Research on fault diagnosis method of electromechanical transmission system based on one-dimensional convolutional neural network with variable learning rate

2.1. Principle of one-dimensional convolutional neural network

Convolutional neural network (CNN) usually consists of five modules: input layer, convolutional layer, pooling layer, fully connected layer and output layer [15]. CNN has been widely used in the field of pattern recognition. Compared with traditional neural networks, it greatly reduces network structural parameters, accelerates model training efficiency and reduces the risk of “overfitting” to a certain extent [19].

The difference between one-dimensional convolutional neural network and convolutional neural network is that the dimension of feature vectors is one-dimensional [20]. In the first step, the one-dimensional vibration input signal is prepared. By constructing multiple convolutional layers, pooling layers and using nonlinear activation function, the network can learn the complex features of the data. Next, build a series of fully connected fully connected layers; After the activation function in the last fully connected layer, a multi-dimensional vector consisting of each category probability is output, which is then classified by Softmax to achieve the target output category. Fig. 1. shows the structure of one-dimensional convolutional neural network (1DCNN).

Fig. 1Structure diagram of 1D-CNN

Input layer: The function is to preprocess the original vibration signal in segments, and divide the input signal according to the set time step. The feature extraction layer includes a convolution layer and a pooling layer, which receives vibration data from the input layer, and uses multiple convolution kernels in the convolution layer to extract features from the original vibration signal to obtain multiple feature vectors. The maximum pooling operator reduces the dimension of the feature vector and improves the robustness of nonlinear features. Multiple alternating convolutional pooling layers achieve hierarchical extraction of nonlinear features of input signals. The classification layer consists of two fully-connected layers, of which the first fully-connected layer implements the “flattening” operation on the features, that is, all feature vectors are connected end to end to form a one-dimensional vector. The number of neurons in the second fully connected layer is consistent with the number of fault categories, and the Softmax regression classifier is used to achieve the target output category [15].

One-dimensional convolutional layer: It is composed of several one-dimensional convolution units (convolution kernels), and the parameters of each convolution kernel are obtained by the back propagation algorithm to obtain their optimal values. The purpose of the convolution operation in the convolutional layer is to extract the features of the input samples. The more complex the convolutional network, the more complex the features can be extracted through continuous iterations. Convolution formula:

where: $w_{i,c}^l$ is the input characteristic diagram; $c^{l-1}$ is the serial number of the network layer; $x_i^{l-1}$ is the weight parameter; $b_i^l$ is network offset and $x^l$ is output.

One-dimensional pooling layer: Commonly used are maximum pooling and average pooling. As shown in Fig. 2.

The connection layer: Map the learned “distributed feature representation” to the sample label space.

Classifier: With the “Softmax” classifier, the Softmax classifier is a common linear classifier, which is a generalization of Logistic Regression classifier. The Softmax classifier completes the multi-classification problem. The formula is as follows:

where, $z^o\left(j\right)$ represents the output value of the $J$th neuron in the output layer, $z^o\left(k\right)$ indicates the output value of the $K$th neuron in the output layer and $M$ represents the total number of categories [22].

Fig. 2Schematic diagram of average pooling and maximum pooling

2.2. Principle of learning rate

In machine learning, learning rate is the tuning parameter in the optimization algorithm. Learning rate is an important super parameter in supervised learning and deep learning, and the symbol is $\eta$, it determines whether and when the objective function can converge to the local minimum. The appropriate learning rate can make the objective function converge to the local minimum in the appropriate time.

However, the selection of learning rate is very difficult, which is determined by the trainers. High learning rate means that the weight update action is larger, so it may take less time to converge to the optimal weight. However, too high a learning rate will lead to too large a beat, which is not accurate enough to reach the best advantage. Since a small learning rate is conducive to the stability of the system, most trainers tend to choose a small learning rate value, which ranges from 0.001 to 0.1 [23].

The value of learning rate is particularly critical to overcome the problem of gradient descent method. An excellent learning rate algorithm can set the appropriate learning rate at different stages of training, so that the model can converge to the optimal solution faster [24]. Too small learning rate will cause slow convergence of the model, and too large learning rate will cause large jitter of the loss function. Therefore, an appropriate learning rate algorithm is very important in the process of depth model training. Table 1 introduces several common learning rate algorithms [25].

