不确定性下的多学科设计优化研究
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摘要
随着科学技术的发展,工程系统越来越复杂,其设计研发涉及到多个学科领域,并且学科之间存在着较强的耦合关系。多学科设计优化(Multidisciplinary Design Optimization, MDO)是一种复杂耦合系统设计的综合方法,其充分利用学科间的耦合作用,从系统的角度对复杂耦合系统进行优化设计,以期获得系统的整体最优解,达到提高产品性能、降低成本和缩短设计周期的目的。
不确定性广泛存在于实际复杂耦合系统中,其大致可分为随机不确定性和认知不确定性两类。为获得高可靠性和高安全性的复杂耦合系统,考虑不确定性对系统的影响已成为工程系统设计的焦点之一。针对连续变量和参数含有随机不确定性的情形,基于可靠性的多学科设计优化受到了广泛关注,并取得了丰硕的研究成果。本文基于可能性理论,研究了连续变量和参数仅含认知不确定性的MDO问题、连续变量和参数同时含有随机和认知不确定性的MDO问题、单学科随机和认知不确定性下的混合离散变量设计优化问题、随机和认知不确定性下的混合离散变量MDO问题,拓展和完善了不确定性下MDO的理论体系,为不确定性下的多学科耦合系统的设计提供了有效的方法。
本文的研究成果主要体现在如下几个方面：
(1)基于可能性的多学科设计优化(Possibility Based MDO, PBMDO)。当连续变量和参数仅含有认知不确定性时,建立了MDO环境下的不确定性分析模型,提出了PBMDO问题的两种优化求解方法：PBMDO的顺序优化和可靠性评估法(PBMDO in framework of Sequential Optimization and Reliability Assessment, PBMDO-SORA); PBMDO的安全系数法(PBMDO in framework of Safety Factor based Approach, PBMDO-SFA)。
(2)随机和认知不确定性下的多学科设计优化(Mixed Variables MDO, MVMDO)。当连续变量和参数同时含有随机和认知不确定性时,建立了MDO环境下的不确定性分析模型,提出了MVMDO问题的两种优化求解方法：MVMDO的顺序优化和可靠性评估法(MVMDO in framework of SORA, MVMDO-SORA); MVMDO的安全系数法(MVMDO in framework of SFA, MVMDO-SFA)。
(3)单学科随机和认知不确定性下的混合离散变量设计优化(Random/Fuzzy Continuous Discrete Variables Design Optimization, RFCDV-DO)。单学科中,当离散、连续变量和参数同时含有随机和认知不确定性时,基于条件失效可能性,推导和提出了两种不确定性分析方法；提出了求解RFCDV-DO问题的顺序优化和可靠性分析方法(Random/Fuzzy SORA, RFSORA)。
(4)随机和认知不确定性下的混合离散变量多学科设计优化(Random/Fuzzy Continuous Discrete Variables MDO, RFCDV-MDO)。当离散、连续变量和参数同时含有随机和认知不确定性时,在单学科不确定性分析方法的基础上,建立了MDO环境下两种不确定性分析模型；提出了求解RFCDV-MDO问题的顺序优化和可靠性分析方法(RFCDV-MDO in framework of SORA, RFCDV-MDO-SORA)。
With the development of science and technology, engineering system becomes more and more complex. Design of the system will involve multi-discipline field, and there are coupling relationships among disciplines. Multidisciplinary design optimization (MDO) is a synthesis method for design of complex and coupled system: with the aim of improving performance, reducing cost and shortening design period, it fully utilizes the coupling relationships among disciplines, and proceeds design optimization from system point of view to obtain the global optimum of a complex and coupled system.
