# Data-Driven Health Assessment in Flight Control System
## 5 Certain Type Aircraft Flight Control System Health Assessment
### Health Assessment for a Single Flight
\Bigg{)} \tag{18}\]  
Meanwhile, the rough sets reduction algorithm is used to assign weights of main hydraulic pressure and retracting time as follows:  
\[w\ =\ \Big{(} \begin{array}{cccc}0.3766&0.6234\end{array} \Big{)}, \tag{19}\]  
According to the above Equation (6), the evaluation vector is:  
\[b_{4}\ =\ wr\ =\ \Big{(} \begin{array}{cccc}0.5633&0.4367&0&0\end{array}  \Big{)}, \tag{20}\]  
The evaluation vector is quantified based on Equation (7) above to obtain the health index of the flap channel \(SCHI\ =\ 0.8908\). Similarly, the deterioration degree function parameters of the other three channels are constructed in Table 4. In which, the transfer coefficient is defined as the slope of control surface deflection and joystick displacement curve. The deterioration degree of the characteristic parameters is obtained and the membership value is calculated finally the health index of the channel can be obtained. The relative deterioration degrees of the above characteristic parameters are calculated as follows:  
\[d\ =\ ( \begin{array}{cccc}0.5706&0.5160&1\end{array} ), \tag{21}\]  
Based on the membership function above, the membership vectors of three channels are obtained as:  
\[R_{1}\ =\ \Big{(} \begin{array}{cccc}0&0.0524&0.9676&0\end{array} \Big{)}, \tag{22}\]  
\[R_{2}\ =\ \Big{(} \begin{array}{cccc}0&0.3758&0.6242&0\end{array} \Big{)}, \tag{23}\]  
\[R_{3}\ =\ ( \begin{array}{cccc}0&0&0&1\end{array} ), \tag{24}\]  
The weights of characteristic parameter in each channel are sets: \(w_{i}\ =\ 1,i\ =\ 1,2,3\).Using the above method, the health indices of the pitch channel, the yaw channel, and the roll channel are obtained as 1, 1, and 1. With the rough sets reduction algorithm, the weights of the four channels are obtained again as in Figure 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Characteristic Parameters** & \(X_{\mathbf{max}}\) & \(X_{\mathbf{min}}\) & \(X_{\mathbf{\alpha}}\) & \(X_{\mathbf{b}}\) \\ \hline pitch channel’s transfer coefficient \(K_{1}\) & 0.2331 & 0.1113 & 0.1276 & 0.1575 \\ yaw channel’s transfer coefficient \(K_{2}\) & 2.7778 & 0.2445 & 0.3074 & 0.3758 \\ roll channel’s left transfer coefficient \(K_{3}\) & \(-0.1840\) & \(-0.4146\) & \(-0.2335\) & -0.1911 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The deterioration degree function parameters of the other three channels. With the health index interval in Table 5, the health state distributions for 60 flights are shown in Figure 8.  
In these 60 flights, flight control system is healthy in 33 flights, functional degradation in 25 flights, and significant decline in functionality in 2 flights. Moreover, the 34 th and the 54 th flights show significant decline in functionality as the red dot in Figure 9, and the 26 thflight shows significant decline in functionality as the green dot in Figure 9. The four channels' health indexes for the three flights (26, 34, and 54 flights) are listed in Table 6 below. Figure 8: The distribution of the different health status of 60 sorties. Figure 7: The CHI of flight control system. Figure 9: Comparison of Analytic Hierarchy Process (AHP) and comprehensive evaluation. This shows that, in the 26 th flight, the SCHI for yaw channel and roll channel are lower, which causes the health state to decline, and in the 34 th and 54 th flights, the SCHI for pitch channel and yaw channel are lower, which causes the health state to have a significant decline in functionality. According to the health characteristics of the three flights, the main reason is that the transfer coefficient \(K_{1}\) of the pitch channel, the transfer coefficient \(K_{2}\) of the yaw channel, and the transfer coefficient of the roll channel are not in normal range.