An algorithm for finding a sequence of design points in reliability analysis. (January 2016) - Wang, Ziqi; Broccardo, Marco; Der Kiureghian, Armen
Highlights: An algorithm for finding a sequence of design points is developed. The algorithm finds the design point through inverse reliability analysis. The algorithm uses the Broyden's good method to solve a set of nonlinear equations. The algorithm is highly efficient compared to i-HLRF algorithm. Abstract: In the analysis of structural reliability, often a sequence of design points associated with a set of thresholds are sought in order to determine the tail distribution of a response quantity. In this paper, after a brief review of methods for determining the design point, an inverse reliability method named the λ -method is introduced for efficiently determining the sequence of design points. The λ -method uses Broyden's "good" method to solve a set of nonlinear simultaneous equations to find the design points for the values of an implicitly defined threshold that is associated with parameter λ . In a special parameter setting, the λ parameter equals the reliability index, thus allowing convenient implementation of the method. Three numerical examples illustrate the accuracy and efficiency of the proposed method.