In practical complex and coupled system, uncertainty widely exists, and it can be divided into aleatory uncertainty and epistemic uncertainty. For achieving high reliable and safe complex and coupled system, the consideration of uncertainty's effect to the system has been a focus of engineering system design. For the case of continuous variables and parameters associated with aleatory uncertainty, Reliability Based Multidisciplinary Design Optimization (RBMDO) has gained increasing attention, and lots of achievements have been achieved. In this paper, based on possibility theory, different design optimization problems are studied:MDO problem with continuous variables and parameters associated with epistemic uncertainty; MDO problem with continuous variables and parameters associated with both aleatory and epistemic uncertainties; in single disciplinary, design optimization problem with discrete and continuous variables and parameters associated with both aleatory and epistemic uncertainties; MDO problem with discrete and continuous variables and parameters associated with both aleatory and epistemic uncertainties. The research in this paper extends and develops the study of MDO under uncertainty, and also provides effective design methods for multi-discipline coupling system.
The contributions of this dissertation are summarized as follows:
(1) Possibility Based Multidisciplinary Design Optimization (PBMDO). In MDO, when continuous variables and parameters are associated with epistemic uncertainty, the uncertainty analysis method is proposed, and two methods for solving PBMDO problems are developed, named as PBMDO in framework of Sequential Optimization and Reliability Assessment (PBMDO-SORA) and PBMDO in framework of Safety Factor based Approach (PBMDO-SFA), respectively.
(2) MDO under both aleatory and epistemic uncertainties (Mixed Variables MDO, MVMDO). In MDO, when continuous variables and parameters are associated with both aleatory and epistemic uncertainties, the uncertainty analysis method is proposed, and also two methods for solving MVMDO problems are developed, named as MVMDO in framework of SORA (MVMDO-SORA) and MVMDO in framework of SFA (MVMDO-SFA), respectively.
(3) Random/Fuzzy Continuous Discrete Variables Design Optimization (RFCDV-DO). In single discipline, when continuous and discrete variables and parameters are associated with both aleatory and epistemic uncertainties, based on conditional possibility of failure, two uncertainty analysis method are developed, and a method, named as Random/Fuzzy SORA (RFSORA), is developed to solve RFCDV-DO problems.
(4) Random/Fuzzy Continuous Discrete Variables MDO (RFCDV-MDO). In MDO, when continuous and discrete variables and parameters are associated with both aleatory and epistemic uncertainties, based on developed uncertainty analysis methods in single discipline, two uncertainty analysis methods are proposed, and also a method of RFCDV-MDO in framework of SORA (RFCDV-MDO-SORA) is developed to solve RFCDV-MDO problems.
不确定性广泛存在于实际复杂耦合系统中,其大致可分为随机不确定性和认知不确定性两类。为获得高可靠性和高安全性的复杂耦合系统,考虑不确定性对系统的影响已成为工程系统设计的焦点之一。针对连续变量和参数含有随机不确定性的情形,基于可靠性的多学科设计优化受到了广泛关注,并取得了丰硕的研究成果。本文基于可能性理论,研究了连续变量和参数仅含认知不确定性的MDO问题、连续变量和参数同时含有随机和认知不确定性的MDO问题、单学科随机和认知不确定性下的混合离散变量设计优化问题、随机和认知不确定性下的混合离散变量MDO问题,拓展和完善了不确定性下MDO的理论体系,为不确定性下的多学科耦合系统的设计提供了有效的方法。
本文的研究成果主要体现在如下几个方面：
(1)基于可能性的多学科设计优化(Possibility Based MDO, PBMDO)。当连续变量和参数仅含有认知不确定性时,建立了MDO环境下的不确定性分析模型,提出了PBMDO问题的两种优化求解方法：PBMDO的顺序优化和可靠性评估法(PBMDO in framework of Sequential Optimization and Reliability Assessment, PBMDO-SORA); PBMDO的安全系数法(PBMDO in framework of Safety Factor based Approach, PBMDO-SFA)。
(2)随机和认知不确定性下的多学科设计优化(Mixed Variables MDO, MVMDO)。当连续变量和参数同时含有随机和认知不确定性时,建立了MDO环境下的不确定性分析模型,提出了MVMDO问题的两种优化求解方法：MVMDO的顺序优化和可靠性评估法(MVMDO in framework of SORA, MVMDO-SORA); MVMDO的安全系数法(MVMDO in framework of SFA, MVMDO-SFA)。
(3)单学科随机和认知不确定性下的混合离散变量设计优化(Random/Fuzzy Continuous Discrete Variables Design Optimization, RFCDV-DO)。单学科中,当离散、连续变量和参数同时含有随机和认知不确定性时,基于条件失效可能性,推导和提出了两种不确定性分析方法；提出了求解RFCDV-DO问题的顺序优化和可靠性分析方法(Random/Fuzzy SORA, RFSORA)。
