Fault diagnosis for rolling bearings based on SPWVD-CNN

Wei-xing CHEN, Xi-xi SUN, Tao WANG

(College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China)

Abstract: Aiming at the shortcoming that the traditional fault diagnosis method of rolling bearings is difficult to extract the effective characteristics of bearing vibration data, a network model SPWVD-CNN based on smooth and pseudo Wigner-Vill distribution (SPWVD) and convolutional neural network(CNN) was proposed. It used smooth and pseudo Wigner-Vill distribution to analyze vibration signals of rolling bearings and Compressed the obtained time-frequency representations as input to CNN. Using the idea of migration learning to train the network, the model had good diagnostic performance for the data of different loads and improved the generalization ability of the network. The experimental results indicate that the average classification accuracy of SPWVD-CNN to bearing fault data is increased to 99.27%, and the overall performance is better than using a single CNN and other traditional fault diagnosis methods.

Key words: Rolling bearing, Fault diagnosis, SPWVD, CNN

The traditional bearing fault diagnosis method based on vibration signal includes three steps of data preprocessing, feature extraction and pattern classification, and the extracted features are generated by time domain [2], frequency domain [3] or time frequency domain [4], and the extracted features are input support vector machine [5-6], decision Tree [7], BP neural network [8] and other classifiers. Wu et al. [9] used the multi-scale permutation entropy of the vibration signal as the input of the SVM classifier for fault diagnosis. Van and Kang [10] calculated energy and time-domain statistical indicators from EMD decomposition results for sensitive feature selection, and applied SVM classifiers to improve bearing defect classification performance. However, the shallow neural network features such as BP neural network and SVM have limited ability to learn and to express, and are easy to fall into local optimum. CNN has good performance in the fields of image processing [11], speech recognition [12], fault diagnosis and so on. Sun et al [13] used CNN to extract the wavelet characteristics of bearing vibration data, and the accuracy of fault classification improved; Wang [14] established an adaptive CNN fault diagnosis model, which was successfully applied to the fault diagnosis of rolling bearings for electric locomotives.

The traditional diagnostic method ignores the frequency information in the sample and the fault recognition rate is low. Aiming at the above problems, a bearing fault diagnosis method based on CNN-SPWVD is proposed, which extracts the two-dimensional characteristics of the original measurement data in time domain and frequency domain. The training network is trained by using the idea of transfer learning, and less training data can be used. A network with strong generalization ability, monitoring vibration data for massive bearings, reducing the difficulty of network training. The method has strong learning ability and high reliability, can accurately monitor the wear state of the rolling bearing, analyze the working condition of the rolling bearing, and find the problem in time in the early stage of the failure to avoid the occurrence of a larger mechanical accident.

1 Theoretical basis of the method

1.1 Smooth and pseudo Wigner-Vill distribution

The collected vibration signal iss(t), and the analytical signalz(t) corresponding tos(t) is obtained by Hilbert transform. The SPWVD method is used to intercept the time axis and the frequency axis by using the window function, and the obtained vibration signal is:

(1)

Whereg(u) is the time domain smoothing window andh(τ) is the frequency domain smoothing window.

1.2 Convolution neural network

The convolutional neural network directly analyzes the original image without complex preprocessing. A typical CNN includes an input layer, a convolutional layer, a pooled layer, and a fully connected layer. CNN can handle complex problems in complex environmental information and context, and utilizes the characteristics of weight sharing to integrate local features of data into multi-layer sensors, which has good performance for fault identification and diagnosis. The CNN network structure is shown in Fig.1.

Fig.1 CNN structure diagram

2 Modeling and analysis of fault diagnosis of rolling bearings based on SPWVD-CNN

2.1 Description of the problem

The vibration signals of rolling bearings in 6 different states are shown in Fig.2, Fig.3 is the normal state and the smooth pseudo Wigner-Ville distribution time frequency representations of the bearing outer ring under different fault positions. Compared with figures 2 and 3, the difference between the faults in the Wigner-Vile distribution time frequency expression is significantly greater than the difference in the time domain of each fault, and the time-frequency graph contains more abundant variation characteristics. Therefore, through SPWVD transform, the fault diagnosis performance of neural network can be improved by extracting the two-dimensional features of data in time domain and frequency domain.

