In this paper, intelligent initial point selection for performance measure approach (PMA) of reliability-based design optimization (RBDO) is proposed to improve computational efficiency of the most probable point (MPP) search. Unlike existing PMA algorithms concentrating on enhancement of the optimization algorithm for MPP search, the proposed method focuses on how to intelligently select an initial point which is close to the true MPP so that fast convergence can be achieved. Since the proposed method provides a new initial point for MPP search, it can be combined with any existing PMA algorithms. To obtain the initial point, the first-order Taylor series expansion with respect to a design vector is applied to MPP in U-space obtained from the previous RBDO iteration. Thus, the Jacobian matrix of the MPP vector with respect to the design vector is derived in an analytical way with no additional function evaluation. The derived Jacobian matrix is validated through numerical study. Comparative study with two existing initial point strategies for MPP search—the origin in U-space and the previous MPP in U-space under the condition of design closeness—shows that the proposed initial point significantly improves efficiency of MPP search in any PMA algorithm with various types of performance functions and input distributions.

本文提出了基于可靠性的设计优化（RBDO）的性能度量方法（PMA）的智能初始点选择，以提高最可能点（MPP）搜索的计算效率。与现有的专注于增强用于MPP搜索的优化算法的PMA算法不同，所提出的方法侧重于如何智能地选择接近于真正MPP的初始点，从而实现快速收敛。由于所提出的方法为MPP搜索提供了新的起点，因此可以与任何现有的PMA算法结合使用。为了获得初始点，将相对于设计矢量的一阶泰勒级数展开应用于从先前的RBDO迭代获得的U空间中的MPP。从而，MPP向量相对于设计向量的雅可比矩阵是以一种分析方式导出的，无需进行其他功能评估。通过数值研究验证了导出的雅可比矩阵。与现有的两种MPP搜索初始点策略（在设计接近性条件下，U空间中的原点和U空间中的先前MPP）的比较研究表明，提出的初始点显着提高了任何PMA算法中MPP搜索的效率。各种类型的性能函数和输入分布。