(4)随机和认知不确定性下的混合离散变量多学科设计优化(Random/Fuzzy Continuous Discrete Variables MDO, RFCDV-MDO)。当离散、连续变量和参数同时含有随机和认知不确定性时,在单学科不确定性分析方法的基础上,建立了MDO环境下两种不确定性分析模型；提出了求解RFCDV-MDO问题的顺序优化和可靠性分析方法(RFCDV-MDO in framework of SORA, RFCDV-MDO-SORA)。
With the development of science and technology, engineering system becomes more and more complex. Design of the system will involve multi-discipline field, and there are coupling relationships among disciplines. Multidisciplinary design optimization (MDO) is a synthesis method for design of complex and coupled system: with the aim of improving performance, reducing cost and shortening design period, it fully utilizes the coupling relationships among disciplines, and proceeds design optimization from system point of view to obtain the global optimum of a complex and coupled system.
In practical complex and coupled system, uncertainty widely exists, and it can be divided into aleatory uncertainty and epistemic uncertainty. For achieving high reliable and safe complex and coupled system, the consideration of uncertainty's effect to the system has been a focus of engineering system design. For the case of continuous variables and parameters associated with aleatory uncertainty, Reliability Based Multidisciplinary Design Optimization (RBMDO) has gained increasing attention, and lots of achievements have been achieved. In this paper, based on possibility theory, different design optimization problems are studied:MDO problem with continuous variables and parameters associated with epistemic uncertainty; MDO problem with continuous variables and parameters associated with both aleatory and epistemic uncertainties; in single disciplinary, design optimization problem with discrete and continuous variables and parameters associated with both aleatory and epistemic uncertainties; MDO problem with discrete and continuous variables and parameters associated with both aleatory and epistemic uncertainties. The research in this paper extends and develops the study of MDO under uncertainty, and also provides effective design methods for multi-discipline coupling system.
The contributions of this dissertation are summarized as follows:
(1) Possibility Based Multidisciplinary Design Optimization (PBMDO). In MDO, when continuous variables and parameters are associated with epistemic uncertainty, the uncertainty analysis method is proposed, and two methods for solving PBMDO problems are developed, named as PBMDO in framework of Sequential Optimization and Reliability Assessment (PBMDO-SORA) and PBMDO in framework of Safety Factor based Approach (PBMDO-SFA), respectively.
(2) MDO under both aleatory and epistemic uncertainties (Mixed Variables MDO, MVMDO). In MDO, when continuous variables and parameters are associated with both aleatory and epistemic uncertainties, the uncertainty analysis method is proposed, and also two methods for solving MVMDO problems are developed, named as MVMDO in framework of SORA (MVMDO-SORA) and MVMDO in framework of SFA (MVMDO-SFA), respectively.
(3) Random/Fuzzy Continuous Discrete Variables Design Optimization (RFCDV-DO). In single discipline, when continuous and discrete variables and parameters are associated with both aleatory and epistemic uncertainties, based on conditional possibility of failure, two uncertainty analysis method are developed, and a method, named as Random/Fuzzy SORA (RFSORA), is developed to solve RFCDV-DO problems.
(4) Random/Fuzzy Continuous Discrete Variables MDO (RFCDV-MDO). In MDO, when continuous and discrete variables and parameters are associated with both aleatory and epistemic uncertainties, based on developed uncertainty analysis methods in single discipline, two uncertainty analysis methods are proposed, and also a method of RFCDV-MDO in framework of SORA (RFCDV-MDO-SORA) is developed to solve RFCDV-MDO problems.
引文
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