## 5 Aircraft Parameter Optimization Method  
After the model is obtained, given the value of (\(X_{L}\), \(X_{D}\), \(X_{A}\), \(X_{I}\), \(X_{m}\), \(X_{S}\)), (\(Ma_{opt}\), \(h_{opt}\)) can be obtained quickly. Therefore, if various parameters change simultaneously, the reaction of the optimal cruise point can be studied. By this way, if the subjective desired cruise point does not coincide with the actual optimal cruise point, the optimal cruise point can be adjusted to the target position by optimizing the aircraft parameters. However, due to the interaction between the aircraft parameters, the coupling relationship between the aircraft parameters needs to be considered when optimization is carried out. Since there is a complex coupling relationship between the aircraft parameters, take the following constraints as examples to illustrate the optimization method of the aircraft parameters based on the neural network model:  
1. The maximum increment of the lift coefficient is 5%, and the drag coefficient will also increase at the same time, and the minimal increment is 1/2 of that of the lift coefficient;
2. The maximum increment of the inlet area is 30%; meanwhile, the aircraft mass and reference area will also increase, and the minimal increments are 1/3 and 1/4 of that of the inlet area, respectively;
3. The maximum increment of the specific impulse is 10%. These constraints can be adjusted according to the actual situation. Now that it is difficult to adjust the optimal cruise Mach number greatly, the optimal cruise altitude is mainly focused. The target of the optimal cruise point is set at (\(Ma5\), 26 km). However, if the aircraft parameters can be changed at the same time, to adjust the optimal cruise altitude to the desired value, there is more than one plan since six relevant aircraft parameters are considered. The fuel consumption after aircraft parameters optimization is different by various adjustment plans. Therefore, in this paper, the plan with the minimum fuel consumption after adjustment is explored. Since there may be more than one solution, under the condition that the optimal cruise point after adjustment is located at (\(Ma5\), 26 km), reducing the fuel consumption is also an objective. The condition that the optimal cruise point is located at (\(Ma5\), 26 km) is reflected in the fitness function in the form of the penalty function, so the fitness function is written as:  
\[fitness=F_{h}+F_{M}+\frac{\widetilde{T}}{g\widetilde{I}_{sp}\widetilde{Ma} \cdot c\cdot\cos\gamma}(1+\frac{\widetilde{h}}{R_{e}}) \tag{25}\]  
where \"\(\sim\)\" indicates that the parameter after adjustment, and the penalty functions \(F_{h}\) and \(F_{M}\) are regarding altitude and Mach number, respectively. \[ \begin{split} F_{h}=\left\{\begin{array}{l}\lambda_{1}\cdot \frac{|\widetilde{I}_{opt}-26|}{26},\;if\;\frac{|\widetilde{I}_{opt}-26|}{26}> \varepsilon\\ 0,\;else\\ \lambda_{2}\cdot\frac{|\widetilde{Ma}_{opt}-5|}{5},\;if\;\frac{|\widetilde{Ma }_{opt}-5|}{5}>\varepsilon\end{array}\right.\\ \lambda_{1}\text{ and }\lambda_{2}\text{ are both large numbers, and }\varepsilon\text{ is a small tolerance.}\end{split}  \tag{26}\]Therefore, the aircraft parameter optimization problem can be expressed mathematically as:  
\[\text{minimize }fitness =F_{h}+F_{M}+\frac{\widetilde{T}}{gI_{sp}Ma_{c}+\cos\gamma}(1+\frac {\widetilde{h}}{K_{e}})\] (27) subject to \[\left\{ \begin{array}{l}X_{L}\leq 1.05\\ X_{D}\geq 1+\frac{1}{2}(X_{L}-1)\\ X_{A}\leq 1.3\\ X_{m}\geq 1+\frac{1}{3}(X_{A}-1)\\ X_{S}\geq 1+\frac{1}{4}(X_{A}-1)\\ X_{I}\leq 1.1\end{array} \right.\]  
The particle swarm optimization algorithm is employed, whose process is outlined in Figure 5. Each particle in the algorithm represents a group of (\(X_{L}\), \(X_{D}\), \(X_{A}\), \(X_{I}\), \(X_{m}\), \(X_{S}\)), and the objective is to minimize the fitness of the particles. The optimal solution should be a group of (\(X_{L}\), \(X_{D}\), \(X_{A}\), \(X_{I}\), \(X_{m}\), \(X_{S}\)), with the lowest fitness computed by (25).