基于响应带的多学科混合不确定性优化方法

For mixed uncertainty widely existing in engineering design, response surface method is an effective way to solve multidisciplinary optimization problem under uncertainties, which is also a research hotspot in the field of engineering optimization. Currently, shortcomings of mixed uncertainty optimization method are as follows: firstly it is difficult to unify expression of multi-source uncertainty when modeling; secondly, on uncertainty analysis, it is hard to calculate the robustness index of objective and reliability index of constrains, and result has a low accuracy; thirdly algorithms of multidisciplinary design optimization under uncertainties are inaccurate and inefficient. In this project, a method of multidisciplinary design optimization under mixed uncertainties based on the so-called response scope is proposed. For mixed uncertainty of parameters, a unified expression of mixed uncertainty of parameters based on Johnson distribution will be proposed; efficient sampling technique will be used to fit the distribution of objectives and constraints, response scope of objectives and constraints will be established by using duality theory, so as to accurately obtain the robustness index of objectives and the reliability index of the constraints; and an efficient mixed uncertainty optimization algorithm based on response scope will be proposed. The software prototype of mixed uncertainty optimization will be built on the self-developed multidisciplinary design optimization platform, and this reseach will be validated by design optimization on electric vehicle. This project is expected to greatly improve the efficiency and accuracy of mixed uncertainty optimization, and to promote the perfectness and development of the theory on multidisciplinary design optimization under uncertainties and reliability design.

混合不确定性广泛存在于工程设计中，响应面方法是解决多学科不确定性优化问题的有效途径，也是工程优化领域的研究热点。目前混合不确定性优化方法存在如下不足：在建模上多源不确定性表达难以统一；在不确定性分析上目标稳健性和约束可靠性指标计算不准确且难以计算；在求解上不确定性多学科优化算法精度和效率低下。为此，本项目提出响应带的概念以解决多学科混合不确定性优化中的问题。针对参数的多源不确定性，提出基于Johnson分布的混合不确定性参数统一表达；通过高效采样拟合目标和约束分布，运用对偶理论建立目标和约束的响应带，从而准确获得目标稳健性指标和约束可靠性指标；提出基于响应带的混合不确定性高效优化算法。在自主研发的多学科设计优化平台上实现混合不确定性优化软件原型，并以电动汽车设计为例进行验证。本研究有望大幅度提高混合不确定性优化的效率和精度，促进多学科不确定性设计优化和可靠性设计理论体系的完善与发展。

混合不确定性广泛存在于工程设计中，响应面方法是解决多学科不确定性优化问题的有效途径，也是工程优化领域的研究热点。目前混合不确定性优化方法由于存在计算复杂性和组织复杂性，目前还未建立完善的理论体系，优化过程及算法还不够成熟，存在如下不足：在建模上多源不确定性表达难以统一；在不确定性分析上目标稳健性和约束可靠性指标计算不准确且难以计算；在求解上不确定性多学科优化算法精度和效率低下。为此，本项目提出响应带的概念以解决多学科混合不确定性优化中的问题。针对参数的多源不确定性，提出了基于Johnson分布的混合不确定性参数统一表达，并采用参数化的Johnson分布拟合各种概率分布，研究实现了基于最小样本空间的Johnson分布拟合方法；通过高效采样拟合目标和约束分布，运用多种方法建立目标和约束的响应带，包括结合正则对偶/三对偶理论和基于响应面的信任域策略，研究实现了一种基于Kriging模型的全局优化方法、采样EGO算法构建目标函数响应带、融合支持向量机和Kriging模型构造可靠性约束边界，从而准确获得目标稳健性指标和约束可靠性指标；提出了基于响应带的混合不确定性高效优化算法，包括基于自适应局部搜索区域采样法的RBDO方法、基于自适应Kriging近似模型的RBDO方法、基于支持向量配对夹持法的双模型RBDO方法以及面向混合不确定性的RBDO方法。在自主版权的多学科设计优化FlowComputer平台上开发实现了混合不确定性优化软件原型，包括不确定性分析组件、不确定性优化组件和不确定性优化算法库。基于该平台，对电动汽车设计进行了验证，建立了电动汽车多学科分析模型并进行学科封装，由优化模块定义电动汽车的优化设计问题，并对各个不确定性参数进行设置，从而完成了多学科混合不确定性优化问题求解。本研究较大幅度提高了混合不确定性优化的效率和精度，促进了多学科不确定性设计优化和可靠性设计理论体系的完善与发展。