3.1. Experimental test system and data acquisition

This experimental test system is composed of the experimental platform of DC servo motor system (including the motor bench and Easy Motion Studio software), and ECON acceleration signal acquisition equipment (including ECON vibration analyzer and PC platform), as shown in Fig. 3. Fig. 3 was taken by the author while doing the experiment in the laboratory of Guangdong Polytechnic Normal University. The measured object was a motor bench, and the experimental content included fault setting and vibration acceleration signal acquisition. Three PCB vibration acceleration sensors were pasted on the motor test bench, respectively at the corresponding positions of the rotating shaft and the bearing base.

The experimental protocol is shown in Table 2. Five fault types were set, including one broken tooth of the transmission belt, two broken teeth (the position of the break point is basically symmetric), shaft imbalance, large friction of the passive wheel and bearing damage, etc. Together with the normal state, a total of six state data were analyzed. The detailed working method is as follows: after setting a state, set the speed parameters through Easy Motion Studio software, drived the motor to rotate normally, and use ECON vibration signal acquisition instrument to collect vibration signals. According to the experimental scheme of the motor, each speed was tested three times, about 25 s for each time. The collected signals were named and saved. Then the collected vibration signals are analyzed, including spectrum analysis and one-dimensional convolution neural network analysis.

Fig. 3Test system

a) ECON vibration analyzer

b) Motor bench

3.2. Vibration signal analysis

Perform spectrum analysis on the collected vibration acceleration signals to understand and observe the dynamic changes and frequency characteristics of different faults, including the main frequency components of the vibration signal, the range of frequency distribution, and the amplitude of each frequency component, so as to obtain information about main frequency values and their corresponding amplitudes that affects the state of the equipment, in order to understand the characteristic information of each fault state of the equipment to a certain extent [26]. The current spectrum analysis is mainly divided into numerical algorithms based on time-domain solution and numerical algorithms based on frequency-domain solution [27]. Among the numerical algorithms based on time-domain solution, the linear acceleration algorithm [28] and Duhamel integral method [29] are the most widely used. The time domain algorithm can be used to determine the dynamic response of the structure under any time-varying external load and initial conditions. Although the time domain algorithm can effectively solve a large number of problems about structural vibration, in some cases, the frequency domain algorithm has more advantages than the time domain algorithm [30-32]. Moreover, due to the introduction of fast Fourier transform (FFT) and other algorithms [33], the operational efficiency of frequency domain algorithms has also been greatly improved. Therefore, frequency domain algorithms have been more and more widely used [34-35]. Therefore, frequency domain analysis is adopted for vibration signal analysis in this experiment.

In this experiment, the normal state of the transmission system, 1 broken tooth of the belt, 2 broken teeth of the belt (the position of the breakpoint is basically symmetrical), shaft unbalance, large friction of the driven wheel, belt break and damage of the bearing were set up. The sampling rate was set to 16384 Hz to collect vibration acceleration signals with sufficient high frequency. Fig. 4 shows the spectrum analysis diagram of vibration acceleration signals in each state at the bearing base position at a speed of 2500 rpm.

It can be seen from Fig. 4 that the overall fluctuation law of the vibration spectrum is similar in the normal state and various fault states. The frequency component corresponding to the maximum amplitude value is about 200 Hz, which corresponds to the meshing frequency between the belt and the output shaft belt wheel. In addition to the main frequency peak, there are also multiple modulation edge bands on both sides of the peak with similar characteristic distributions. It can be seen that the overall law of the spectrum between the normal state and the fault state is similar, and it is difficult to identify specific fault characteristics. Therefore, intelligent diagnosis and recognition can be carried out through the deep learning convolutional neural network method.

Fig. 4Spectrum diagram of vibration acceleration signal

a) Normal

b) Belt broken tooth 1

c) Belt broken teeth 2

d) Dynamic unbalance

e) Large friction

f) Belt breakage

g) Bearing damage

4.1. Identification analysis for all fault conditions

The 1D-CNN network model is constructed for the data samples under all fault states, and its parameters are shown in Table 3. The input of its one-dimensional convolution neural network is the vibration signal data samples in each state. Through this model, the segmented preprocessing data samples are trained, learned and identified.

