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Indexed by:期刊论文

Date of Publication:2017-02-01

Journal:STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION

Included Journals:SCIE、EI、ESI高被引论文

Volume:55

Issue:2

Page Number:601-612

ISSN No.:1615-147X

Key Words:Reliability analysis; HL-RF iterative algorithm; Discrete Chaotic dynamic system; Directional stability Transform method; Convergence control

Abstract:The HL-RF iterative algorithm of the first order reliability method (FORM) is popularly applied to evaluate reliability index in structural reliability analysis and reliability-based design optimization. However, it sometimes suffers from non-convergence problems, such as bifurcation, periodic oscillation, and chaos for nonlinear limit state functions. This paper derives the formulation of the Lyapunov exponents for the HL-RF iterative algorithm in order to identify these complicated numerical instability phenomena of discrete chaotic dynamic systems. Moreover, the essential cause of low efficiency for the stability transform method (STM) of convergence control of FORM is revealed. Then, a novel method, directional stability transformation method (DSTM), is proposed to reduce the number of function evaluations of original STM as a chaos feedback control approach. The efficiency and convergence of different reliability evaluation methods, including the HL-RF algorithm, STM and DSTM, are analyzed and compared by several numerical examples. It is indicated that the proposed DSTM method is versatile, efficient and robust, and the bifurcation, periodic oscillation, and chaos of FORM is controlled effectively.