## 3 Results
### Risk Determination Based on RUL Prediction  
In the case study, the key component of weapon systems, the turbine engine, is taken as an example for analyzing risks. The data is derived from the experiment conducted by a commercial modular simulation software C-MAPSS as shown in Figure 5.  
The C-MAPSS simulates the operation of a turbine engine with 900,000-pound thrust and records monitoring signals. Based on the principle of thermodynamics, two failure modes are designed: high-pressure compressor degradation and fan degradation. The main functional modules and connections are shown in Figure 6. The simulation runs in the following settings:  
1. The simulation experiment data contains time series of 21 variables. It can be further divided into a training set and a testing set. Each multivariate time series corresponds to a specific engine, meaning that the data can be considered to be generated by engines of different systems. 2. The initial wear condition of each engine might not be identical and there are manufacturing variations, which are considered reasonable and not treated as reasons of engine failures. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Systems** & **Detection Range** & **Communication Range** & **Striking Range** & **Decision Time** \\ \hline S1 & 128.8502018 & 45.00221559 & 41.93626171 & 22.55909356 \\ S2 & 205.1604693 & 36.35948504 & 50.01541323 & 16.53053513 \\ S3 & 156.9600287 & 27.11329846 & 43.28357399 & 16.46184426 \\ S4 & 152.7120943 & 26.19071935 & 53.57115127 & 21.3190886 \\ S5 & 111.5170147 & 15.04553804 & 29.95161145 & 15.33123079 \\ SP1 & 205.1604693 & 150.0713 & 218.758 & 18.44034 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Capabilities of 5 systems. Figure 5: The interface of the simulation platform. 3. There are 3 operational setting parameters that have a substantial impact on an engine's performance. 4. There are noises in the data. 5. The engines operate normally at the initial moment and begin to degrade at some points in time series. In the training set, the cumulative degradation quantity continues to grow until it reaches or exceeds the preset threshold. In the testing set, the time series will terminate when engines fail. As a result, 100 degradation tracks are obtained in the training set and 100 tracks before failure in the testing set. The training data is used to establish the RUL prediction model of engines, and the testing set is used to test the feasibility of the model. The monitoring data is shown in the scatter plots in Figure 7. Each plot visualizes the 100 degradation tracks of one variable in the training set. The engine code, the operation cycle and the 3 operational setting parameters are not shown in the figure. Due to the fact that the constant variable is unable to reflect the evolution of engine degradations, variable 1, 5, 6, 10, 16, 18, and 19 are not regarded as feature variables. What's more, the tracks exhibit different trends in terms of variable 9 and 14, so variable 9 and 14 are inadequate to describe the degradation process. Then, the variation coefficients of the rest 12 variables are calculated based on the degradation data and the results are shown in Table 4. According to the rule of eliminating variables with small variation coefficients, variable 3, 4, 11, 15, 17, 20 and 21 are chosen as the base variables that represent engine degradation characters. According to the RUL prediction method, the remaining life of the engines in the testing set can be estimated by matching the testing data with the reference tracks. Then, the risks can be obtained. The results are shown in Table 5.