Hybrid reliability method based on the univariate dimension-reduction method and rotational transformation of variables
Fan Wenliang1,2,3 Zhou Qingyu2 Li Zhengliang1,2
1. Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China
2. School of Civil Engineering, Chongqing University, Chongqing 400045, China
3. University of California-Irvine, California 92697, USA
Abstract：Classical first-order reliability method (FORM) is inappropriate for reliability analysis with implicit or strong nonlinear performance function, and the second-order reliability method (SORM) is more accurate, but involving complex theory and implementation. To exploit the merits of both FORM and response surface method (RSM), the most probable point (MPP) in FORM and RSM are effectively combined. In this work, the general FORM with Nataf transform and difference method is introduced firstly| secondly, the univariate dimension-reduction approximation model is introduced into rotationally transformed performance function| thirdly, each component function is further approximated by the quadratic polynomial function based on the function value and its gradient of MPP and the function value of the additional point, so that the approximated entire performance function can be obtained| furthermore, importance sampling method is applied to calculating the probability of failure for the approximated performance function| finally, the accuracy and efficiency of the proposed hybrid method are verified based on numerical and engineering cases, and the results show that the proposed method has the characteristics such as good precision, high performance and wide application to both implicit and explicit performance functions.
范文亮 周擎宇 李正良. 基于单变量降维模型和坐标旋转的可靠度混合分析方法[J]. 土木工程学报, 2017, 50(5): 12-18.
Fan Wenliang Zhou Qingyu Li Zhengliang. Hybrid reliability method based on the univariate dimension-reduction method and rotational transformation of variables. 土木工程学报, 2017, 50(5): 12-18.
