耦合系统考虑可靠性的多学科设计优化分解方法

Decomposition method for coupled system reliability-based multidisciplinary design optimization

为了减少基于可靠性的多学科设计优化的计算成本,提出了一种面向耦合多学科设计优化的分解方法。定义了函数计算成本矩阵来处理可靠性函数的随机性,给出了根据函数随机特征计算函数计算成本矩阵的方法,同时定义了耦合关系矩阵来处理函数之间的耦合性,给出了识别耦合变量集的算法;基于函数计算成本矩阵和耦合关系矩阵提供的信息,改进了整体计算成本等评价指标的度量方法;利用遗传算法进行分解,寻求整体计算成本最小的分解方案;通过电子封装的多学科设计优化算例对上述方法进行了验证,通过与两个已有分解方案的对比表明,该方法能够显著减少整体计算成本。该方法与传统方法相比具有两个优势:一方面可以识别和分解耦合变量,使其能够用于耦合系统的分解;另一方面可以将可靠性函数平均分解到各子任务中,以获得更少的整体计算成本。

To reduce the computational cost of Reliability-based Multidisciplinary Design Optimization（RBMDO）,a novel decomposition method oriented to coupled RBMDO was presented.Function Cost Table（FCT） was defined to tackle the randomness of reliability functions,and the computational method for FCT cost based on randamness characteristics of reliability functions was presented.Coupling Dependency Table（CDT） was also defined to cope with the coupling relationship between function,and an algorithm to identify and decompose the coupling variables was presented.Moreover,the measurement method for evaluation index of total computational cost was improved based on the information provided by FCT and CDT.Genetic algorithm was applied to obtain the minimal total computational cost decomposition solution.This method was verified by an electronic packaging RBMDO problem.Compared to two existing decomposition solutions,this method significantly reduced the total computational cost.Compared to traditional approach,this method had two advantages： on one hand,the coupled variables could be identified and decomposed so that it could be used for the coupled system decomposition;on the other hand,reliability functions were decomposed into average various sub-tasks to obtain less cost of the overall computation.