Nataf transformation based univariate decomposable polynomial RSM for engineering reliability analysis

¹ Education Center of Experiments and Innovations, Harbin Institute of Technology, Shenzhen, Guangdong, China
² School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, Guangdong, China

^* Corresponding author: liugaixia@hit.edu.cn

Abstract

For engineering problems, the correlation exists among the common random variables. For those with highly correlated variables accompanying the high nonlinearity, large error would be induced if ignoring the influence of their correlation matrix. Considering correlated variables, an executing mode of polynomial response surface method based on Nataf transformation and univariate decomposition is introduced in this paper, called as N-UDPRSM. The correlated variables can be converted into the independent standard normal space and all of the univariate component polynomials can be determined separately. Besides, high order terms can be adopted into N-UDPRSM to balance the accuracy and efficiency for high nonlinear engineering problems. The corresponding practical implementation for engineering reliability analysis is designed in detail. A typical engineering structure is studied. The results indicate that it performs well in balancing accuracy and efficiency, and it also preserve some superiority contrast with other state-of-art methods.