A NEW TWO-POINT ADAPTIVENONLINEAR APPROXIMATION METHOD FOR RELIABILITY ANALYSIS

A two-point adaptive nonlinear approximation (referred to as TANA4) suitable for reliability analysis is proposed. Transformed and normalized random variables in probabilistic analysis could become negative and pose a challenge to the earlier developed two-point approximations; thus a suitable method that can address this issue is needed. In the method proposed, the nonlinearity indices of intervening variables are limited to integers. Then, on the basis of the present method, an improved sequential approximation of the limit state surface for reliability analysis is presented. With the gradient projection method, the data points for the limit state surface approximation are selected on the original limit state surface, which effectively represents the nature of the original response function. On the basis of this new approximation, the reliability is estimated using a first-order second-moment method. Various examples, including both structural and non-structural ones, are presented to show the effectiveness of the method proposed.