多学科设计优化中近似模型与求解策略研究

发布时间：2018-04-11 02:29

本文选题：多学科设计优化 + 近似模型　；参考：《华中科技大学》2012年博士论文

【摘要】：工程产品的设计优化涵盖众多学科、涉及多种因素,而且各个学科、因素之间相互作用、相互耦合,使得工程产品的设计优化过程异常复杂,难以获得满足产品整体性能最佳的设计方案。多学科设计优化(MDO)正是针对这一问题而形成的一种系统综合设计优化的方法论,其通过充分探索和利用各学科间相互耦合所产生的协同效应,来获取工程产品整体性能最优的设计方案。受各学科仿真需要花费庞大计算量、学科间信息交互耦合等因素的影响,计算复杂性和组织复杂性成为了MDO的两大难点。近似模型是一种在满足设计精度的前提条件下,对复杂、隐式或未知的函数关系进行简化替代的方法,能够极大地降低工程产品设计优化中庞大的计算量；求解策略是一种对复杂系统进行协调解耦的计算框架,能够有效地降低工程产品设计优化中组织的复杂性。当前,近似模型和求解策略已经成为MDO领域中两大研究热点。本文从降低工程产品多学科设计优化中计算复杂性和组织复杂性两方面入手,对近似模型和求解策略进行了详细研究：在近似模型方面,提出了基于基因表达式编程(GEP)的近似模型构建方法,并将其与MDO中常见近似模型的性能进行了对比；在求解策略方面,提出了基于Kriging的广义协同优化求解策略,针对多目标MDO问题,进一步提出了基于GEP和Nash均衡的多目标求解策略；并结合小水线面双体船船型参数设计优化实例对本文所提出的方法进行了验证,取得了很好的应用效果。首先,给出了MDO问题的数学描述,对MDO中近似模型与求解策略的相关概念和术语进行了定义,在此基础上,提出了近似模型与求解策略的研究框架。其次,提出了基于GEP的近似模型构建方法并总结了GEP近似模型与MDO中三种常见近似模型的优缺点和适用范围。采用GEP智能进化算法对工程产品多学科设计优化中输入设计变量和输出观测响应之间复杂、隐式或未知的函数关系进行近似替代,在避免高强度仿真、降低计算量的同时,能为设计人员提供简洁、直观的显式函数表达式,有助于他们获得设计变量变化对未知观测响应的影响程度,进行灵敏度分析。在考虑大、小两种样本规模的情况下,从预测精度、鲁棒性、透明度和计算效率四个方面将GEP近似模型与MDO中三种常见近似模型(即响应面、Kriging和径向基函数模型)进行了全面而详尽的比较,总结了四种近似模型的优缺点和适用范围,为工程产品设计人员对近似模型的选用提供指导和参考。然后,提出了基于Kriging的广义协同优化求解策略。该求解策略消除了原有协同优化求解策略中系统级设计变量和对应子系统级局部变量之间的不一致性以及耦合变量取值范围差异所带来的不一致性。此外,基于Kriging的广义协同优化求解策略利用Kriging模型对子系统级优化目标(即系统级广义一致性约束)和子系统分析模型进行近似替代,消除了原有一致性约束形式的非光滑、不连续特性,同时降低了子系统分析的计算量和计算时间,提高了工程产品设计优化的求解效率。接着,提出了基于GEP和Nash均衡的多目标求解策略。利用GEP近似模型构建各个博弈参与者(或子系统)的理性反应集(RRS),通过计算所有参与者RRS的交集来获得Nash均衡解,极大地降低了计算量,提高了求解工程产品多目标MDO问题的效率。随后,将本文所提出的方法应用于小水线面双体船船型参数的设计优化,进行应用验证。结果表明,本文所提出的方法能够极大地降低工程产品多学科设计优化中计算和组织的复杂性,从而有效地支持工程产品的设计优化。最后,对本文的研究工作进行了总结,并指出了今后的研究方向。
[Abstract]:The design optimization of engineering products covers a wide range of disciplines , involving many factors , and the interaction between various disciplines and factors . The design optimization process of engineering products is very complex and it is difficult to obtain the optimal design scheme to meet the overall performance of the product . The multi - disciplinary design optimization ( MDO ) is the two major difficulties of MDO .
The solution strategy is a computational framework for the coordination decoupling of complex systems , which can effectively reduce the complexity of organization in engineering product design optimization . At present , approximate model and solution strategy have become two hot topics in MDO field .
In this paper , the approximate model and the solution strategy are discussed in detail from the aspects of computational complexity and organizational complexity in the optimization of multi - disciplinary design of engineering products . In the approximate model , the approximate model construction method based on GEP is proposed and compared with the performance of common approximate models in MDO ;
In the aspect of solving strategy , a generalized cooperative optimization solution strategy based on Kriging is proposed , aiming at the multi - objective MDO problem , a multi - objective solution strategy based on GEP and Nash equilibrium is further proposed .
Combined with the design optimization example of the ship type parameter of the small water - line surface , the method proposed in this paper is verified , and the good application effect is obtained .
Firstly , the mathematical description of MDO problem is given , and the concept and terminology of approximate model and solution strategy in MDO are defined . On this basis , the research framework of approximate model and solution strategy is proposed .
Secondly , the advantage and disadvantage and application range of three common approximate models in the GEP approximation model and MDO are presented . By using the GEP intelligent evolutionary algorithm , the complex , implicit or unknown function relation between the input design variables and the output observation responses in the multi - disciplinary design optimization of engineering products is approximated . In the case of large and small sample sizes , three common approximate models ( i.e . , response surface , Kriging and radial basis function models ) in the design variables are compared .
In addition , based on Kriging ' s generalized collaborative optimization solution strategy , the system - level optimization objective ( i.e . , the system - level generalized consistency constraint ) and the sub - system analysis model are replaced by Kriging model , which eliminates the non - smooth and discontinuous characteristics of the original consistency constraint form , reduces the calculation amount and calculation time of the sub - system analysis , and improves the solving efficiency of the engineering product design optimization .
Then , a multi - objective solution strategy based on GEP and Nash equilibrium is proposed . The rational reaction set ( RRS ) of each game participant ( or subsystem ) is constructed by using the GEP approximation model , and the Nash equilibrium solution is obtained by calculating the intersection of all participants RRS , which greatly reduces the calculation amount and improves the efficiency of solving the multi - target MDO problem of the engineering product .
Then , the method proposed in this paper is applied to the design optimization of the ship - type parameters of the small water - plane double hull ship , and the application verification is carried out . The results show that the method proposed in this paper can greatly reduce the complexity of calculation and organization in the multi - disciplinary design optimization of engineering products , thus effectively supporting the design optimization of engineering products .
Finally , the research work of this paper is summarized , and the future research direction is pointed out .

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：G642;O242.1

【引证文献】