A new look at the response surface method for reliability analysis using
chaos theory
Ding Youliang, Li Aiqun and Deng Yang
College of Civil
Engineering, Southeast University, Nanjing 210096, China
Abstract:
To overcome excessive computation errors and
convergence failures encountered in an iterative calculation of the reliability
index using the response surface method (RSM) for some nonlinear limit state
functions, this study investigates an essential factor based on chaotic dynamics
theory. The bifurcation diagrams of the reliability index are presented for some
typical nonlinear limit state functions, and the computation results from the
mapping functions due to the RSM iterations show the complicated dynamic
phenomena such as the periodic oscillation, as well as bifurcation and chaos.
From the numerical examples, it is concluded that the parameter of selection
range f plays an important role in the convergence of the RSM iteration, and an
improved RSM iterative algorithm is proposed with regard to the incorporation of
the iterative sequential function of selection range f. The proposed method is
shown to be efficient and to yield accurate results.
Keywords: structural reliability; response surface
method; chaotic dynamics; convergence failure; selection range; nonlinearity