As shown in Fig. 5, it can be seen that after about 5000 iterations, the loss value of the training set and validation set are roughly between 1.35 and 1.4, and the accuracy of the training set and validation set are roughly between 0.8 and 0.9, indicating that the training effect is not ideal. According to the confusion matrix, the recognition degree of each fault type can be known. The recognition degree of the normal state is 0.93, the state of broken tooth 1 is 0.54, the state of broken teeth 2 is 0.91, and the recognition degree of the rest of the fault states is 1, as shown in Fig. 6. The fault states of broken tooth 1 and broken teeth 2 are easy to be confused and difficult to distinguish.

Fig. 5Loss function and accuracy of training and verification

a)

b)

Fig. 6Confusion matrix

4.2. Recognition and analysis under the fault state of removing broken tooth 1

According to the above analysis, the effect of broken tooth fault state is not ideal. The reason is that the broken tooth 1 fault was realized by artificially cutting off one tooth on the inner side of the belt, which is actually a slight fault state, and the vibration response signal of this state is very close to the normal state. Therefore, after removing the fault state of broken tooth 1, the identification analysis is carried out to further grasp the factors affecting the identification accuracy.

The network structure parameters still use the data in Table 3, and the learning results are shown in Fig. 7. After about 5,000 training iterations, the loss values of the training set and the validation set dropped to between 1.1 and 1.15, the accuracy of the training set and the validation set rose to between 0.9 and 1.0, the accuracy was improved, and the training effect was gradually ideal. It is verified that the fault of broken tooth 1 is similar to the normal state data, and it is indeed difficult to identify, which is consistent with the actual situation. The confusion matrix diagram is shown in Fig. 8. The recognition degree of normal state is 0.97, the recognition degree of broken teeth 2 fault is 0.98, and the recognition degree of other faults is between 1.00, and the recognition degree is greatly improved.

Fig. 7Loss function and accuracy of training and verification

a)

b)

Since the fault degree of broken teeth 2 is also in a slight range, it is also very close to the normal situation. In order to further verify the conclusion, after removing the fault state data of broken teeth 2, the remaining states are trained and learned. After about 3000 training iterations, the loss value of training set and validation set is between 0.9 and 0.95, and the accuracy of training set and validation set is above 0.99. According to the confusion matrix, the recognition degree of each fault is 1.00, and the recognition accuracy is 100 %.

Fig. 8Confusion matrix

4.3. Comparison of identification results under different number of fault states

Based on the above analysis, all the fault state data are trained and tested, and the effect is not ideal. The fault of broken tooth 1 was easily confused with the normal state, and the recognition degree was as low as 0.54. After removing the fault of broken tooth 1 and retraining and testing, the recognition degree has been improved, but the recognition degree is only 0.97 in the normal state, and there is also a recognition error between the fault state of broken teeth 2 and the normal state. After removing all broken tooth fault states, retraining and testing was carried out. It was found that the fault identification degree is improved to 1.00 when the number of training iterations is reduced. The results are shown in Table 4. In general, except for the fault states of broken tooth 1 and broken teeth 2, which are very close to the state data, which are easily confused with the normal state, the network model has high diagnostic and recognition accuracy for the rest of the fault states, and the method is feasible.

5.1. Different convolution kernel sizes

a) Try to change the size of the convolution kernel from 3 to 5, and verify whether modifying the size parameter of the convolution kernel can improve the recognition degree. After testing, as shown in Fig. 9, it can be seen that after about 5000 iterations, the loss value of the training set and the validation machine is roughly between 1.25 and 1.3, and the accuracy of the training set and the validation set is roughly between 0.85 and 0.9, the confusion matrix in Fig. 10. shows that the recognition degree is 0.54 under the fault state of broken tooth 1 and 0.94 under the fault of broken teeth 2, and the training effect was still not ideal.

Fig. 9Loss function and accuracy of training and verification

a)

b)

b) Continue to try to change the size of the convolution kernel to 7. After training and testing, the following results are obtained: After about 5000 iterations, the loss values of the training set and the validation set are roughly between 1.3 and 1.4, and the loss values of the training set and the validation set are roughly between 1.3 and 1.4. The accuracy of training set and validation set is roughly between 0.85 and 0.9. The training effect is mediocre. It can be seen from the confusion matrix in Fig. 11. that the recognition rate in the fault state of broken tooth 1 is only 0.31, and it was more identified as the fault state of broken teeth 2, which was seriously confused.

Therefore, the size of the convolution kernel is not as large as possible. When the size of the convolution kernel is selected to be 5, the overall recognition degree is relatively high.

