## 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  
The lifetime features of the small-sample data are brought into Equations (9)-(11) for preprocessing and into Equations (12) and (14) for lifetime feature matching, and based on the advantages of LSTM in processing and predicting long- and short-term information in time series, the instantaneous lapse rate \(\hat{H}_{c}(t)\) and standard deviation \(\hat{S}_{c}(t)\) of the lifetime features after completing feature matching preprocessing are used as LSTM inputs, and the standard remaining lifetime \(l_{c}(t)\) after completing feature matching preprocessing is used as LSTM output to establish a small-sample adaptive remaining lifetime prediction model based on feature matching preprocessor-LSTM neural network [30]. The prediction model is shown in Figure 3.  
Figure 3: Model flow chart. Step 1 Based on the data provided by the enterprise from the reliability life provided by the manual, the reliability function \(R(t)\) is calculated by Equation (4), and the undefined parameter value \(\eta\) of the failure rate function is derived, and the failure rate function \(H(t)\) is calculated by Equation (6). Step 2 After deriving the complete lapse rate function, a series of instantaneous lapse rates \(H(t)\) are derived based on the mechanical product lapse rate model. Step 3 According to the general life characteristic curve, construct the life characteristic standard deviation model Equation (8), or use the measured life characteristic data by Equation (5) to find the standard deviation \(S(t)\) of mechanical product life characteristics in each time period. Step 4 takes the obtained instantaneous failure rate \(H(t)\) and standard deviation \(S(t)\) of a series of RV reducers as matching thresholds, substitutes the measured life feature data \(r(t)\) into the adaptive life matching model Equations (12) and (14) for feature matching, and obtains the input feature instantaneous failure rate \(\hat{H}_{c}(t)\) and life feature standard deviation \(\hat{S}_{c}(t)\) of the small-sample adaptive remaining life prediction model and the output feature standard remaining life \(l_{c}(t)\). Step 5 The instantaneous failure rate \(\hat{H}_{c}(t)\) and the standard deviation \(\hat{S}_{c}(t)\) of the lifetime features after feature matching preprocessing are used as LSTM inputs, and the standard remaining lifetime \(l(t)\) after completing feature matching preprocessing is used as LSTM output, which is imported into the LSTM neural network for fitting to obtain the predicted remaining lifetime \(\hat{l}_{c}(t)\). **3. Adaptive Remaining Life Prediction for Small Samples of Bearings Based on Feature Matching Preprocessor-LSTM**  
In order to verify the validity of the proposed model, the bearing life dataset from Xi'an Jiaotong University [31] was used as the research object, and its dataset acquisition process is shown in Figure 4. Two acceleration sensors were used for testing the vibration data in horizontal and vertical directions, respectively. The sampling parameters were set as shown in Table 1, and a total of 123 sets of experimental data were obtained. Figure 4: Bearing accelerated life test bench. The bearing life dataset from Xi'an Jiaotong University was brought into the constructed model for remaining life prediction according to steps 1 to 5. Following the flow of the above model, the instantaneous failure rate and standard deviation of the partial set were calculated and substituted as the main features into the small-sample adaptive remaining life prediction model based on LSTM neural network [32,33]. Ten random groups of data are set for sampling simulation, and among the ten randomly selected groups, interpolation is used, i.e., every other group of data is used as the experimental set, and a total of five groups are obtained for network training and five groups are used for model testing, where the number of neuron nodes is set to 180.