## 2 Coupling Analysis of Risk Factors
### Coupling Relationship Assessment Based on the DEMATEL Model  
DEMATEL technology is primarily applied to quantify the direct-indirect coupling relationship of risk factors, through which the importance-causality diagram can be established to analyze the importance and attribution degree according to the position of each factor [36]. Moreover, the DEMATEL model provides a reasonable basis for the Bayesian network, mainly reflected in the following two aspects. One is to establish the structure of the BN based on the direct-relation matrix, and the other is to parameterize the BN based on the conditional probability of factors calculated on the direct-indirect matrix. The specific steps of DEMATEL analysis are as follows [30; 31; 32; 33; 37]. 1. Define the Evaluation Scale  
The degree of causality among risk factors is defined as k levels, i.e., 0, 1, 2,..., k - 1, where 0 represents no causal relationship, and k-1 represents the strongest causal relationship. 2. Establish a Direct-Relation Matrix  
The expert scoring method is used to evaluate the degree of direct causal relationship between two risk factors, and the direct-relation matrix \(M\) is then obtained by averaging the scores of each factor. If there are m kinds of risk factors, a matrix of m \(\times\) m will be determined, in which the element \(p_{ij}\) represents the degree of direct influence of the factor \(i\) on the occurrence of factor j. It is clear that the diagonal elements of the matrix are 0 because we focus on the relationship between different factors. 3. Normalize the Direct-Relation Matrix  
\[M1=M\times\alpha=M\times\frac{1}{\sum_{i,j=1}^{m}p_{i,j}}. \tag{1}\]  
According to the theory of matrix operation, the direct-relation matrix should be normalized to ensure the matrix convergence during the power series operation. In this paper, the sum of all matrix elements is used to normalize the matrix. 4. Calculate the Direct-Indirect Matrix  
The direct-indirect matrix takes all the indirect effects among factors into account, and these indirect effects can be represented by the state transition process in the theory of absorbing a Markov chain matrix; moreover, the degree of the effect will decrease as the number of state transitions increases. During matrix operating based on the above theory, \(M1\) represents the direct-relation matrix, \(M1^{2}\) represents the secondary-relation matrix, indicating the causal effect of risk factor \(F_{i}\) on \(F_{j}\) considering \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Code** & **Event** & **Guided** & **Deviation** & **Risk Type** & **Cause of Deviation** & **Hazard Effect** & **Measures** \\ \hline \multirow{3}{*}{\(Q_{1}\)} & pre-take-off & \multirow{3}{*}{mission} & Missing & \multirow{3}{*}{\(F_{41}\)} & \multirow{3}{*}{\(F_{41}\)} & Potential & \multirow{3}{*}{
\begin{tabular}{c} Strength safety \\ training and \\ inspection \\ \end{tabular} } \\  & preparation & & Missing & & & & & \\ \cline{1-1} \cline{5-7}  & & & & & & & \\ \cline{1-1} \cline{5-7}  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The improved hazard and operability analysis (HAZOP). the indirect effect of one risk factor, as shown in Figure 1(a), \(M1^{3}\) represents the cubic-relation matrix, indicating that the causal effect of risk factor \(F_{i}\) on \(F_{j}\) considering the indirect effect of two risk factors, as shown in Figure 1(b), and so on. \(M1^{x}\) thus represents the \(x^{\text{th}}\) relation matrix. The direct-indirect matrix \(M2\) can be calculated through a synthesis operation of the direct and indirect causal relationships according to Equation (2), and the element \(p_{i,j}^{{}^{\prime\prime}}\) in \(M2\) can be used to evaluate the causal effect of risk factor \(F_{i}\) on \(F_{j}\) considering the indirect effects of all the risk factors. \[M2=\lim_{x\rightarrow\infty}\left(M1+M1^{2}+M1^{3}+\cdots+M1^{x}\right)=M1(I- M1)^{-1} \tag{2}\]  
\[M2=\left(