基于多维PC扩展的多学科稳健优化算法研究

Robust multidisciplinary design optimization based on multidimensional polynomial chaos expansion

针对多维不确定性下的多学科稳健设计优化问题,以随机不确定性因素的均匀分布和正态分布并存状况为例,提出一种新的以Legendre polynomials和Hermite polynomials为基础与多维多项式混沌方法,构建多维不确定性量化模型,完成多学科稳健设计优化框架的研究。同时将多维稳健优化方法应用于多学科设计优化的实际工程算例散货船优化论证中,并与文献的单维稳健优化方法进行比较。结果表明,在多维不确定性因素影响下,采用多维多项式混沌方法解决多学科稳健设计优化问题,其优化结果与确定性多学科设计优化结果相差不大,能够得到较为稳健的计算优化结果,有效减少和避免设计优化方案失效的可能性。

Aiming at the robust multidisciplinary design optimization with multidimensional uncertainty, by analyzing the coexistence situation of uniform distribution and normal distribution of stochastic uncertainties, the multidimensional polynomial chaos algorithm was derived through the analysis of legendre polynomials and Hermite polynomials, the multidimensional uncertainty quantification model was also constructed, the framework of robust muhidisciplinary design optimization was completed in this paper. At the same time, this proposed multidimensional polynomial chaos algorithm was applied to the practical engineering example of bulk carrier optimization with comparison to the conventional one-dimensional optimization method in the reference. The results showed that the optimization results were quite the same with the deterministic ones using the multidimensional polynomial chaos method for robust muhidiseiplinary design optimization problem, which can effectively reduce and avoid the failure possibility of optimization design.