## 4 Experiments, Results, and Discussion  
The training parameters of the proposed algorithm are tuned after repeating the experiment in reason to attempt the best score value in Equation (17) and the minimum RMSE using Equation (18) for the test set in both Equations (17) and (18). \[S=\left\{ \begin{array}{l}\sum_{i=1}^{Z}e^{-d_{i}/13}-1,d_{i}<0\\ \sum_{i=1}^{Z}e^{-d_{i}/10}-1,d_{i}\geq 0\end{array} \right. \tag{17}\]  
\[\text{RMSE}=\sqrt{\frac{1}{Z}{\sum_{i=1}^{Z}d^{2}}}, \tag{18}\]  
According to the PHM 2008 challenge [22], the scoring function penalizes the latent prediction \(d_{i}\geq 0\) more than early ones \(d_{i}<0\) for maintenance reasons. Too late prediction might delay maintenance operations, and too early prediction might not be harmful but consumes more maintenance resources. Figure 4 explains that the sparseness of the RMSE and score function towards higher values is less than the others towards zero, which confirms the credibility of the results. Figure 4: Scoring functions for the testing set results. Experimental results lead to the parameters shown in Table 1.  
A set of training mini batches was ignored during training of the RUL prediction models with the contribution of the USS strategy. This can contribute to training time reduction and avoiding divergence of training weights. Figure 5 illustrates the reaction of USS strategy towards the useless mini batches by showing the indexes of ignored and selected mini batches. It is obvious that USS conditions shown previously in Equation (9) are confirmed in Figure 5. The RMSE error of each selected chunk of data is bigger than the one before it. During training, the DFF by the intervention of TD error minimization function-based RLS can contribute to the prediction algorithm adaptation towards variations in the newly arrived data. By adapting weights gradually to enhance the approximation function, the accuracy of the prediction will remain stable and always converges to the desired value. Figure 6 shows the variation of DFF during training. If the TD changes too much, it means that the new coming training data has also different characteristics from the first ones, which consequently forces the training weights \(\beta\) to adapt towards these new changes. The adaptation of \(\beta\) is a result of updating the forgetting factor \(\lambda\), and the amount of changes is controlled by the user hyper-parameters expressed in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{C}\) & \(\mathbf{\lambda_{\min}}\) & \(\mathbf{\lambda_{\max}}\) & \(\gamma\) & \(\mu\) & \(I\) & \(\mathbf{n}\) & \(\mathbf{G}\) \\ \hline
100 & 0.98 & 1 & \(10\times 10^{-6}\) & 0.98 & 100 & 205 & RELU \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training parameters of the proposed algorithm. Figure 5: The behavior of USS (Updated Selection Strategy) strategy towards the unused training mini batches. The training model was tested using new data (unknown to the model) from a test set of FD001. Additionally, the example of curve fitting of the RUL target function in Figure 7 proves that the proposed approach has an acceptable performance. The response of the designed network in Figure 7 is plotted using a set of different life cycles of different engines from the test set. The proposed approach performances are compared with a set of other recent approaches in the literature. The results from Table 2 indicate that the proposed algorithm has the ability to achieve a low score value depending on less training samples and less training time.