Abstract

To deal with the problem of the difficult optimization search and expensive computational cost caused by large-scale design variables, the hierarchical optimization design system based on the global sensitivity analysis method is established in this paper. The M-OAT method is used to analyze the global sensitivity of the design variables, according to the sensitivity information to layer design variables, then optimize the design variables in each hierarchy. Through the study of the hierarchical optimization design of airfoils and wings, compared with the normal parameter optimization design system, the hierarchical optimization design system based on the global sensitivity analysis method can reduce effectively the number of design variables in a single optimization, reduce the difficulty of the optimization search, improve the convergence speed of the optimization, gain better optimization results at the same time. For optimization design with large-scale design variables, the hierarchical optimization design system based on the global sensitivity analysis method is a sort of effective ways of design.

Highlights

  • expensive computational cost caused by large⁃scale design variables

  • the hierarchical optimization design system based on the global sensitivity analysis method is established in this paper

  • The M⁃OAT method is used to analyze the global sensitivity of the design varia⁃ bles

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Summary

Introduction

本文将全局灵敏度分析方法与气动优化设计相 结合,根据设计变量对目标函数的灵敏度信息对设 计变量进行分层,然后建立基于全局灵敏度分析方 法的分层优化设计系统,对翼型以及机翼进行分层 优化设计,并与普通的全参数优化系统对比分析。 计算结果表明分层优化系统可以有效减少单次优化 时的设计变量数目,减少优化搜索难度,加快优化收 敛速度,同时获得较好的优化结果。 由于 M⁃OAT 和 Sobol 方法都依赖于样本数据, 不同的样本数量会对结果产生重要影响,因此在具 体计算过程中,逐渐增加样本数量,根据不同样本数 量下的计算结果来判断灵敏度分析方法的分析效率 和分析精度。 算例中将会用到 2 个测试函数,如表 1 所示。 2 个测试函数中 n 均代表矢量 x 的维数,xi 为[0,1] 之间均匀分布的输入变量,参数 ai 影响着 xi 的灵敏度大小,且 ai 越小,灵敏度值则越大。 分别使用 M⁃OAT 方法和 Sobol 方法对函数进行设 计变量 的灵敏度计算, 以检验各灵敏度分析方法 性能。

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