# Data-Driven Health Assessment in Flight Control System
## 4 Health Assessment Method  
### Fuzzy Comprehensive Evaluation  
The failure record in actual system operation data may be less inevitable, which leadsto the commonly used neural network method and the gray clustering method being less accurate. The fuzzy comprehensive evaluation fuzzily divides the characteristic parameters into several intervals, which constructs the characteristic parameters' fuzzy evaluation matrix in a specific channel, and then performs a row-by-row weighted calculation on this matrix to obtain a channel evaluation vector and gets the channel's health index. During this process, each factor's evaluation is completed by the best value, so it is only necessary to obtain the evaluation value through the comparison benchmark for the fault sample, which avoids the classification boundary ambiguity caused by the fewer fault samples [16]. The specific steps are shown as follows:  
(1) Selecting characteristic parameters: characteristic parameters that reflect each channel's health state are selected as in Figure 2, which are used as evaluation factors. In this figure, \(n_{1}\), \(n_{2}\), \(n_{3}\), and \(n_{4}\) are the number of characteristic parameters contained in the four channels. (2) Establishing the health state interval set: The interval set is hierarchical set of health state of each characteristic parameter and channel. Assuming that there are m levels, the health state interval set can be expressed as:  
\[L\ =\ \{l_{1}l_{2}\cdots l_{m}\}, \tag{2}\]  
Where \(L\) means the health state of each characteristic parameter. Then the relative degradation degree analysis is introduced to normalize each characteristic parameter and construct a membership function with this relative deterioration degree. (3) Calculating the membership row vector of each characteristic parameter: With the above-mentioned health state interval fuzzily calculation, the corresponding factor membership row vector can be obtained as:  
\[r_{ij}\ =\ \Big{\{}\ r_{ij}^{1}\ \ \ r_{ij}^{2}\ \ \cdots\ \ \ r_{ij}^{m}\ \Big{\}}, \tag{3}\]  
where, \(i\ =\ 1,2,3,4\) represents the four channels, \(j\ =\ 1,2\cdots n_{i}\), \(n_{i}\) indicates the number of characteristic parameters in channel \(X_{i}\) in Figure 2. \(m\) is the interval number of health stateinterval sets. (4) Constructing the fuzzy evaluation matrix: With the membership row vector calculation of each characteristic parameter, the membership row vectors of all characteristic parameters in thechannel are combined to construct the fuzzy evaluation matrix:  
\[R_{i}\ =\ \left( \begin{array}{ccc}r_{i1}^{1}&\cdots&r_{i1}^{m}\\ \vdots&\ddots&\vdots\\ r_{in_{i}}^{1}&\cdots&r_{in_{i}}^{m}\end{array} \right)=\ \Big{(}\ r_{i}^{1}\ \ \ r_{i}^{2}\ \ \cdots\ \ r_{i}^{m}\ \Big{)}, \tag{4}\]  
where \(i\ =\ 1,2,3,4\), \(m\) is the health state interval number, \(n_{i}\) is the characteristic parameters number of channel \(X_{i}\). (5) Determining the weight vector of the characteristic parameters in the channel: Based on the characteristic parameters selection in Equation (1), the rough sets reduction described in Section 3.2 below is used to identify the importance of factors for the upper level factors, and then the weight vector is constructed as:  
\[w_{i}\ =\ \Big{\{}\ w_{i1}\ \ \ w_{i2}\ \ \cdots\ \ \ w_{in_{i}}\Big{\}}\, \tag{5}\]  
(6) Calculating evaluation vector: With the weights \(w_{i}\) of the characteristic parameters in the same channel and the fuzzy evaluation matrix \(R_{i}\), the evaluation vector of the channel \(X_{i}\) is computed as:  
\[b_{i}\ =\ w_{i}R_{i}\ =\ \Big{\{}\ b_{i}^{1}\ \ \ b_{i}^{2}\ \ \cdots\ \ \ b_{i}^{m}\ \Big{\}}, \tag{6}\]  
Figure 2: Flight control system characteristic parameter.