Fig.2 Time domain waveform diagrams in different fault states

Fig.3 Waveform diagram of SPWVD vibration signal

2.2 Fault diagnosis process

Aiming at the characteristics of the failure state of rolling bearing and the non-stationary nonlinearity of vibration signal, the SPWVD method is combined with CNN to extract the characteristics of data in time dimension and frequency dimension, so as to improve the efficiency of fault diagnosis.

The bearing fault diagnosis process based on SPWVD-CNN is shown in Fig.4. It is divided into three phases: source task phase, parameter transfer phase, and target task phase. After the vibration data is SPWVD transformed, the time-frequency map is obtained, grayed out and normalized, and the image size is reduced to 64×64 as the input of CNN. The CNN network is trained by the idea of migration learning to realize the bearing fault diagnosis classification.

Then he started off in pursuit, making his way through bushes and briars, and never stopped all day; but in the evening the stag entirely disappeared, and when golden lad came to look about him he found himself just opposite a hut in which lived a witch

Fig.4 Fault diagnosis flowchart based on SPWVD- CNN

2.3 Network training method

Transfer Learning (TL) improves the performance of target tasks by learning source tasks. The CNN is trained with a small amount of source data under a certain load condition, and the network is applied to fault diagnosis under multiple working conditions. The fault diagnosis process created according to the TL idea can effectively reduce the network training period and improve the generalization ability of the network.

The source data and the target data are as shown in equations (2) and (3), respectively:

Ds={Xs,Ts}

(2)

Dt={Xt,Tt}

(3)

Among them,Ds、Dtrepresent source data and target data respectively.XsandXtrepresent the source sample and the target sample, respectively, andTsandTtrepresent the corresponding labels.

The source task and the target task are as shown in equations (4) and (5), respectively:

Ys=fs(Xs,θs)

(4)

Yt=ft(Xt,θt)

(5)

Wherefsrepresents mapping fromXstoYs, andftrepresents mapping fromXttoYt.YsandYtare actual outputs, andTsandTtare the expected outputs of the source task and the target task, respectively.θs,θtare the parameters of the source task and the task, respectively. {Xs,Ts}, {Xt,Tt} are data with different distributions or with different spatial characteristics.

In this study, the source data and the target data are normal data and fault vibration data under different load conditions. The migration learning finds some related attributes in the source data {Xs,Ts} and obtains the mappingfsin the source task. Then, after the mappingfsis migrated to the target task, the mapping in the target taskftis learned from the target data {Xt,Tt}.

The TL and the CNN are used in combination, and the trainedulayer is transmitted to thevlayer in the target network through migration learning, whereu

Table 1 CNN architecture for standardizing transport networks

3 Case analysis

3.1 Structure data sets

Bearing vibration data was selected from the open bearing vibration data of the Western Reserve University. This experiment uses the 6205-2RS JEM SKF bearing to produce three single point defects through electrical discharge machining. The vibration data of the bearing in four states is collected, namely: normal condition, rolling element failure (BD), inner ring failure (IR), outer ring failure (OR), the fault diameter is 0.007 inches, and the load is 0,1,2,3hp, respectively. The sampling frequency is 12 kHz. Outer Ring Fault (OR) has three fault locations: Center OR, Quadrature OR, OR in the opposite position. Each type of fault sample has 400 samples, each containing 1 200 data points. 20% of the samples of different health status were randomly selected as test samples, and the rest were used as training samples. The data set is shown in Table 2.

Table 2 Different fault sample numbers and label settings

3.2 Analysis of diagnostic performance of SPWVD-CNN under different working conditions

The training and testing of the network in this article was performed on a single computer (Intel Core (TM) 3.4 GHz processor, 64 GB RAM). The original image has a resolution of 128×128, compressed to 64×64 by SPWVD and used as a network input. The hidden layer is composed of two layers of convolution and two layers of sampling, and the convolution of the first and second convolution layers. The number of cores is 16 and 32, the convolution kernel is 3×3, the activation function is sigmoid function, the maximum sampling is used, and the dropout rate is 0.02.

