# A New Life Prediction Scheme for Mechanical System with Considering the Mission Profile Switching
## 4 Results and Discussion
### The Prediction Accuracy of the Proposed Method
#### 4.3.2 The Prediction Accuracy of Multiple Samples  
For a single lifecycle sample, the proposed method can obtain good prediction results under different lengths. In this section, the applicability of the proposed method will be further verified. Randomly select 100 sets of lifecycle data from set #2 and calculate the predicted life according to the steps in Section 4.2. The selected lifecycle data are divided into two parts: The first 2/3 is used as the sample to be predicted and the latter 1/3 is used to validate the prediction result under the mission profile experienced by the latter 1/3 data. The results are shown in Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mission Profile** & **Operating Condition** & **The Proportion** & **The Predicted Result** \\ \hline \multirow{6}{*}{1} & 1 & 3.68\% & \multirow{6}{*}{351.9989} \\  & 2 & 14.47\% & \\  & 3 & 32.05\% & \\  & 4 & 5.26\% & \\  & 5 & 14.49\% & \\  & 6 & 30.05\% & \\ \hline \multirow{6}{*}{2} & 1 & 41.23\% & \multirow{6}{*}{327.6221} \\  & 2 & 10.11\% & \\  & 3 & 9.98\% & \\ \cline{1-1}  & 4 & 10.21\% & \\ \cline{1-1}  & 5 & 21.40\% & \\ \cline{1-1}  & 6 & 7.07\% & \\ \hline \multirow{6}{*}{3} & 1 & 18.79\% & \multirow{6}{*}{337.2681} \\  & 2 & 12.03\% & \\ \cline{1-1}  & 3 & 12.59\% & \\ \cline{1-1}  & 4 & 22.53\% & \\ \cline{1-1}  & 5 & 15.04\% & \\ \cline{1-1}  & 6 & 19.02\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The predicted result under different mission profiles when mission profile switching. As shown in Figure 10, the relationship between the predicted life and actual life is approximately linear. The points in Figure 10 fluctuate basically up and down on \(y=x\). This means that the predicted life is very close to the actual life. However, most of the points are concentrated on the upper side of the \(y=x\). This means the predicted life is larger than the actual life in most cases. Altogether, although the predicted results of the proposed method are larger than the actual results in most cases, the predicted results are very close to the actual results. Therefore, for most lifecycle data, the proposed method can obtain good prediction results when the mission profile is known. In addition, in the case of multiple samples, we further explain the prediction results of the proposed method under the different lengths of the samples to be predicted and the different number of historical samples simply. Firstly, five samples are selected and, then, for each selected sample, the first 1/2, 2/3, and 4/5 are used as the samples to be predicted, respectively. Correspondingly, the latter 1/2, 1/3, and 1/5 are used to verify the RUL prediction results. Secondly, the prediction experiments with 50, 100, 150, and 200 historical samples are conducted to discuss the influence of the number of historical samples. In addition, in order to eliminate the random influence, 20 trails with randomly  
Figure 10: The predicted results of multiple samples. Figure 9: The predicted results under different lengths of the sample to be predicted. RUL, remaining useful life. choosing historical samples under the fixed sample number are employed, and the average Mean Squared Errors (MSEs) are shown in Figure 11, where MSE is calculated as follows:  
\[\text{MSE}= \frac{1}{SN}\sum_{i=1}^{SN}(px_{i}-\hat{x}_{i})^{2} \tag{6}\]  
where \(px_{i}\) is the prediction value of the data set \(i\), \(\hat{x}_{i}\) is the real value of the data set \(i\), and \(SN\) is the number of the predicted data sets. As shown in Figure 11, the MSE of the proposed method decreases with the increasing length of the samples to be predicted. Meanwhile, the MSE of the proposed method decreases with the increasing number of historical samples. These phenomena are basically consistent with common sense. Meanwhile, the focus of our proposed method is to solve the problem that most of the current prediction methods cannot solve, rather than to improve the prediction accuracy of the conventional problems.