The Earthquake Engineering Online Archive

Optimization Algorithms for Structural Reliability Analysis

Liu, Pei-Ling; Der Kiureghian, Armen

UCB/SEMM-1986/09, Dept. of Civil Engineering, University of California, Berkeley, 1986-07, 41 pages (500/C23/86/09)

In certain applications of structural reliability, it is required to find points on the limit-state surface with minimal distance to the origin of a standard space. This problem can be formulated as a constrained optimization program and can be solved by several standard algorithms. In this report, six constrained optimization methods are investigated to determine their applicability for solving the structural reliability problem. These include primal methods, penalty methods, dual methods, Lagrange methods, and two algorithms previously used in reliability analysis. The underlying concepts of each method are introduced and its performance is investigated with due consideration to the properties of the algorithm and the structure of the reliability problem. Four criteria are proposed to serve as the bases of comparison: generality, robustness, efficiency, and capacity. Among the algorithms studied, the gradient projection method (a primal method) is found to satisfy all four criteria. One widely used algorithm is shown to lack robustness in certain situations. A modification to this algorithm is introduced to enhance its stability. This modified version, although not globally convergent, is found to be more efficient than the gradient projection method in several examples studied.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-86-09.pdf (2 MB)