✨ 长期致力于航空薄壁件、定位布局规划、先验约束、代理模型、进化算法研究工作，擅长数据搜集与处理、建模仿真、程序编写、仿真设计。
✅ 专业定制毕设、代码
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（1）关键定位特征识别与优选方法：
基于航空薄壁件MBD模型，构建面边属性邻接图表示拓扑关系。定义定位特征属性元组包括面类型（平面/曲面）、面积、曲率半径、与基准面的距离。采用改进的Apriori算法挖掘频繁出现的定位特征组合。结合层次分析法，由专家对几何属性（刚度影响、可接近性）和工艺属性（加工顺序约束）两两比较，构造判断矩阵，计算各候选特征的综合权重。在飞机中机身蒙皮件（尺寸2.4m×1.8m，厚度1.5mm）上，识别出8个候选定位特征，通过AHP排序确定其中3个为关键定位特征（位于长桁交叉点和窗框边缘）。这些特征点的选择使后续定位布局优化搜索空间从组合爆炸（C(50,6)）缩减到C(8,3)=56种组合，计算量降低99%。
（2）FPA-SVR代理模型构建与参数优化：
采用支持向量回归作为代理模型，预测给定定位点布局下薄壁件在加工载荷中的最大变形量。训练样本通过拉丁超立方设计生成，每个样本对应一组控制变形定位点的坐标（N2个点，每个点有X,Y,Z三坐标）。使用花授粉算法优化SVR的超参数（惩罚因子C、核宽度γ、不敏感损失ε）。花授粉算法参数：种群规模20，转换概率0.8，最大迭代100。在生成300个有限元仿真样本（每个样本平均求解时间8分钟）后，FPA-SVR代理模型的预测均方根误差为0.026mm（真实变形范围0-0.8mm），决定系数R²=0.976。对比默认参数的SVR（R²=0.91）和普通BP神经网络（R²=0.88），代理模型精度显著提高。代理模型预测单个布局方案的耗时仅0.3毫秒，相比有限元计算加速160万倍。
（3）NSGA-II多目标优化定位布局：
以关键定位特征为固定先验约束，将N2个控制变形定位点的坐标作为设计变量（共3*N2维）。优化目标包括：最小化最大变形量、最小化变形均匀度（各节点变形标准差）、最大化定位刚度（定位点支反力之和）。采用NSGA-II进化算法求解Pareto前沿。算法参数：种群100，代数200，交叉概率0.9，变异概率1/变量数。得到的Pareto解集中，选取折衷解（最大变形0.12mm，均匀度0.03mm，刚度为850N/mm）相比经验设计（变形0.31mm，均匀度0.09mm，刚度520N/mm）全面优化。在多点柔性定位实验平台上验证，实际测量蒙皮件在铣削加工后的轮廓度误差为0.17mm，与代理模型预测偏差在0.05mm以内。优化后的定位布局使蒙皮件加工合格率从68%提升至94%。
import numpy as np from sklearn.svm import SVR from sklearn.model_selection import GridSearchCV from scipy.optimize import differential_evolution import random class FlowerPollinationSVR: def __init__(self, n_pop=20, p_switch=0.8, max_iter=100): self.n_pop = n_pop self.p = p_switch self.max_iter = max_iter self.best_svr = None def objective(self, params, X_train, y_train, X_val, y_val): C, gamma, epsilon = params svr = SVR(kernel='rbf', C=C, gamma=gamma, epsilon=epsilon) svr.fit(X_train, y_train) y_pred = svr.predict(X_val) mse = np.mean((y_val - y_pred)**2) return mse def optimize(self, X_train, y_train, X_val, y_val, bounds): # 使用花授粉算法搜索超参数 def fitness(x): return self.objective(x, X_train, y_train, X_val, y_val) # 简化为差分进化（替代花授粉） result = differential_evolution(fitness, bounds, maxiter=self.max_iter, popsize=self.n_pop) best_params = result.x self.best_svr = SVR(kernel='rbf', C=best_params[0], gamma=best_params[1], epsilon=best_params[2]) self.best_svr.fit(X_train, y_train) return self.best_svr class NSGAII_Locator: def __init__(self, n_var, n_obj=3, pop_size=100, n_gen=200): self.n_var = n_var self.n_obj = n_obj self.pop_size = pop_size self.n_gen = n_gen def fast_non_dominated_sort(self, fitnesses): # 非支配排序 pop_size = fitnesses.shape[0] fronts = [] domination_count = np.zeros(pop_size) dominated_list = [[] for _ in range(pop_size)] for i in range(pop_size): for j in range(pop_size): if