# Security Situation Assessment for Terminal Area Control System Operation Based on BN-ISSA-ELM
## 2 Materials and Methods
### ISSA-ELM Risk Probability Prediction Model
#### 2.2.3 Primary Indicator Probability Prediction Based on ISSA-ELM  
The procedural steps for the principal indicator assessment model of the terminal area control system's operational safety situation, based on the ISSA-ELM, are as follows. Step 1. Data Import and Preprocessing: Import the data, partition it into training and testing sets, and perform the requisite preprocessing processes to guarantee data integrity. Step 2. Initialization of the Sparrow Population: Employ the Opposite-Based Learning approach (as demonstrated in Equation (1)) to implement population initialization. Establish the initial settings for the ISSA and specify the quantity of neurons in the hidden layer of the ELM. Step 3. Training the ISSA-ELM Model: The fitness function is calculated using the training set. The following equation then guides the grading of the fitness values:  
\[\text{Fitness}=\left\|f_{i}-y_{i}\right\| \tag{8}\]  
In Equation (8), \(y_{i}\) signifies the genuine value, whereas \(f_{i}\) indicates the anticipated value. Step 4. Position Updates: Update the positions of the finders, joiners, and scouts according to the following equations:  
Use Equation (2) to update the finder's position. Use Equation (9) to update the joiner's position. Use Equation (10) to update the scout's position. After performing these updates, obtain the new positions of the sparrows along with their corresponding fitness values. Finally, update both the individual and global best positions based on the newly calculated fitness values. \[X_{ij}^{\text{t+1}}=\left\{ \begin{matrix}Q\cdot\exp\left(\frac{X_{\text{ worst}}^{\text{t}}-X_{ij}^{\text{t}}}{\xi^{2}}\right),&\text{if i}>\frac{n}{2}\\ X_{\text{p}}^{\text{t+1}}+\left|X_{ij}^{\text{t}}-X_{\text{p}}^{\text{t+1}} \right|\cdot A^{+}\cdot L,&\text{otherwise}\end{matrix} \right. \tag{9}\]  
In Equation (9), Xp represents the best position of the producer; Xworst denotes the worst position of the producer. The elements of matrix A are randomly assigned values of either 1 or \(-1\). \(A^{+}=A^{\text{T}}\left(AA^{\text{T}}\right)^{-1}\) is the pseudoinverse of matrix A. When i \(>\frac{n}{2}\), the i-th joiner, which has a lower fitness value, does not obtain the optimal solution. \[X_{ij}^{\text{t+1}}=\left\{ \begin{matrix}X_{\text{best}}^{\text{t}}+\varphi \cdot\left|X_{ij}^{\text{t}}-X_{\text{best}}^{\text{t}}\right|,&\text{if f}_{i}>f_{g}\\ X_{ij}^{\text{t}}+\kappa\left(\frac{\left|X_{ij}^{\text{t}}-X_{\text{ worst}}^{\text{t}}\right|}{(f_{i}-f_{w})+\epsilon}\right),&\text{if f}_{i}=f_{g}\end{matrix} \right. \tag{10}\]In Equation (10), \(X_{\text{best}}\) stands for the best position; \(\varphi\), which is the step size control parameter, follows a standard normal distribution; \(\kappa\) belongs to the range of \([-1,1]\). The current fitness value of an individual within the population is represented by \(f_{i}\), while \(f_{g}\) and \(f_{\omega}\) denote the best and worst fitness values, respectively. The conditions \(f_{i}\) is greater than \(f_{g}\) indicates that the sparrow is on the periphery of the population and is vulnerable to predation, while \(f_{i}\) is equal to \(f_{g}\) suggests that the scout needs to move closer to the other sparrows to reduce the risk of being attacked. The term \(\varepsilon\) is a small constant added to prevent division by zero during calculations. Step 5. Levy Flight Update: Levy flight was used to modify the existing positions of the search agents. Thereafter, the locations of the search agents were revised in accordance with Equations (6), (9) and (10). This creates variety in the positions, augmenting the algorithm's exploration capabilities. Step 6. Iteration Regulation: Once we reached the maximum number of iterations and identified the global optimum, we ceased the iteration process and proceeded to step (7). Otherwise, we reverted to step (4) to persist in changing the positions of the sparrows and enhancing the search. Step 7.