier to achieve the classification of different faults of rolling bearings and gearboxes. Dou et al. (Dou, J. Yang, J. Liu, et al., A rule-based intelligent method for fault diagnosis of rotating machinery, Knowl.-Based Syst. 36 (2012) 1–8.) used the frequency domain features and time domain dimensionless features of fault-bearing data as the input of the classifier, and discussed the performance of K-nearest neighbor algorithm, probabilistic neural network and particle swarm optimization-SVM in fault diagnosis. Although these methods have achieved good results, they require the selection of effective features designed manually and are difficult to meet the analysis requirements of various fault data in engineering practice.

[0004] In recent years, various deep learning algorithms have been successfully applied to the field of fault diagnosis due to their powerful feature extraction and modeling representation capabilities. However, in actual industrial applications, due to their complex architectures, it is very difficult to fully design and train deep neural networks, and there are many difficulties in aspects such as feature extraction and optimization of a large number of parameters.

[0005] Therefore, we propose a bearing fault diagnosis method based on Legendre multi-wavelet transform to solve the problems in the prior art: complex architecture, very difficult to fully design and train deep neural networks, and many difficulties in aspects such as feature extraction and optimization of a large number of parameters. Summary of the Invention

[0006] The object of the present invention is to design a bearing fault diagnosis method based on Legendre multi-wavelet transform to solve the problems in the prior art: complex network structure, very difficult to fully design and train deep neural networks, and many difficulties in aspects such as feature extraction and optimization of a large number of parameters.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A bearing fault diagnosis method based on Legendre multi-wavelet transform, comprising the following steps:

[0009] S1. Use the vibration signal of a certain fault type under a certain load as the original signal data;

[0010] S2. Obtain X samples as a sample set in a way of overlapping segmented sampling for the original signal data, and divide the X samples into N training sets and M test sets, and X = N + M;

[0011] S3. Decompose the vibration signals of the above training set and test set once by 3 Legendre wavelets to obtain the corresponding low-frequency signal components and high-frequency signal components;

[0012] S4. Calculate the values of the digital features RMS and SD of the low-frequency signal components and high-frequency signal components respectively;

[0013] S5. Use the digital features RMS and SD of the training set as the fault feature vector set and input them into the BPNN classifier to train the BPNN classifier model;

[0014] S6. Input the test set into the trained BPNN classifier to verify its accuracy;

[0015] Furthermore, the fault types include:

[0016] Inner ring fault, outer ring fault, and rolling element fault with a single point fault diameter of 0.007 inches;

[0017] Inner ring fault, outer ring fault, and rolling element fault with a single point fault diameter of 0.014 inches;

[0018] Inner ring fault, outer ring fault, and rolling element fault with a single point fault diameter of 0.021 inches

[0019] Normal state bearing without artificial damage fault.

[0020] Further, the calculation of the RMS is as follows:

[0021]

[0022] Where X represents the overall sample; x represents the sample; n represents the total number of samples.

[0023] Further, the calculation of the SD is as follows:

[0024]

[0025] Where X represents the overall sample; x represents the sample; n represents the total number of samples;

[0026] Further, after 1 - level decomposition by 3 Legendre wavelets, the corresponding low - frequency signal components and high - frequency signal components are obtained. The decomposition method of the Legendre wavelet includes:

[0027] Divide the vibration signal into odd and even parts, and perform 1 - level Legendre multi - wavelet transform on the divided odd and even samples respectively: Convert a section of signal into corresponding low - frequency and high - frequency coefficients through the scaling basis function and wavelet basis function. The resolution level is determined by The decomposition process is described as follows:

[0028]

[0029]

[0030] Where, and respectively represent the low - frequency coefficient and high - frequency coefficient at the resolution level of j. Call the approximation part, and call the detail part; The value of m depends on the current resolution level j + 1 and the formula m = 2 j ;

[0031] At this time, the signal is decomposed into the approximation part and the detail part, and the mathematical expression is as follows:

[0032]

[0033] wherein represents a certain section of the signal, which is composed of the superposition of the results of the above approximate part and the detail part, and satisfies the following conditions:

[0034]

[0035] This indicates that the error approximation value obtained by signal decomposition will exponentially decrease and converge to with the improvement of the resolution and the increase in the number of Legendre multi-wavelets.

