## 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 data are sampled every 0.5 s. The experiment was conducted at room temperature, and the model parameters of the main equipment of the experimental platform are shown in Table 2.  
The collected experimental data are shown in Table 3.  
According to step 1 to step 5, firstly, according to the definition of B10 life [36] in the manual of mechanical products, when the unreliability is 0.1, its reliable life is  
\[L_{h}=K\times\frac{N_{0}}{N_{m}}\times\left(\frac{T_{0}}{T_{m}}\right)^{\frac {10}{3}} \tag{15}\] \begin{table}
\begin{tabular}{c c} \hline
**Equipment** & **Model** \\ \hline Servo Motor & Panasonic MSME502 GCG \\ Torque Sensor & NCNJ-101(0 \(\pm\) 15 N\(\cdot\)m) \\ RV reducer & RV-20E \\ Torque Sensor & NCNJ-101(0 \(\pm\) 200 N\(\cdot\)m) \\ Magnetic Powder Brake & FZ400A-1 \\ \hline \end{tabular}
\end{table} 
Table 2: RV reducer platform model parameters. Figure 6: RV reducer test experimental platform. \(t_{1}=0.2\) s; \(t_{2}=0.5\) s; \(t_{3}=0.2\) s; \(t_{em}=0.05\) s, substituting the data into Equations (16) and (17), we get  
\[ \begin{array}{ll}T_{m}&=\sqrt[10]{\frac{t_{1}\cdot N_{1}\cdot T_{1}}{\frac{10 }{3}+t_{2}\cdot N_{2}\cdot T_{2}}{\frac{10}{3}+\cdots+t_{n}\cdot N_{n}\cdot T_{ n}}{t_{1}\cdot N_{1}+t_{2}\cdot N_{2}+\cdots+t_{n}\cdot N_{n}}}\\ &=158.8611\\ &N_{m}&=\frac{t_{1}\cdot N_{1}+t_{2}\cdot N_{2}+\cdots+t_{n}\cdot N_{n}}{t_{1} +t_{2}\cdots+t_{n}\cdot N_{n}}\\ &=17.8947\\ \end{array}  \tag{20}\]  
Also check the manual of the RV reducer and get \(N_{0}=20\) r/min; \(T_{0}=167\) N\(\cdot\)m Substitute the data into Equation (15) to get  
\[L_{h}=K\times\frac{N_{0}}{N_{m}}\times(\frac{T_{0}}{T_{m}})^{\frac{10}{3}}=7921.1 \tag{22}\]  
Then from Equation (5) we get  
\[F(t)=1-e^{-(L_{h}/\eta)^{m}}=0.1 \tag{23}\]  
where \(m\) is taken as the empirical constant 2. When \(m=2\), the solution is \(\eta=24403\), then  
\[H(t)=\frac{f(t)}{R(t)}=\frac{2}{24403}.\frac{t}{24403};t\geq 0 \tag{24}\]  
According to the failure rate model Formula (6), the standard deviation model Formula (8), and the life characteristic matching preprocessor model Formulas (12) and(14), a small-sample adaptive life curve matching model of the RV reducer is established, as shown in Table 4.  
After establishing the threshold models for the instantaneous failure rate as well as the standard deviation, the experimentally measured 200-h actual data of the RV reducer were preprocessed by Equations (9)-(11) and imported into Equations (12) and (14) adaptive life matching models, and the instantaneous failure rate and standard deviation after completing the matching were imported into the LSTM neural network as the input, and the remaining life was used as the output, and the interpolation method was used to construct a training set and a test set for model training [37] to determine the remaining life of the RV reducer, and the obtained results are shown in Figure 7[38]. It can be seen from Figure 7 that the predicted data has a general effect at the beginning, but the fitting error gradually decreases from the 8 th sample, because the experimental data is only 200 h of sample data, which is far less than the full cycle life, which can be regarded as a small sample data, which verifies the feasibility and effectiveness of the model based on it. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Instantaneous Failure Rate** & **Standard Deviation** & **Remaining Life** \\ (h\({}^{-1}\)) & **(h)** & **(h)** \\ \hline \(1.93\times 10^{-6}\) & 0.175675 & 7721.1 \\ \(5.11\times 10^{-6}\) & 0.35135 & 7521.1 \\ \(8.29\times 10^{-6}\) & 0.527025 & 7321.1 \\ \(1.15\times 10^{-5}\) & 0.7027 & 7121.1 \\ \(1.47\times 10^{-5}\) & 0.878375 & 6921.1 \\ \(1.78\times 10^{-5}\) & 1.05405 & 6721.1 \\ \(2.10\times 10^{-5}\) & 1.229725 & 6521.1 \\ \(2.42\times 10^{-5}\) & 1.4054 & 6321.1 \\ \(2.74\times 10^{-5}\) & 1.581075 & 6121.1 \\ \(3.06\times 10^{-5}\) & 1.75675 & 5921.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Remaining life table corresponding to failure rate and standard deviation.