## 4 Experimental Validation and Result Analysis
### RUL Prediction Process and Result Analysis  
#### 4.2.1 RUL Prediction Process  
The operating system of the computer used is Windows 11, 64-bit, with a processor of Intel(R) Core (TM) i7-10875H/NVIDIA GeForce RTX 2060, and the deep learning framework is MATLAB v2024a. To ensure fair comparison with other neural network models, the deep learning networks used for comparison are BiGRU (Bidirectional Gated Neural Network) and CNN-LSTM (Hybrid Model of Convolutional Neural Network and LSTM Network). The size of the hidden units significantly affects the network prediction performance. Insufficient hidden units lead to poor feature learning, while a large number increases the complexity of the network. Therefore, in this paper, the BiLSTM layer hidden units are determined through minimum validation loss. The selection of hidden units is performed by calculating the validation loss of each pair of hidden units (H1, H2), which correspond to the first and second BiLSTM layers, respectively. The forward and backward layers of each  
Figure 12: Health indicator and failure threshold. BiLSTM have the same number of hidden units, while the output layer size is equal to 1. The A-DBiLSTM model output is flattened through fully connected layers and maintained in the range of 0-1 using a sigmoid activation function. Regression is performed on the final output to predict RUL labels, and the RMSE is used as the loss function of the regression layer, the network hyperparameters obtained through Bayesian automatic optimization. In this study, the RUL prediction process aims at optimizing the training of the network by learning current health conditions from short sequence data. The parameter settings of the RUL prediction model mentioned in Table 6. Additionally, it lists the network parameters of the comparative algorithms BiGRU and CNN-LSTM. The reliability of the prediction results of the proposed method is evaluated using a 95% confidence level, the formula for calculating the confidence interval is as follows [49]:  
\[CON=[\hat{\mu}_{con}-z_{\delta/2}\cdot\frac{s}{\sqrt{\pi_{y}}},\hat{\mu}_{con}+ z_{\delta/2}\cdot\frac{s}{\sqrt{\pi_{y}}}] \tag{47}\]  
where \(\hat{\mu}_{con}\) represents the sample mean of multiple prediction results. In the paper, predictions are repeated 50 times. \(z_{\delta/2}\) denotes the quantile of the standard normal distribution, with a confidence level of 95%, \(z_{\delta/2}\) = 1.96, \(s\) stands for the standard deviation of the prediction results, and \(n_{y}\) represents the sample size of the test set [49]. Calculate the average of all prediction results [49]:  
\[\hat{\mu}_{con}=\frac{1}{n_{y}}\sum_{r}^{n_{y}}x_{r} \tag{48}\]  
where \(x_{r}\) denotes the prediction result for the \(r\)-th time. \begin{table}
\begin{tabular}{l l l} \hline
**Model** & **Layer Name** & **Detailed Description** \\ \hline \multirow{6}{*}{Posed method} & & Number of hidden layer neurons: \\  & & BiLSTM1 = 93, BiLSTM2 = 93; \\  & BiLSTM1, BiLSTM2, Fully & Fully \\  & connected layer, & layer2 = 25, Output vector dimension:1; \\  & Regression layer & Learning rate: 0.0098; Batch size: 64; \\  & & Number of iterations: 2000; \\  & & Dropout rate: 0.147; Activation function: \\  & & Relu. Regression layer = 1 \\ \hline \multirow{6}{*}{BiGRU} & & Number of hidden layer neurons: 240; \\  & GRU, & Fully connected layer: 40; \\  & Fully connected layer, & Output vector dimension: 1; Learning \\  & Regression layer & rate: 0.001; Batch size: 64; \\  & & Regression layer & Number of iterations: 2000; Dropout rate: \\  & & 0.15; Activation function: Relu. \\  & & Regression layer = 1 \\ \hline \end{tabular}
\end{table} 
Table 6: Detailed network structure.