## 1. Data acquisition

In the experiment, the gear fatigue life test-bed as shown in Figure 1 is used to monitor the vibration acceleration and noise of the gear, and the sensor position of the main test box is determined. As shown in Figure 2, the real-time monitoring data obtained by the corresponding sensor is used as the experimental data set. Continuous experiments make the surface of the gear crack and continue to expand until the occurrence of broken teeth. At different times, the gear vibration will have obvious changes. The signal collected in this paper is the vibration acceleration signal of the gear, which is a physical quantity continuously changing with time, and can represent the degradation state of the gear from operation to fault.

## 2. Data prediction

By comparing the predicted value with the fault threshold and recording the current operation time TN and the time TP when the predicted value exceeds the threshold, the predicted remaining life is trul ‘= TP TN, and trul is used to represent the actual remaining life of the gearbox, trul = 77.17-tn. The accuracy of residual life prediction can be expressed as follows:

### 2.1 Determination of DBN structure

In the experiment, the connection weight between visible layer and hidden layer is 0-1, and the generalization error of neural network ensemble is 0.5. After many experiments, the learning rate of BP algorithm is set to 0.005. Figure 3 and Figure 4 are the results of 10 experiments after training the model with the data of 75 h running time. Figure 3 shows the MSE obtained by MLP and DBN on data set d-data as the number of hidden layers increases from 1 to 7. MLP and DBN use the same number of hidden neurons in each hidden layer. It can be seen that when the hidden layer is 1-3 layers, the MSE of both layers are in a downward trend. When the hidden layer is more than 3 layers, the MSE of both layers is in an upward trend, but the change of DBN is relatively gentle. Therefore, the DBNs in this paper are all set as three hidden layers.

When the number of hidden elements is [20,10], [15,10] and [10,5], the mean square error is the smallest. Therefore, the DBN in this paper consists of three RBMs. The input eigenvector is 1 × 5, the output data is 1 × 1 。

This is shown in Figure 4 λ = It can be seen from the figure that the corresponding mean square error changes with the evolution algebra at 0.8, 0.3 and 0.05 λ 8 and 0. 3, λ When it is 0.05, the decrease is slower. In the three cases, the model tends to be flat near the 24th generation and complete convergence. In addition, when λ The minimum error is 0.3. So the penalty coefficient is set in the experiment λ = 0． 3 。

### 2.2 Analysis of prediction results

Figure 5 shows the change of gear vibration acceleration with running time. The horizontal axis represents the running time of the gear and the vertical axis represents the eigenvalue. It can be seen that in the process of gear performance degradation, the change of eigenvalue presents a nonlinear upward trend. The data on the acceleration sensor is d-data, and the threshold value of gear fault is y = 76.38 mm / S2.

Figure 6 shows the fitting results of DBN Integrated Model 70 h before the application of d-data and the prediction of the corresponding test set. The transverse axis is the running time of the gear, and the longitudinal axis is the eigenvalue. The dotted line represents the true value of the training set, the dotted line represents the fitting value of the training set, the triangular line represents the test set, and the * line represents the predicted value.

The MSE of the training set and the test set of the integrated model and a single DBN at different times are compared. It can be seen that the average error between the training set and the test set is 0.13 lower than that of a single DBN × 10－2。 It can be concluded that there is a big difference between the predicted residual life and the real value at 30-50 H. With the increase of monitoring acceleration data, the absolute error between the predicted value and the actual value of the residual life gradually decreases. When the prediction time is 70 h, the failure time is 75.83 h, and when the prediction time is 75 h, the failure time is 77 h, which is 10.83% higher than that of 70 H. Two charts show that the proposed method can predict the residual life well, and has better generalization performance than a single DBN.