基于改进PATC的不确定性多学科设计优化方法研究

发布时间：2018-03-06 21:17

本文选题：不确定性多学科设计优化　切入点：概率目标级联法　出处：《华中科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：对于不确定环境下的多学科设计优化问题，用确定性多学科设计优化方法求解很难保证产品的可靠性和稳健性。因此，将传统的多学科设计优化方法与不确定优化方法相结合引起了广大学者的关注与研究，并形成了不确定性多学科设计优化（Uncertaintybased Multidisciplinary Design Optimization， UMDO）方法。其中，概率目标级联（ProbabilisticAnalytical Target Cascading，PATC）方法是一种很有潜力的UMDO方法，，它继承了目标级联方法（Analytical Target Cascading，ATC）的各种特点，具有严格的收敛性。但是，在PATC中，每个子系统均采用传统嵌套双循环优化策略，并且各子系统的一致性通过传统的协调策略来保证，这使得PATC方法的不确定性优化效率和系统协调效率不是很高。为了探索更高效的PATC方法，本文对PATC方法进行了深入研究，重点改进了其不确定优化策略和协调策略。首先，针对PATC的不确定性优化策略，本文研究了基于混合均值法（Hybrid MeanValue，HMV）的单层序列规划与可靠性分析（Sequential Optimization and ReliabilityAssessment，SORA）策略，用于改进PATC方法中的嵌套双层循环策略，提出了HMV-PATC方法，建立了该方法的求解模型和流程，并验证了该方法的可行性和高效性。其次，针对HMV-PATC的协调策略，本文分析对比了各种协调策略，分别将拉格朗日对偶方程（Lagrangian Duality Function，LDF）和二次外罚函数(Quadratic ExteriorPenalty Function，QEPF)方法作为HMV-PATC方法的协调策略，建立了LDF-HMV-PATC和QEPF-HMV-PATC的数学模型和求解流程，并应用到一个几何规划问题的求解中，结果显示两种方法都具有获得最优解的能力，并且QEPF方法的协调效率比LDF方法的效率更高。由于在QEPF中罚系数更新步长的设置对结果有很大的影响，因此本文对其做了进一步研究，在上述算例的基础上，研究了其罚系数更新步长与优化效率和收敛性的关系，为罚因子更新步长的选取提供了依据。最后，将QEPF-HMV-PATC应用到了工程实例中，采用QEPF-HMV-PATC方法实现了齿轮减速器的概念多学科设计优化，获得了理想的设计效果。
[Abstract]:For the multidisciplinary design optimization problem in uncertain environment, it is difficult to ensure the reliability and robustness of the product by using the deterministic multidisciplinary design optimization method. The combination of traditional multidisciplinary design optimization method and uncertain design optimization method has attracted the attention and research of many scholars, and formed the uncertain multidisciplinary design optimization method named Uncertainty-based Multidisciplinary Design Optimization (UMDO). Probabilistic Analytical Target cascading (UMDO) is a potential UMDO method, which inherits the characteristics of Analytical Target cascading (ATC) and has strict convergence. Each subsystem adopts the traditional nested double-loop optimization strategy, and the consistency of each subsystem is guaranteed by the traditional coordination strategy, which makes the uncertainty optimization efficiency and system coordination efficiency of PATC method not very high. In order to explore more efficient PATC method, the PATC method is deeply studied in this paper, and its uncertain optimization strategy and coordination strategy are improved. Firstly, aiming at the uncertainty optimization strategy of PATC, this paper studies the single layer sequence planning and reliability analysis based on Hybrid mean value (HMV), which is used to improve the nested double-layer cycle strategy in PATC method, and proposes the HMV-PATC method. The solution model and flow chart of the method are established, and the feasibility and efficiency of the method are verified. Secondly, aiming at the coordination strategy of HMV-PATC, this paper analyzes and compares various coordination strategies. The Lagrangian Duality function method and the Quadric ExteriorPenalty function QEPF method are used as the coordination strategies of the HMV-PATC method, respectively. The mathematical model and solution flow of LDF-HMV-PATC and QEPF-HMV-PATC are established and applied to a geometric programming problem. The results show that both methods have the ability to obtain the optimal solution. And the coordination efficiency of QEPF method is higher than that of LDF method. Because the setting of penalty coefficient update step size in QEPF has great influence on the result, this paper makes further research on it, and based on the above examples, The relationship between the updating step size of penalty coefficient and the optimization efficiency and convergence is studied, which provides the basis for the selection of the update step size of penalty factor. Finally, the QEPF-HMV-PATC is applied to the engineering example, the concept of gear reducer is optimized by QEPF-HMV-PATC method, and the ideal design effect is obtained.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB47

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