A multi-point univariate decomposition method for structural reliability analysis

A new multi-point univariate decomposition method is presented for structural reliability analysis involving multiple most probable points (MPPs). The method involves a novel function decomposition at all MPPs that facilitates local univariate approximations of a performance function in the rotated Gaussian space, Lagrange interpolation for univariate component functions and return mapping to the standard Gaussian space, and Monte Carlo simulation. In addition to the effort in identifying all MPPs, the computational effort in the multi-point univariate method can be viewed as performing deterministic response analysis at user-selected input defined by sample points. Compared with the existing multi-point FORM/SORM, the multi-point univariate method developed provides a higher-order approximation of the boundary of the failure domain. Both the point-fitted SORM and the univariate method entail linearly varying cost with respect to the number of variables. However, the univariate method with less than nine sample points requires fewer calculations of the performance function than the point-fitted SORM. Numerical results indicate that the proposed method consistently generates an accurate and computationally efficient estimate of the probability of failure.