Journal Article

A new directional stability transformation method of chaos control for first order reliability analysis

Yang, Dixiong, Meng, Zeng, Li, Gang, Zhan, Lichao

2017

Overview

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.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V
• Subject: Algorithms / Bifurcations / Computational Mathematics and Numerical Analysis / Control stability / Convergence / Design optimization / Directional stability / Dynamic stability / Engineering / Engineering Design / Feedback control / Iterative algorithms / Iterative methods / Liapunov exponents / Limit states / Reliability analysis / Reliability engineering / Research Paper / Robust control / Robustness (mathematics) / Stability analysis / Structural reliability / Theoretical and Applied Mechanics / Transformations (mathematics)