煙幕干擾彈投放策略優化：模型與算法整合框架

基于文獻研究和問題需求分析，我們構建了完整的模型與算法整合框架。

一、整體建模框架

1. 核心問題分解

• 物理層：煙幕彈道運動與擴散特性建模
• 博弈層：導彈識別與決策機制建模
• 優化層：多機協同投放策略優化
• 環境層：風場干擾建模與補償

2. 模型整合架構

輸入層 → 處理層 → 輸出層
(環境參數) (模型協同計算) (最優投放方案)

二、關鍵模型實現

1. 煙幕彈道與擴散模型

運動學建模：

# 彈道軌跡計算（含風場補償）
def smoke_trajectory(v_drone, heading, wind_vector, drop_time):# 初始速度合成v_init = vector_transform(v_drone, heading)v_total = v_init + wind_vector  # 風場補償# 彈道計算（考慮重力加速度）trajectory = []for t in np.arange(0, burst_time, dt):x = v_total.x * ty = v_total.y * t - 0.5 * g * t**2z = v_total.z * ttrajectory.append((x, y, z))return trajectory# 擴散特性建模
def smoke_diffusion(burst_point, time_elapsed, wind_vector):# 云團沉降center = burst_point + np.array([0, -3*time_elapsed, 0])# 擴散半徑radius = initial_radius + diffusion_rate * time_elapsed# 濃度分布（高斯模型）concentration = max_concentration * np.exp(-0.5 * (distance/radius)**2)return center, radius, concentration

2. 導彈識別與決策模型

智能響應機制：

# 目標識別評估
def missile_recognition(missile_pos, target_pos, smoke_concentration):# 視線遮蔽率計算total_obscuration = calculate_obscuration(missile_pos, target_pos)# 識別置信度衰減match_confidence = base_confidence * (1 - total_obscuration)return (match_confidence >= recognition_threshold), match_confidence# 決策狀態機
def missile_decision(missile_state, recognition_result, duration):if missile_state == "SEEKING":return "TRACKING" if recognition_result else "SEEKING"elif missile_state == "TRACKING":if not recognition_result:return "SEARCHING" if duration > max_tracking_time else "TRACKING"return "TRACKING"elif missile_state == "SEARCHING":new_path = calculate_new_path(last_known_pos, true_target_pos)return "SEARCHING"

3. 遮蔽效能評估模型

光學遮蔽計算：

def calculate_obscuration(missile_pos, target_pos, smoke_clouds):total_transmission = 1.0# 路徑積分計算for cloud in smoke_clouds:path_length = calculate_path_through_cloud(missile_pos, target_pos, cloud)extinction = mass_extinction_coeff * cloud.concentration * path_lengthtotal_transmission *= np.exp(-extinction)return 1 - total_transmission  # 遮蔽率def is_effective_obscuration(obscuration_rate):return obscuration_rate > effectiveness_threshold

4. 多無人機協同模型

分布式協同框架：

class DroneCoordinator:def __init__(self, drones, missiles):self.drones = dronesself.missiles = missilesself.assignment = {}def assign_targets(self):# 最優任務分配for missile in self.missiles:best_drone = min(self.drones,key=lambda drone: self.calculate_assignment_cost(drone, missile))self.assignment[missile] = best_dronedef coordinate_plan(self, current_time):# 生成協同方案return {drone.id: self.generate_drop_plan(drone, self.assignment[missile])for missile, drone in self.assignment.items()}

三、優化算法設計

1. 分層優化架構

單機參數優化（PSO算法）：

def optimize_drone_parameters(drone, missile):# 目標函數：最大化遮蔽時長def objective(params):speed, heading, drop_time, burst_time = paramsreturn -simulate_single_drop(drone, missile, speed, heading, drop_time, burst_time)# 參數邊界bounds = [(70, 140), (0, 2*np.pi), (0, max_time), (0, max_time)]return pso(objective, bounds)