# Time Series Feature Selection Method Based on Mutual Information
## 3 Experiments
### C-MAPPS Datasets  
As shown in Figure 2, the structure diagram of the aero-engine based on CMAPSS contains several components such as a fan, combustion chamber, high-/low-pressure booster, turbine, nozzle, etc.  
Table 1 shows the relevant parameters of the C-MAPSS dataset and the monitoring data for each work cycle. Gaussian white noise is added to the monitoring data to simulate the actual sensor noise. This dataset can realistically simulate engine systems with high reliability.  
In the CMAPSS dataset, some sensor signals are constant and do not vary with engine operation. After removing these data, the CMAPSS dataset has 14 sensor signals in total, that is, the data dimension of the original data space is reduced from 21 dimensions to 14 dimensions. Further, in order to reduce the redundancy between variables, based on the idea of the feature selection of maximum correlation and minimum redundancy, before feature selection, the variables with high redundancy are removed according to the mutual information value between the variables. Figure 3 shows the mutual information  
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Symbol** & **Description** & **Unit** \\ \hline
1 & T2 & Total temperature at the fan inlet & \({}^{\circ}\)R \\
2 & T24 & Total temperature at the low-pressure booster outlet & \({}^{\circ}\)R \\
3 & T30 & Total temperature at the high-pressure booster outlet & \({}^{\circ}\)R \\
4 & T50 & Total temperature at the low-pressure turbine outlet & \({}^{\circ}\)R \\
5 & P2 & Pressure at the fan inlet & psia \\
6 & P15 & Total pressure of the external bypass & psia \\
7 & P30 & Total pressure at the high-pressure booster outlet & psia \\
8 & Nf & Physical speed of the fan & rpm \\
9 & Nc & Physical speed of the core engine & rpm \\
10 & epr & Engine pressure ratio (P50/P2) & — \\
11 & Ps30 & Static pressure at the high-pressure booster outlet & psia \\
12 & Phi & Ratio of fuel flow and P30 & pps/psi \\
13 & NRf & Corrected speed of the fan & ppm \\
14 & NRc & Corrected speed of the core engine & rpm \\
15 & BPR & \multicolumn{1}{c}{Bypass ratio} & — \\
16 & farB & Gas–air ratio of the combustion chamber & — \\
17 & htleed & Bleed air entropy & — \\
18 & Nf\_dmd & Set speed of the fan & rpm \\
19 & PCNfR\_dmd & Set corrected speed of the core engine & rpm \\
20 & W31 & Cooling bleed air flow of the high-pressure turbine & lbm/s \\
21 & W32 & Cooling bleed air flow of the low-pressure turbine & lbm/s \\ \hline \end{tabular}
\end{table}
Table 1: Engine sensor data description [45].  
Figure 2: Structure diagram of the C-MAPPS aero-propulsion system.  
thermodynamic of 14 sensor signals in the C-MAPSS dataset. The diagonal value of the thermogram is 1, and it is symmetrical with the diagonal.  
From Figure 3, it can be seen that some sensor signals are highly correlated. For example, the value of mutual information between s9 and s14 is 1, indicating that there is a high degree of redundancy between them. From Table 1, it can be seen that s9 represents the physical speed of the core engine, and s14 represents the corrected speed of the core engine. The measured values of the two are highly correlated, and the calculated mutual information is consistent in a physical sense. Based on the mutual information matrix, the system features are further filtered. With 0.95 as the threshold (manually set), some redundant features are deleted, and a total of nine sensor signals in the system can be obtained, that is, from 21 dimensions of the original data space to 9 dimensions after mutual information filtering among variables.