基于几何模型建设与约束优化的烟幕干扰弹的最优投放策略

Optimal Deployment Strategy of Smoke Screen Disturbing Bombs Based on Geometric Model Construction and Constraint Optimization

摘要: 烟幕干扰弹通过爆炸进行烟雾扩散，达到干扰导弹、保护重要目标不被袭击的效果，能否合理投放烟幕干扰弹，能直接影响战斗效能和战斗胜败。本文从解析几何、约束优化等方面，深入研究了无人机投放烟幕干扰弹的优化方法，以无人机、导弹和烟幕弹的初始位置、运动规律、运动方向、爆炸特性等为参数，算出了无人机的位置公式、导弹位置方程以及云团遮蔽方程，以精准求出烟幕弹的最佳投放时机，达到最佳遮蔽效果。区别于传统距离判据，本文采用基于“视线穿透”的几何相交模型，精确判断导弹与目标之间视线的遮蔽情况，尤其针对圆柱体目标的表面关键边缘点进行逐点分析，确保遮蔽判定的严密性。在建模过程中，充分考虑了重力加速度、投放间隔、云团下沉速度等客观因素，并摒弃了“永久丢失目标”的简化假设，引入基于导引头视场角(FOV)与重捕获概率的动态博弈模型，将问题从静态优化提升至更具现实意义的动态优化范畴。为此，我们将灵活运用解析几何相关知识、约束优化、粒子群算法、多阶段分解、动态规划(DP)等方法，构建数学模型与优化算法，规划干扰弹的最佳投放方案。我们首先确定了无人机、导弹的初始状态、重要坐标，和运行规律等重要数据信息，得到完整参数，结合实际情况中的诸多客观因素，保证本次优化方案的可行性。

Abstract: Smoke screen decoys disperse smoke through explosion to interfere with missiles and protect important targets from being attacked. Whether smoke screen decoys can be reasonably deployed can directly affect combat effectiveness and the outcome of the battle. This paper deeply studies the optimization method of unmanned aerial vehicle (UAV) deploying smoke screen decoys from aspects such as analytic geometry and constrained optimization. Taking the initial positions, motion laws, motion directions, and explosion characteristics of UAVs, missiles, and smoke screen decoys as parameters, the position formula of UAVs, the position equation of missiles, and the cloud cover equation are calculated to accurately determine the best deployment time of smoke screen decoys and achieve the best shielding effect. Different from the traditional distance criterion, this paper adopts a geometric intersection model based on “line-of-sight penetration” to accurately judge the shielding situation of the line-of-sight between the missile and the target. Especially for the key edge points on the surface of cylindrical targets, point-by-point analysis is conducted to ensure the strictness of the shielding judgment. In the modeling process, objective factors such as gravitational acceleration, deployment intervals, and cloud descent speed are fully considered, and the simplified assumption of “permanent target loss” is abandoned. A dynamic game model based on the field of view (FOV) of the seeker and the probability of re-acquisition is introduced, elevating the problem from static optimization to a more practical dynamic optimization category. For this purpose, we will flexibly apply relevant knowledge of analytic geometry, constrained optimization, particle swarm algorithm, multi-stage decomposition, and dynamic programming (DP) to construct mathematical models and optimization algorithms and plan the best deployment scheme for decoys. First, we determine the initial states, important coordinates, and operation rules of UAVs and missiles, and obtain complete parameters. Combined with many objective factors in the actual situation, the feasibility of this optimization scheme is guaranteed. Firstly, we determine the initial states, important coordinates, and operation rules of UAVs and missiles, and obtain complete parameters. We combine various objective factors in the actual situation to ensure the feasibility of the optimization plan.