## 3 Process of Design Optimization  
### Definition of Design Problems  
The installation of aft fins on low-spin fin-stabilized projectiles can provide weather stability, and a specific cant angle is utilized to achieve low spin and minimize dispersion. This section is dedicated to the robust integrated optimization design of the aerodynamic shape and exterior trajectory of pulse correction projectiles. To achieve this, a standard low-spin fin-stabilized projectile (as depicted in Figure 4) is utilized as the initial configuration. The static stability and spin design of a fin-stabilized correction projectile have a direct impact on its flight performance and correction efficiency. In engineering applications, the choice of aft fin area, shape, number of fins, and their position relative to the projectile's center of mass determine its static stability. Meanwhile, the cant angle magnitude determines the spin rate of the projectile. In addition, the size of a single pulse  
Figure 3: The framework of the MOSSA. thruster, the number of pulse thrusters, and their axial and radial distances from the thrust center, as well as other correction mechanism parameters, are interconnected with the aerodynamic layout and have a direct impact on the controlled trajectory performance of the projectile. Consequently, this paper considers six design variables to optimize the aerodynamic shape and trajectory of the pulse correction projectile. These variables include the number of fins, the lead edge cant angle of the fins, the axial mounting position of the fins (relative to the projectile nose), the fin deployment area, the size of a single pulse thruster, and the axial eccentricity of the pulse thrusters. Table 1 provides details of the relevant parameters of the initial design configuration, specific design variables, and their value ranges. During the design optimization process, the number of fins is discretized and rounded off. The primary concern for the tactical and technical performance of the pulse correction projectile is its correction capability, followed by its maximum range of controlled trajectory and flight stability. Instead, there are constraints on the angle of attack \(\delta\) of the projectile, with \(\delta_{\text{max}}<15^{\circ}\) based on engineering experience. The specific mathematical model and constraints for optimization are discussed in Sections 3.2 and 3.3. In Section 3.2, a DK surrogate model is utilized to obtain deterministic Pareto optimal solutions, while Section 3.3 applies an SK surrogate model to obtain robust Pareto optimal solutions for the pulse correction projectile. Section 3.4 conducts a comparative analysis between the deterministic and robust optimization design results of the projectile, and the Pareto design frontier of the corrected missile is obtained based on MOSSA. Additionally, Section 3.4 compares and analyzes the deterministic and robust optimization design results of the pulse correction projectile and presents the Pareto design frontier of the projectile under performance trade-offs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Description** & **Original Configuration** & **Minimum Value** & **Maximum Value** \\ \hline \(N\) & Fin count & 6 & Limited to 4, 5, 6 \\ \(\varepsilon\) & Lead edge cant angle & 6\({}^{\circ}\) & 4\({}^{\circ}\) & 15\({}^{\circ}\) \\ \(R\) & Distance of the leading edge of the & 650 mm & 620 mm & 657 mm \\ \(S\) & Area of a single fin & 20 cm\({}^{2}\) & 7 cm\({}^{2}\) & 25 cm\({}^{2}\) \\ \(I_{\text{imp}}\) & The impulse size of a & 30 N\(\cdot\)s & 30 N\(\cdot\)s & 150 N\(\cdot\)s \\ \(L_{\text{imp}}\) & Asil eccentricity & 100 mm & \(-\)200 mm & 200 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Example optimization problem design variables. Figure 4: Original scheme of projectile. During the design phase, engineering algorithms offer advantages in performing repeated calculations of aerodynamic forces.