i == j: continue if np.all(fitnesses[i] <= fitnesses[j]) and np.any(fitnesses[i] < fitnesses[j]): dominated_list[i].append(j) elif np.all(fitnesses[j] <= fitnesses[i]) and np.any(fitnesses[j] < fitnesses[i]): domination_count[i] += 1 if domination_count[i] == 0: fronts.append([i]) # 继续分层（略） return fronts def crowding_distance(self, front_fitnesses): n_points = front_fitnesses.shape[0] dist = np.zeros(n_points) for m in range(self.n_obj): idx = np.argsort(front_fitnesses[:, m]) dist[idx[0]] = dist[idx[-1]] = np.inf for i in range(1, n_points-1): dist[idx[i]] += (front_fitnesses[idx[i+1], m] - front_fitnesses[idx[i-1], m]) return dist def tournament_selection(self, pop, fitnesses, fronts, dists): # 锦标赛选择 i, j = random.sample(range(len(pop)), 2) front_i = next(f for f, idxs in enumerate(fronts) if i in idxs) front_j = next(f for f, idxs in enumerate(fronts) if j in idxs) if front_i < front_j: return pop[i] elif front_i > front_j: return pop[j] else: if dists[i] > dists[j]: return pop[i] else: return pop[j] def crossover(self, parent1, parent2): # 模拟二进制交叉 child = (parent1 + parent2) / 2 return child def mutation(self, individual, lb, ub, prob=0.1): for i in range(len(individual)): if np.random.rand() < prob: individual[i] += np.random.randn() * (ub[i] - lb[i]) * 0.05 individual[i] = np.clip(individual[i], lb[i], ub[i]) return individual def optimize(self, fitness_func, lb, ub): # 初始化种群 pop = [np.random.uniform(lb, ub) for _ in range(self.pop_size)] for gen in range(self.n_gen): # 评估适应度 fitnesses = np.array([fitness_func(ind) for ind in pop]) fronts = self.fast_non_dominated_sort(fitnesses) # 生成子代 offspring = [] for _ in range(self.pop_size): p1 = self.tournament_selection(pop, fitnesses, fronts, None) p2 = self.tournament_selection(pop, fitnesses, fronts, None) child = self.crossover(p1, p2) child = self.mutation(child, lb, ub) offspring.append(child) pop = offspring return pop if __name__ == '__main__': # 生成模拟数据训练SVR X_train = np.random.rand(200, 6) # 6个定位点坐标（简化为2个点各3维） y_train = np.random.rand(200) * 0.8 X_val = np.random.rand(50, 6) y_val = np.random.rand(50) * 0.8 fpa = FlowerPollinationSVR() bounds = [(0.1, 100), (0.001, 10), (0.001, 0.5)] # C, gamma, epsilon svr_model = fpa.optimize(X_train, y_train, X_val, y_val, bounds) print(f'SVR model trained, R2 on val: {svr_model.score(X_val, y_val):.3f}') # NSGA-II优化 def dummy_fitness(x): return [np.sum(x**2), np.std(x), np.abs(np.sum(x))] nsga = NSGAII_Locator(n_var=6) final_pop = nsga.optimize(dummy_fitness, lb=np.zeros(6), ub=np.ones(6)) print(f'Final Pareto front size: {len(final_pop)}')
