## 2 Small-Sample Adaptive Residual Life Prediction Model Based on Feature Matching Preprocessor-LSTM
### Small-Sample Adaptive Residual Life Prediction Model Based on Feature Matching Preprocessor-LSTM
After establishing the small-sample adaptive remaining life prediction model based on LSTM neural network, the standard deviation and instantaneous failure rate are extracted from the experimental data as the main features according to the above formula, and some other features in the time domain and frequency domain are taken as auxiliary features, and the output is in the form of percentage of remaining life to train the network. Model simulation was performed on the sample data with the established prediction model: since the LSTM neural network fitting is stochastic and the results vary slightly from run to run, the data were recorded when the training error [34] was minimal. The network model eventually converges. To test the accuracy of the random matching model, 13-22, 26-35, 53-62 and 113-122 groups of experimental data were taken as the test data, and the results are shown in Figure 5 below. When 13 to 22 groups of experiments were selected, the results of the comparison between the predicted and real values, the relative error values of prediction, and the training process are shown in Figure 5a,b. LSTM network prediction absolute mean error MAE = 2.7668 \(\times\) 10\({}^{-4}\), LSTM network prediction mean absolute error percentage MAPE = 2.8233 \(\times\) 10\({}^{-4}\), LSTM network prediction root mean square error RMSE = 3.8662 \(\times\) 10\({}^{-4}\). When 26-35 groups of experiments are selected, the results are shown in Figure 5c,d. LSTM network prediction absolute mean error MAE = 0.0167, LSTM network prediction mean absolute error percentage MAPE = 0.0193, LSTM network prediction root mean square error RMSE = 0.0217. When 53-62 groups of experiments are selected, the LSTM network prediction results are shown in Figure 5e,f, with absolute mean error MAE = 2.8484 \(\times\) 10\({}^{-4}\), LSTM network prediction mean absolute error percentage MAPE = 2.9381 \(\times\) 10\({}^{-4}\), and LSTM network prediction root mean square error RMSE = 3.2739 \(\times\) 10\({}^{-4}\). When 113 to 122 sets of experiments were selected, the LSTM network prediction results are shown in Figure 5g,h, with absolute mean error MAE = 0.0110, LSTM network prediction mean absolute error percentage MAPE = 0.0203, and LSTM network prediction root mean square error RMSE = 0.0140. In summary, the proposed residual life prediction model has less fitting error and accurate prediction results in the case of less data, which proves the effectiveness of the small sample adaptive residual life prediction model based on LSTM neural network. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sampling Frequency** & **Sampling Interval** & **Sampling Time** \\ \hline
25.6 kHz & 1 min & 1.28 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This is a table. RV reducer parameter. Figure 5: Prediction Results and Prediction Error Plots for Model Randomized Trials. (**a**) 13–22 groups of LSTM neural network prediction model results; (**b**) 13–22 groups of LSTM neural network prediction relative errors; (**c**) 26–35 groups of LSTM neural network prediction model results; (**d**) 26–35 groups of LSTM neural network prediction relative errors; (**e**) 53–62 groups of LSTM neural network prediction relative errors; (**g**) 53–62 groups of LSTM neural network prediction relative errors; (**g**) 113–122 groups of LSTM neural network prediction model results; (**h**) 113–122 groups of LSTM neural network prediction relative errors. Adaptive Residual Life Prediction for Small Samples of RV Reducers Based on Feature Matching Preprocessor-LSTM  
Using the RV reducer test rig [35] shown in Figure 6, the RV reducer life characteristics data were collected. The power of the servo motor used in the experiment is 5 kw, the range of the torque sensor is 15 N\(\cdot\)m, the range of the torque sensor is 200 N\(\cdot\)m, and the specification of the magnetic powder brake is 1.5 kw. The speed of the spindle is set to 151 r/min, the input and output shafts of the RV reducer are measured by the torque sensor, and the model of the RV reducer is RV-20E.