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论文类型：期刊论文

发表时间：2013-03-01

发表刊物：JOURNAL OF MECHANICAL DESIGN

收录刊物：SCIE、EI、Scopus

卷号：135

期号：3

ISSN号：1050-0472

关键字：reliability analysis and optimization; iterative algorithms; numerical instabilities; chaotic dynamics; stability transformation method; convergence control

摘要：Iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in iterative procedures of solving some nonlinear problems. In the present paper, the essential causes of numerical instabilities including periodic oscillation and chaos of iterative solutions are revealed by the eigenvalue-based stability analysis of iterative schemes. To understand and control these instabilities, the stability transformation method (STM), which is capable of tackling numerical instabilities of iterative algorithms in reliability analysis and design optimization, is proposed. Finally, several benchmark examples of convergence control of PMA (performance measure approach) for probabilistic analysis and the SORA (sequential optimization and reliability assessment) for reliability-based design optimization (RBDO) are presented. The observations from the benchmark examples indicate that the STM is a promising approach to achieve convergence control for iterative algorithms in reliability analysis and design optimization.