基于自适应稀疏混沌多项式的鲁棒性优化方法

Robust optimization method based on adaptive sparse polynomial chaos

针对传统混沌多项式面临的“维度灾难”以及依赖实际任务和经验人为给定正交多项式展开阶次等问题,基于相关向量机回归求解展开系数的稀疏解并结合交叉验证判别法,发展了一种基于自适应稀疏混沌多项式的不确定性量化方法。函数算例测试结果表明,所发展方法相比于传统回归法混沌多项式所需样本更少且精度更高。进一步,将基于自适应稀疏混沌多项式的不确定性量化方法与NSGA-II多目标优化算法及Kriging模型相结合,建立了鲁棒性设计优化框架。考虑加工误差不确定性的影响,以叶栅总压损失系数的均值最小和方差最小为目标函数,完成了某动力涡轮叶栅气动鲁棒性设计优化。优化后,平均总压损失系数有所降低,对加工误差不确定性的敏感性程度显著降低。两个代表优化设计个体总压损失系数均值和方差分别降低了16.41%和98.57%,总压损失系数性能核算分别减小了13.43%和2.82%。最后,对流场进行分析,揭示了优化设计气动性能提高的原因。

Traditional polynomial chaos is faced with “curse of dimensionality”,and relies on practical tasks and experience to artificially determine the order of orthogonal polynomial expansion.In this paper,an Uncertainty Quantification(UQ) method based on Adaptive Sparse Polynomial Chaos(ASPC) is developed by using relevance vector machine regression to solve the sparse solution of the expansion coefficient and combining with the cross-validation method.The results of the functional example test show that the proposed method requires fewer samples,and is more accurate than the traditional regression method of polynomial chaos.In addition,a Robust Design Optimization(RDO) framework is established by combining the UQ method based on ASPC,the NSGA-II algorithm and the Kriging model.Considering the influence of manufacturing error uncertainty,the aerodynamic RDO of a power turbine cascade is completed with the objective functions of minimising the mean and the variance of the total pressure loss coefficient of cascade.The optimization results in a reduction in the mean of total pressure loss coefficient and a significant reduction in the degree of sensitivity to manufacturing error uncertainty.The mean and variance of the two representative optimized design individuals decrease by 16.41% and 98.57%,respectively,and the total pressure loss coefficient decreases by 13.43% and 2.82%,respectively.Finally,the flow field is analyzed,and the reasons for improved aerodynamic performance of the optimized design are revealed.