烟幕干扰弹的投放策略

Smoke Jamming Bomb Delivery Strategy

摘要: 在现代信息化战争中，为了保护“真目标”，可通过无人机投放烟幕干扰弹实施对来袭导弹的干扰，从而避免其发现真目标，针对2025年高教社杯全国大学生数学建模竞赛$A$ 题中的场景，主要是在特定策略下求解单架无人机投放单枚烟幕干扰弹对单枚导弹的有效遮蔽时长。对此，首先依据运动学方程分步骤建立相关运动轨迹模型；由于真目标结构特征，采用蒙特卡洛采样方法进行采样，并根据目标各表面实际面积加权分配采样点，同时对采样点数量进行收敛性分析；在此基础上规定有效遮蔽的判定条件：若烟幕云团对所选取的采样点实现90%遮蔽，则为有效遮蔽。此外，对关键参数进行灵敏度分析，评估研究得出的投放策略在实战环境下的鲁棒性。基于上述构建有效遮蔽时长计算模型，通过Python实现数值求解，最终得到有效遮蔽时长为1.40 s。研究结果可为在实战中投放烟幕干扰弹干扰敌方导弹提供量化参考，也验证了数学建模在复杂攻防场景中的应用价值。

Abstract: In modern information warfare, to protect “real targets,” smoke screen interference munitions can be deployed by drones to disrupt incoming missiles, thereby preventing their detection. This study addresses Scenario $A$ of the 2025 Higher Education Press Cup National College Students Mathematical Modeling Competition, focusing on determining the effective shielding duration of a single drone’s smoke screen munition against a missile under specific strategies. The approach involves establishing a step-by-step trajectory model based on kinematic equations. Given the structural characteristics of real targets, a Monte Carlo sampling method is employed to allocate sampling points according to the actual surface areas of each target, while simultaneously convergence analysis was performed on the number of sampling points, establishing the effective concealment criterion: a smoke cloud cluster is deemed effective if it achieves 90% concealment of the selected sampling points. Furthermore, sensitivity analysis of key parameters was conducted to evaluate the robustness of the proposed deployment strategy in real-world scenarios. By developing a computational model for effective concealment duration and implementing it through Python, the study determined the effective duration to be 1.40 seconds. These findings provide a quantitative reference for deploying smoke interference munitions to disrupt enemy missiles in combat, while also demonstrating the practical value of mathematical modeling in complex offensive and defensive scenarios.