考虑认知不确定性的多学科设计优化方法

【作者】 魏娟；

【导师】 杨波；

【作者基本信息】 电子科技大学 ， 机械制造及其自动化， 2010， 硕士

【摘要】 多学科系统的学科之间存在耦合关系。传统的设计方法是采用递进的设计模式,设计时没有充分考虑学科间的耦合效应的影响。对于昂贵、复杂的高耦合大型多学科系统,高质量、稳定的性能是设计的重点之一。传统方法不能很好的解决这些问题。近年来,借鉴并行协同设计学及集成制造技术的思想,出现了针对大型、复杂系统的多学科设计优化(Multidisciplinary Design Optimization, MDO)方法,其优点是设计时考虑复杂产品的高耦合性,可获得系统的整体最优解。在产品的设计过程中,存在大量的不确定性因素。学术界将这些不确定性划分为随机不确定性(Aleatory Uncertainty)和认知不确定性(Epistemic Uncertainty)两大类。从数学角度看,前者的背景是关于不确定性变量的统计数据信息充足,其概率分布清晰可知;后者的背景是关于不确定性变量的统计数据信息不足,无法获得其准确的概率分布。近年来,考虑不确定性的设计优化方法越来越受到关注。在实际工程情况中,往往同时存在随机和认知不确定性。目前在考虑不确定性的多学科设计优化领域,已有的方法大都是针对随机不确定性,考虑认知不确定的多学科设计优化方法非常少见。因此,本文开展了以下几个方面的研究:(1)基于概率论和可能性理论,建立了一种同时包含随机和认知不确定性的单学科设计优化数学模型。基于顺序优化及可靠性估计(SORA)方法可以简化优化算法结构和提高计算效率,提出了顺序优化及并行不确定性估计(SOCUA)优化算法对上述模型进行优化,并通过一个数学算例和一个工程算例验证了其可行性和有效性。(2)基于不确定性分析的一种高效方法——性能测量法(PMA)以及MDO中三种典型的单学科优化策略,提出了多级可行法下的性能测量方法(PMA-MDF)、并行分析及设计下的性能测量方法(PMA-SAND)、单级可行法下的性能测量方法(PMA-IDF),将三种算法分别用于了基于可能性的多学科设计优化(PBMDO)中的可能性分析,通过算例验证了其可行性并比较了这三种算法的有效性。(3)针对多学科系统中存在认知不确定性,将可能性理论引入多学科设计优化中,建立了基于可能性的多学科设计优化的数学模型,并针对模型提出了顺序优化及可能性评估(SOPA)框架下的基于可能性的多学科设计优化的多级可行法(PBMDO-SOPA-MDF)、基于可能性的多学科设计优化的并行分析及设计法( PBMDO-SOPA-SAND )、基于可能性的多学科设计优化的单级可行法(PBMDO-SOPA-IDF)优化上述模型。最后通过算例验证了这三种算法的可行性并比较其有效性。更多还原

【Abstract】 There is coupling relationship between the disciplines of the multidisciplinary system. The traditional design approaches use the progressive design method, which fails to fully consider the coupling effect. For any expensive and complex multidisciplinary system, high quality and stable performance are the key objectives of its design, which may not be easily achieved by traditional design approaches. In recent years, the Multidisciplinary Design Optimization (MDO) appraoch has been proposed to handle the large-scale and complex system design in light of the concepts of Parallel Collaborative Design and Integrated Manufacturing Technology. The advantage of MDO is that it takes into consideration the highly coupling relationship of complex systems and thus can obtain the global optimal solution.In the product design process, there often exist a lot of uncertainties, which are classified into two categories in the literature, i.e., aleatory uncertainty and epistemic uncertainty. From the mathematical point of view, the background of the aleatory uncertainty is that there are adequate statistical data and the probability distributions can be known. The background of epistemic uncertainty is that there lack sufficient data/information to derive the probability distributions. In recent years, the design optimization under uncertainty has attacted more and more attention. In engineering practice, both aleatory uncertainty and epistemic uncertainty often exist. However, existing methods of MDO under uncertainty generally consider only the aleatory uncertainty, methods considering the epistemic uncertainty are quite rare. Therefore, this paper carries out the following researches:(1) Based on the probability theory and possibility theory, a single-disciplinary design optimization model is proposed which considers both aleatory and epistemic uncertainties. To solve the proposed model, a sequential optimization and concurrent uncertain assessment (SOCUA) optimization algorithm is proposed, which is based on the sequential optimization and reliability assessment (SORA) method which is effective in simplifying optimization algorithm structure and improving the computational efficiency. A numerical example and a real-life example are given to verify the feasibility and efficiency of the proposed model and algorithm.(2) Based on the performance measure analysis (PMA),which is a method that is effective in reducing the computational complexity of uncertain analysis, and three typical single-disciplinary optimization methods in MDO, three algorithms for possibility analysis in possibility-based multidisciplinary design optimization (PBMDO)are proposed, i.e., performance measure analysis-multidisciplinary feasible method (PMA-MDF), performance measure analysis-simultaneous analysis and design (PMA-SAND) and performance measure analysis-individual discipline feasible method (PMA-IDF). An example is given to verify the feasibility and to compare the efficiency of the three proposed algorithms.(3) Because multidisciplinary system often has epistemic uncertaint, possibility theory is introduced into MDO and the mathematical model of PBMDO is established. Three algorithms are proposed based on the framework of sequential optimization and possibility assessment (SOPA), i.e., possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- multidisciplinary feasible method (PBMDO-SOPA-MDF), possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- simultaneous analysis and design (PBMDO-SOPA-SAND) and possibility based multidisciplinary design optimization- sequential optimization and possibility assessment- individual discipline feasible method (PBMDO-SOPA-IDF). An example is given to verify the feasibility and to compare the efficiency of the three proposed algorithms.更多还原