Gradient-based response surface approximations for design optimization

本文主要研究一种梯度响应面模型及其在气动优化设计中的应用。目前应用广泛的多项式响应面模型是连续可导的，采用梯度信息构造完全二阶多项式响应面模型，所需样本数与设计参数个数呈线性关系。首先通过改进实验设计方法，快速生成满足精度要求的样本并确定梯度响应面模型。随后通过函数实验验证梯度响应面模型的精度，及该模型在多极值函数最值搜索中的有效性。最后由伴随方法快速求解气动优化设计目标函数的梯度信息，并开展基于梯度响应面模型和复合形法的叶片压力反设计和效率优化设计。结果表明：基于梯度响应面模型的优化方法在全局最优及提高优化效率两方面均有出色表现，基于该优化方法的气动优化设计能够显著改善叶片的气动性能。This paper presents a gradient-based response surface (GBRS) model and its applications to the aerodynamic design optimization. Since the widely used polynomial response surface model is continuous and differentiable, the gradients of the original response can be involved in constructing the quadratic polynomial response surface model. For the quadratic GBRS model, the number of the required samples depends linearly, instead of quadratically on the number of design parameters. Firstly, the samples are determined through the modified design of experiment with shortened sampling time to construct the GBRS model. Then function experiments are performed to evaluate the accuracy of GBRS model and its effectiveness in searching for the global minimum. Finally the gradients for constructing the GBRS model are calculated by the adjoint method and then an inverse design and an optimization design for improving the efficiency of a cascade are performed based on the GBRS model and the complex method. Results demonstrate that the optimization method based on the GBRS model is feasible and effective for obtaining the global optimum with high optimization efficiency; and the aerodynamic performance of the cascade can be significantly improved.国家自然科学基金; 中国博士后科学基金(SCI(E)EI中文核心期刊要目总览(PKU)中国科技核心期刊(ISTIC)中国科学引文数据库(CSCD)11911-196