Abstract: A multi-objective robust optimization design method of adaptive incremental Kriging model was proposed. Firstly, according to the structural characteristics and optimization objectives, the incremental Kriging surrogate model was constructed, and a hybrid sampling strategy was proposed to improve the adaptability of the incremental Kriging surrogate model. Secondly, the Cauchy mutation MOPSO(CMMOPSO) algorithm was proposed. By improving the inertia weight factor, individual learning factor and social learning factor, and introducing the Cauchy mutation strategy, the efficiency and precision of the optimization model were improved. Finally, an optimization model was constructed with the structural parameters as the design variables, the standard deviation of the performance indicators as the objective, and the 3σ variable reduction interval as the constraint. The optimal solutions of multi-objective robust optimization were obtained combining CMMOPSO and grey correlation analysis. Analysis results of the example show that the proposed method may obtain a high-precision structural optimization model with fewer performance function calls, and the optimization results have faster convergence rate and better robustness than that of traditional methods.

Key words: incremental Kriging surrogate model, mixed point strategy, multi-objective particle swarm optimization(MOPSO) algorithm, multi-objective robust optimization design

摘要： 提出了一种自适应增量Kriging模型的多目标稳健优化设计方法。依据结构特征及优化目标，构建了增量Kriging代理模型，并提出混合加点采样策略，提高增量Kriging代理模型的自适应性；提出了柯西变异多目标粒子群优化(CMMOPSO)算法，通过改进惯性权重因子、个体学习因子和社会学习因子，同时引入柯西变异策略，提高优化模型求解的效率和精度；构建以结构相关参数为设计变量、性能指标标准差为目标、3σ变量缩减区间为约束的优化模型，综合CMMOPSO算法和灰色关联分析获得多目标稳健优化最优解。算例分析结果表明，所提方法不仅能够以较少的性能函数调用次数获得高精度结构优化模型，而且优化结果与传统方法相比，收敛速度更快、稳健性更好。

关键词: 增量Kriging代理模型, 混合加点策略, 多目标粒子群算法, 多目标稳健优化设计