# Data-Driven Health Assessment in Flight Control System
## 5 Certain Type Aircraft Flight Control System Health Assessment
### Health Assessment for a Single Flight  
The characteristic parameters of four channels need to be determined firstly for comprehensive health index, and then the health state assessment of the single flight can be completed. Take the flap channel as an example, the pilot inputs the command by position handle and the hydraulic electromagnetic switch will be open according to this command signal; the high-pressure oil will enter the pipeline through the electromagnetic valve to drive motor, which drives the flap drive shaft to rotate. During this process, the main hydraulic pressure's variation will directly change the flap retracting force and affect the flap system's performance. So, the main hydraulic pressure is taken as the characteristic parameter of the flap's health state. Moreover, based on the flap failure mode, the jamming  
Figure 3: Flight data in Excel table. of the transmission mechanism component will slow down the retracting speed or even stop retracting, so the flap retraction and extension time is introduced as the second characteristic parameter. To get the membership, the main hydraulic pressure needs to be normalized with the relative degradation degree, and Table 3 gives the parameters of relative degradation function in Equation (11), and then the relative deterioration degree of the main hydraulic pressure is obtained as 0. As the evaluation steps shown in Section 3.1, health state interval set with four levels is established as: health, slight degradation, severe degradation, and warning. Since the characteristic parameter has become a normalized value by relative deterioration degree analysis, the distribution functions of the descending, intermediate, and ascending types are selected to construct the membership function to cover the deterioration interval:  
\[\mathrm{r}_{l_{1}} = \left\{ \begin{array}{cc}1&d<0.1\\ \frac{1}{2}-\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.2)&0.1\leq d\leq 0.3\\ 0&d>0.3\end{array} \right\}, \tag{12}\]  
\[\mathrm{r}_{l_{2}} = \left\{ \begin{array}{cc}0&d<0.1\\ \frac{1}{2}+\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.2)&0.1\leq d\leq 0.3\\ 0&1&0.3\leq d\leq 0.4\\ \frac{1}{2}-\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.5)&0.4<d<0.6\\ 0&d\geq 0.6\end{array} \right\}, \tag{13}\]  
\[\mathrm{r}_{l_{3}} = \left\{ \begin{array}{cc}0&d<0.4\\ \frac{1}{2}+\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.5)&0.4\leq d\leq 0.6\\ 1&0.6\leq d\leq 0.7\\ \frac{1}{2}-\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.8)&0.7<d<0.9\\ 0&d\geq 0.9\end{array} \right\}, \tag{14}\]  
\[\mathrm{r}_{l_{4}} = \left\{ \begin{array}{cc}0&d\leq 0.7\\ \frac{1}{2}+\frac{1}{2}\sin\frac{\pi}{0.2}(d-0.8)&0.7\leq d\leq 0.9\\ 1&d\geq 0.9\end{array} \right\}, \tag{15}\]  
which are shown in Figure 4.  
Then the membership of the main hydraulic pressure can be obtained as follows:  
\[r_{41} = \left( \begin{array}{ccc}0.0886&0.9114&0&0\end{array} \right), \tag{16}\]  
Figure 4: The membership function. \begin{table}
\begin{tabular}{c c} \hline \hline
**Function Parameters** & **Value** \\ \hline x\({}_{\mathrm{max}}\) & 2229 \\ x\({}_{\mathrm{min}}\) & 80.566 \\ x\({}_{\mathrm{z}}\) & 1900 \\ x\({}_{\mathrm{b}}\) & 2185 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative deterioration degree parameters of main hydraulic pressure. Since the sampling time interval of the original data is 1 s, the normalized data has a smaller discrimination. Therefore, 20 experts are invited to judge the flap's retraction and extension time, and there are 17 experts who believe that flap system is healthy, three experts think the flap is slightly damaged, and no experts think the flap is failed. The single factor membership value of the retraction and extension time is obtained as follows:  
\[r_{42}\ =\ \Big{(} \begin{array}{cccc}0.85&0.15&0&0\end{array} \Big{)}, \tag{17}\]  
The membership vectors of two characteristic parameters are combined as follows:  
\[R_{4}\ =\ \Bigg{(} \begin{array}{cccc}0.0886&0.9114&0&0\\ 0.85&0.15&0&0\end{array}