[0036] The present invention has the following beneficial effects:

[0037] The present invention uses Legendre multi-wavelet transform to perform multi-scale extraction of the fault essential features of the bearing signal characteristics, and identifies them through a BPNN classifier, constructing an LW-BPNN bearing fault diagnosis method; when used for bearing fault diagnosis, only two statistical parameters RMS and SD and a BPNN classifier are required to complete the fault identification with a relatively high diagnosis rate, effectively reducing the complexity of the framework, and it is also simpler and more convenient in terms of feature extraction and parameter optimization;

[0038] The present invention uses Legendre multi-wavelet transform to perform multi-scale extraction of the fault essential features of bearing data. Compared with traditional wavelets, the Legendre multi-wavelet basis has characteristics such as compact support, vanishing moments, orthogonality, and rich regularity. These advantages can not only thoroughly identify the essential features of various fault categories of the bearing, but also greatly reduce the complexity of extracting the optimal features;

[0039] Compared with deep learning methods, the present invention does not require strong hardware devices, does not need to design a model with a complex network structure, and is more feasible and valuable in practical engineering applications. And the method of the present invention has achieved good diagnostic accuracy and is very convenient in actual industrial applications and on-line diagnosis of rotating machinery. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solution of the present invention, the implementation process of the present invention will be described below with examples, and the drawings used in the examples will be briefly introduced.

[0041] Figure 1 is the original signal data of BF07;

[0042] Figure 2 are the low-frequency coefficients (a-1, b-1, c-1) and high-frequency coefficients (a-2, b-2, c-2) obtained by Legendre wavelet transform of BF07;

[0043] Figure 3 The diagnostic accuracy of the four methods under 10-fold cross-validation;

[0044] Figure 4 This is the overall flowchart of the method of the present invention. Detailed implementation manners

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be specifically noted that the specific examples described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] Generally speaking, the present invention designs a new fault diagnosis method: Legendre multi-wavelet transform is used to extract the essential fault features of bearing signals at multiple scales + BPNN classification diagnosis, that is, the LW-BPNN bearing fault diagnosis method.

[0047] I. Decomposition principle of Legendre wavelet

[0048] The Legendre wavelet transform refers to converting a segment of signal into corresponding low-frequency and high-frequency coefficients through a group of basis functions (scaling basis functions and wavelet basis functions). The following formula describes the decomposition process with the resolution level from :

[0049]

[0050]

[0051] Among them, and respectively represent the low-frequency coefficient and the high-frequency coefficient at the resolution level of j; (in matrix form) is called the approximation part, and (in matrix form) is called the detail part; the value of m depends on the current resolution level j + 1 and the formula m = 2 j (for example: when the current resolution level is ¾, that is, j + 1 = 3, then m = 4). For a detailed introduction of other variables involved in the above formula, please refer to the paper (Alpert B, Beylkin G, Gines D, et al. Adaptive Solution of Partial Differential Equations in Multiwavelet Bases[J]. Journal of Computational Physics, 2002, 182(1): 149-190).

[0052] At this time, the signal It is decomposed into an approximation part and a detail part, and the mathematical expression is as follows:

[0053]

[0054] Where represents a certain segment of the signal and satisfies the following conditions:

[0055]

[0056] The above formula shows that the error approximation obtained by signal decomposition decreases exponentially and converges to .

[0057] Based on the above principle, the process of decomposing the bearing vibration signal by Legendre multi-wavelet is as follows: First, the vibration signal is sampled in overlapping segments, and the obtained segmented signal is called a sample. Then, the sample is divided into odd and even parts, and the odd and even samples after division are respectively subjected to one Legendre multi-wavelet transform (the approximation part and the detail part mentioned above are obtained at this time). Finally, the transformed results are superimposed. This is the process of the signal after one Legendre multi-wavelet transform.

