基于均值一次二阶矩方法的稳健性优化设计

Robust Optimization Design Based on Mean Value First Order Second Moment Method

关键词:  均值一次二阶矩  蒙特卡洛模拟  稳健性  分位数区间

Key words:  Mean value first order second moment  Monte-Carlo simulation  Robust  Quantile interval

摘要:

为解决传统基于蒙特卡洛模拟的稳健性优化方法计算效率较低的问题，提出一种基于均值一次二阶矩方法的稳健性优化设计方法。首先，利用泰勒展开方法将函数在随机输入参数均值点展开；然后，利用一次二阶矩方法求解函数的均值以及标准差；最后，结合分位数区间方法建立稳健性优化模型并进行优化求解。优化结果显示，与基于蒙特卡洛模拟方法相比，提出的稳健性优化方法在保证计算精度的情况下，计算时间仅为其1%左右，更加适合工程稳健性优化计算。

Abstract:

Considering the low calculation efficiency of traditional Monte-Carlo simulation based robust optimization approach， a robust optimization method based on mean value first order second moment model is presented. Firstly， the performance function is expanded by using Taylor expansion at mean values of random input parameters. And then， the mean and standard deviation of performance function can be obtained through the first order second moment method. Finally， a robustness optimization model is constructed using quantile interval method and the optimal solution be solved. The results show that the proposed method computation time is only about 1% of traditional Monte-Carlo simulation based method and can achieve perfect accuracy. It is more suitable engineering robust optimization.