基于高阶矩的稳健优化设计研究

采用随机响应量的前四阶统计矩来度量目标函数和概率约束条件的稳健性, 通过引入“权重因子”来确定新构造的目标函数中原 函数和敏感系数的比重, 利用加权组合法将稳健优化设计这一多目标优化问题转化为单目标问题, 从而建立新的基于高阶矩的稳健优化设计数学模型. 矩估计方法可高效地评估目标函数和概率约束条件的统计矩, 且不需要搜索技术, 因此不构成嵌套循环(即稳健优化过程是单循环的), 从而可以大大降低优化的计算工作量. 对多个桁架结构进行了确定性优化设计、可靠性优化设计、传统的和该文所提的稳健优化设计, 验证了所建立的基于高阶矩的稳健优化设计数学模型的合理性和正确性, 比较并解释了计算所得的优化结果.

THE ROBUST OPTIMIZATION DESIGN BASED ON MOMENT ESTIMATION METHOD

Robust design is a widely used method for design under uncertainty to seek an optimal solution where the design objective is insensitive to the variations of input variables while the design feasibility under the variations is maintained.In this paper,the first four statistical moments,i.e.,mean,variance,skewness and kurtosis,are used to measure the robustness of the objective function and probabilistic constraints.With the weighting factor method,a new robust design problem is modeled as a single objective optimization problem on the basic of first four statistical moments.We present moment estimation method as a rigorous method for statistical moment calculation and sensitivity computation with arbitrary input distributions and examine its effectiveness when applied to robust design.Three robust design examples of truss structures are provided to check the feasibility and effectiveness of robust design using moment estimation method and the proposed sensitivity analysis.