[0058] II. Refer to Figure 4 , and the detailed steps of the intelligent fault diagnosis method based on Legendre multi-wavelet are as follows:

[0059] The experimental data in this experiment come from the public measured bearing fault vibration data provided by the CWRU bearing data center. The bearing vibration signal is collected from an accelerometer near the motor drive end, and the sampling frequency is 12 kHz. A single-point fault is introduced into the test bearing (6205-2RS JEM SKF) by electrical discharge machining, resulting in three degrees of damage with diameters of 0.007, 0.014, and 0.021 inches respectively. According to the different fault locations, the bearing fault types are divided into three types: inner race fault (IR), outer race fault (OR), and rolling element fault (BF). Plus the normal condition (NC) bearing without artificial damage fault, all bearings are tested under four different motor loads (0, 1, 2, and 3 hp). Therefore, for each load condition, there are a total of ten types of fault modes, namely: BF07, BF14, BF21, IR07, IR14, IR21, OR07, OR14, OR21, and NC. Only the ten fault modes under one load are experimentally described in the following of the present invention. Table 1 shows the detailed description of the bearing data set under load 3.

[0060] Table 1 Specific description of the bearing data set

[0061] Bearing type BF BF BF IR IR IR OR OR OR NC Fault diameter 0.007 0.014 0.021 0.007 0.014 0.021 0.007 0.014 0.021 - Status abbreviation BF07 BF14 BF21 IR07 IR14 IR21 OR07 0R14 OR21 - Category label 1 2 3 4 5 6 7 8 9 10

[0062] The following steps will introduce how the proposed Legendre multi-wavelet transform combined with the BPNN classifier accomplishes bearing fault recognition.

[0063] Step 1: Use the vibration signal of a certain fault type under a certain load as the original signal data.

[0064] Step 2: Obtain 100 samples as a sample set by resampling the input signal, and then divide the sample set into a training set (80%) and a test set (20%).

[0065] Step 3: The vibration signal is decomposed once by 3 Legendre wavelets to obtain the corresponding low-frequency and high-frequency signal components. Calculate the values of the digital features RMS and SD from the signal components according to the above formulas (9) and (10), and use them as the extracted fault feature vectors.

[0066] Then, use the digital features calculated from the signal components corresponding to each signal in the sample training set as the feature vector set, and input it into the BPNN classifier for state recognition.

[0067] Step 4: Finally, normalize the fault feature vector set obtained from the sample training set to between 0 and 1, train the BPNN classifier, and then input the test set into the BPNN classifier to verify the health state of the bearing.

[0068] III. A specific embodiment of the present invention

[0069] Taking the BF07 fault type under load 3 as an example to illustrate the specific process of this experiment. As Figure 1 shown in the original signal data of the BF07 fault type, 100 samples are obtained from the BF07 vibration signal in a partially overlapping manner through a sliding window, and randomly divided into a training set (80%) and a test set (20%) according to a certain ratio. Each data sample is a measured vibration signal segment containing 4096 data sampling points.

[0070] The above-mentioned 4096-point bearing fault data samples are decomposed once by 3 Legendre wavelets to obtain the corresponding low-frequency signal components and low-frequency signal components. Figure 2 Shown in the low-frequency signal components and low-frequency signal components obtained after the BF07 is decomposed once by 3 Legendre wavelets. The decomposed low-frequency and high-frequency coefficient matrices are respectively represented as and . Calculate the values of the digital features (RMS and SD) of 6 signal components for each sample according to the above formulas (9) and (10). Finally, use the RMS and SD values corresponding to the signal components of the training set samples as the feature vector set, and input it into the BPNN classifier to start training the classifier model.

[0071] After the classifier training is completed, the test data is then input into the model to verify its accuracy (if the accuracy is met, the final BPNN classifier is obtained and used to diagnose bearing faults; if the accuracy is not met, the sample set is expanded and the classifier training is continued until the accuracy requirement is met).

[0072] To verify the effectiveness of the present invention, the method of the present invention (LW-BPNN) will be compared with Daubechies wavelet + BPNN (DW-BPNN), Daubechies wavelet + SVM (DW-SVM), and Legendre wavelet + SVM (LW-SVM) in terms of diagnostic accuracy as shown in Tables 2, 3, and 4 below. They are the accuracies of the test sets obtained by RMS, SD, and RMS+SD respectively. It can be seen from the tables that this method has achieved good recognition accuracy, verifying the effectiveness of this method.