Experiment under different load conditions and different network training schemes. The experimental steps are as follows: First, C1 is used to train the network, C2, C3, and C4 test the network to verify the generalization ability of the network; then, C2 is used for training. Network, C1, C3, C4 test network; secondly, C3 is used to train the network, C1, C2, C4 test network; finally, C4 is used to train the network, C1, C2, C3 test network. The accuracy of network classification is shown in Table 3. Migration learning improves network diagnostic performance, increases the generalization ability of the network, and verifies the effectiveness of migration learning.

In order to evaluate the performance of the method, the weight of the training data samples is taken into account. 80% of the training data of each program is considered from the source data set. By performing the same experiment on different numbers of training data, the training data is occupied. The ratio of fault diagnosis will be different. As shown in Table 4, when 80% of the vibration data in the training data set is used for different schemes, the network classification performance is the best.

Table 3 Network classification accuracy under different training schemes

Continued Table

Table 4 Classification accuracy of training samples of different scales

3.3 Analysis of diagnostic performance of SPWVD-CNN and traditional methods

First, with C1 as the source task and C2 as the target task, the classification accuracy of the migration learning and non-migration learning networks is evaluated. No migration learning means training the network from scratch. As shown in Table 5, compared with the network using migration learning, the network classification accuracy rate with migration learning is obviously improved. The accuracy of the two networks is the same for Normal. For other types of failures, the network using migration learning is better than the network performance without migration learning. As shown in Fig.5, the network training time required to achieve the same training classification accuracy is shorter than that of the network that does not apply migration learning. After 80 iterations, the accuracy of network classification using migration learning reached 98.96%, and the network without migration learning needs to iterate 160 times to achieve the same classification accuracy. The experimental results show that using the migration learning idea improves the classification accuracy of the network and shortens the training time.

Table 5 Comparison of Network Classification Accuracy Based on Transfer Learning Thoughts and Non-transfer Learning Thoughts

Fig.5 Network training accuracy

The traditional methods such as SPWVD-CNN and SPWVD, NN-TL and CNN are compared under four load conditions. The experimental results are shown in Table 6.

In the C1 state, the average classification accuracy of SPWVD-CNN for the six fault states is 99.27%, which is 17.16%, 6.06%, and 1.62% higher than the single SPWVD method, the CNN method, and the CNN network method using migration learning. In the C2 state, the average classification accuracy of SPWVD-CNN for 6 fault states is 99.13%, which is 16.58%, 5.8%, and 1.6% higher than the single SPWVD method, CNN method, and CNN network method using migration learning; In the state, SPWVD-CNN has an average classification accuracy rate of 99.20% for six fault states, which is 15.74%, 6.6%, and 1.94% higher than the single SPWVD method, CNN method, and CNN network method using migration learning; Under the SPWVD-CNN, the average classification accuracy rate of the six fault states is 99.02%, which is 17.52%, 6.46%, and 1.06% higher than the single SPWVD method, the CNN method, and the CNN network method using migration learning. For 6 different bearing faults and different loads, the accuracy of SPWVD-CNN is significantly better than the traditional method. The SPWVD-CNN model has good stability and high sample classification accuracy.

4 Conclusion

For the typical non-stationary nonlinear rolling bearing fault vibration signal, the traditional data feature extraction method is not only time-consuming, but also error-prone, which cannot play the role of fault diagnosis. The SPWVD-CNN network proposed in this paper uses the smooth pseudo WVD to construct a time-frequency map and uses the CNN network to extract features. Using the thought training network of migration learning, the diagnostic efficiency of rolling bearing fault state is improved. Experiments on the classification of rolling bearing fault states show that the fault classification accuracy of the network is higher than the traditional fault diagnosis method and a single CNN, which has better performance. The research in this paper is based on laboratory simulation data. The author will further verify the practicability of the SPWVD-CNN network in the rolling bearing composite fault system.