Fig. 10Confusion matrix

Fig. 11Confusion matrix

5.2. The case of different sync size

Try to adjust the step size to verify that fault recognition is improved. The original step size is adjusted from 1 to 2. After about 5000 iterations, the loss value of training set and validation set is between 1.3 and 1.4, and the accuracy of training set and validation set is roughly between 0.8 and 0.9. According to the confusion matrix Fig. 12, the recognition rate of broken tooth 1 fault state is 0.34, and 51 % of them are still identified as broken teeth 2 fault, which is not ideal. Moreover, the overall recognition tended to decrease, so the attempt to change the step size did not have the desired effect.

After the above two parameter modifications, the analysis did not get the ideal effect, so we tried to modify the convolution kernel size and step size at the same time for analysis. After about 5000 iterations, the loss values on the training and validation sets are roughly between 1.3 and 1.4, and the accuracy on the training and validation sets are roughly between 0.8 and 0.9. The confusion matrix shows that the recognition degree was 0.88 in the normal state and 0.48 in the fault state of broken tooth 1. The recognition accuracy between the faults of broken tooth 1 and broken teeth 2 was not ideal, especially the fault of broken tooth 1 was identified as the fault of broken teeth 2, as shown in Fig. 13.

Fig. 12Confusion matrix

Fig. 13Confusion matrix

5.3. Different number of convolution layers

Since neither convolution kernel nor step size can be changed to improve fault identification, now we try to increase the number of convolution layers based on convolution kernel of 5 and step size of 2, and increase the original three-layer convolution layer to four-layer convolution layer to verify whether the fault identification can be improved. The confusion matrix is shown in Fig. 14. The recognition accuracy of broken tooth 1 fault is still not significantly improved, and there is no significant difference in the overall state recognition degree. Therefore, the method of increasing the number of convolution layers fails to make the result better.

Fig. 14Confusion matrix

5.4. Use different activation functions

We tried to adjust the activation function to Relu and Tanh functions respectively on the basis of the network structure with convolution kernel size of 5, but the recognition results were not improved for the normal state, broken tooth 1 fault state and broken teeth 2 fault state.

By comparing the recognition accuracy of the above adjusted parameters, it was found that the fault identification degree of the network structure with convolution kernel of 5 was better than that of the network structure with other parameters, as shown in Table 5.

5.5. Try VGG11 model

After the above optimization parameters, the desired effect is still not achieved, so we want to optimize the network. The above adjustment is based on one-dimensional convolution neural network. This time, we try to use the classical VGG model. VGG model belongs to the deep convolution neural network model, including VGG11, VGG13, VGG16 and VGG19 models. However, because the VGG11 model has the least number of network layers, less network parameters and low training time cost [36], the VGG11 model is preferred when optimizing the algorithm.

The model is built and tested. It can be seen from Fig. 15 that after about 5000 iterations, the loss value of training set and verification set is about 1.3 to 1.4, and the accuracy rate of training set and verification set is about 0.8 to 0.9. The confusion matrix diagram shows that the recognition degree under normal condition is 0.58, the recognition degree under broken tooth 1 fault condition is 0.45, and the recognition degree under broken tooth 2 fault condition is 0.76, as shown in Fig. 16. None of them is ideal, and there is no obvious improvement compared with one-dimensional convolution neural network, as shown in Table 6.

Fig. 15Loss function and accuracy of training and verification

a)

b)

Fig. 16Confusion matrix

5.6. Summary of parameter selection

According to the characteristics of samples, the basic structure of the classical model VGG was adapted to construct a one-dimensional convolutional neural network. Since the recognition is still not ideal when the convolution kernel is 3, attempts are made to expand the convolution kernel, increase the global attention of the convolution kernel, capture global features, and then conduct training. Since it is verified that the means of expanding convolution kernel has no obvious effect on the improvement of fault recognition degree, the small verification step size has an impact on the recognition degree. Adjusting the convolution kernel size can reduce the number of sample parameters after convolution, reduce the sample complexity and improve the training rate. It has been verified above that changing the size of convolution kernel and changing the size of step cannot improve the recognition, so try to change the number of convolution layers. Generally speaking, changing the number of convolutional layers can change the depth of the network, making the training more efficient and affecting the accuracy of recognition. Different activation functions can change the linear fitting ability and learning efficiency of the model. However, in the case of small and similar fault states, all the states cannot be well identified by the above method of parameter adjustment. Try again to optimize the network model, try VGG11 model, but the ideal effect is not achieved.