[0073] Figure 3 The figure shows the diagnostic accuracies of the four methods under 10-fold cross-validation. It can be seen from the figure the stability of the present invention in fault diagnosis. Combining the above advantages, it can be seen that the method of the present invention is very convenient to implement in actual industrial applications and on-line diagnosis of rotating machinery.

[0074] Table 2 Average test accuracy obtained by RMS

[0075] Method BF07 DW-SVM 0.9920±0.004000 DW-BPNN 0.9990±0.002000 LW-SVM 0.9950±0.003162 LW-BPNN 1.0000±0.000000

[0076] Table 3 Average test accuracy obtained by SD

[0077] Method BF07 DW-SVM 0.9820±0.006782 DW-BPNN 0.9980±0.002449 LW-SVM 0.9830±0.008718 LW-BPNN 0.9990±0.002000

[0078] Table 4 Average test accuracy obtained by RMS+SD

[0079] Method BF0 DW-SVM 0.9890±0.010198 DW-BPNN 0.9980±0.002449 LW-SVM 0.9880±0.005099 LW-BPNN 1.0000±0.000000

[0080] The above describes the basic principle, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the limitations of the above examples. What is described in the above examples and the specification is only the principle of the present invention. Without departing from the principle of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of protection required. The scope of protection required by the present invention is defined by the appended claims and their equivalents.

Claims

1. A bearing fault diagnosis method based on Legendre multi-wavelet transform, comprising the following steps: S1. Use the vibration signal of a certain fault type under a certain load as the original signal data; S2. Obtain X samples as a sample set by means of overlapping segmented sampling of the original signal data, and divide the X samples into N training sets and M test sets, and X = N + M; S3. Decompose the vibration signals of the above training set and test set once by 3 Legendre wavelets to obtain the corresponding low-frequency signal components and high-frequency signal components; S4. Calculate the values of the digital features RMS and SD of the low-frequency signal components and high-frequency signal components respectively; S5. Use the digital features RMS and SD of the training set as the fault feature vector set and input it into the BPNN classifier to train the BPNN classifier model; S6. Input the test set into the trained BPNN classifier to verify its accuracy; After decomposing once by 3 Legendre wavelets to obtain the corresponding low-frequency signal components and high-frequency signal components, the decomposition method of the Legendre wavelet includes: Divide the vibration signal into odd and even parts, and perform 1 - order Legendre multi - wavelet transform on the divided odd and even samples respectively: convert a section of signal into corresponding low - frequency and high - frequency coefficients through scaling basis functions and wavelet basis functions, and the resolution level is determined by The decomposition process is described as follows: ； ； Among them, and respectively represent the low-frequency coefficient and the high-frequency coefficient at the j-th level of resolution; is called the approximation part, and is called the detail part; the value of m depends on the current resolution level j + 1 and the formula m = 2 j ; At this time, the signal is decomposed into an approximation part and a detail part, and the mathematical expression is as follows: ； Among them represents a certain section of signal, which is formed by the superposition of the results of the above approximate part and the detail part, and satisfies the following conditions: ； This indicates that the error approximation obtained from signal decomposition will decrease exponentially and converge to .

2. The bearing fault diagnosis method based on Legendre multi-wavelet transform according to claim 1, wherein The fault types at least include: Inner ring fault, outer ring fault, rolling element fault with a single-point fault diameter of 0.007 inches; Inner ring fault, outer ring fault, rolling element fault with a single-point fault diameter of 0.014 inches; Inner ring fault, outer ring fault, rolling element fault with a single-point fault diameter of 0.021 inches Normal state bearings without artificial damage faults.

3. A bearing fault diagnosis method based on Legendre multi-wavelet transform according to claim 1, characterized in that, The calculation of the RMS is as follows: ； Where X represents the total sample; x represents the sample; n represents the total number of samples.

4. A bearing fault diagnosis method based on Legendre multi-wavelet transform according to claim 1, characterized in that The calculation of the SD is as follows: ； Where X represents the total sample; x represents the sample; n represents the total number of samples.

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