Convergence analysis of first order reliability method using chaos theory

By Dixiong Yang, Gang Li, Gengdong Cheng. Computers & Structures, 2006

75 citations recorded by the source corpus.

First order reliability method (FORM) for the computation of reliability index has been used widely because of its advantages of the efficiency and effectiveness as well simplicity for many years. There exists the phenomenon of convergent failure in the FORM in calculating the reliability index iteratively for some limit state functions, for which the essential factor is investigated using chaotic dynamics theory in the present paper. The bifurcation plots of reliability index are presented for several typical limit state functions, and the computational results from those mapping functions due to FORM iterations show the complicated dynamics phenomena such as the periodic oscillation, bifurcation and chaos. Moreover, the Lyapunov exponents of non-linear map from FORM are calculated. From the numerical investigation of presented examples, it is concluded that the convergence of FORM does not depend on the curvature of design points of the limit state function, and the quantitative index for identifying the convergence of FORM iterative computation is the Lyapunov exponents of non-linear map corresponding to that limit state function.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cb81b29bd6e36129800a6585602643377af117fc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Francis Tin-Loi
2. Chongmin Song
3. Wei Gao
4. Ping Yi
5. Di Wu
6. Dixiong Yang
7. Xiaojing Li
8. E. Ooi

In Mechanics of Materials

1. Francis Tin-Loi
2. Chongmin Song
3. Wei Gao
4. Ping Yi
5. Di Wu
6. Dixiong Yang
7. Xiaojing Li
8. E. Ooi

In Statistics and Probability

1. Di Wu
2. Chongmin Song
3. Wei Gao
4. Francis Tin-Loi
5. Ping Yi
6. Dixiong Yang
7. Xiaojing Li
8. Behrooz Keshtegar

Citations in the corpus

• Chaos control of performance measure approach for evaluation of probabilistic constraints (2009, methodology): “The iterative number can be reduced further if we increase the factor λ properly ( Yang et al. 2006 ).”
• Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method (2011, methodology): “Monte-Carlo simulation method (MCSM) [13–15], perturbation based stochastic finite element method [7,16–18], spectral stochastic finite element All rights reserved. method [19–21] and other types of stochastic methods [22,23] have been developed to analyze random structures.”
• Chaos control for numerical instability of first order reliability method (2010, methodology): “15459} of reliability index for Example 4 arise [10].”