Assessment of polynomial correlated function expansion for high-fidelity structural reliability analysis

• We proposed a non-intrusive algorithm for structural reliability analysis.
• The proposed approach requires very few actual function evaluations.
• The proposed approach outperforms other available techniques.

Accurate prediction of failure probability of a given structural system subjected to parametric uncertainty often leads to a computationally challenging process requiring considerable amount of time. To overcome this issue, it is advantageous to develop non-intrusive model, that approximates the system response and perform all subsequent operations on the developed model. This paper presents a novel non-intrusive algorithm, referred to as polynomial correlated function expansion (PCFE), for high-fidelity reliability analysis. The proposed method expresses the output in a hierarchical order of component functions which facilitate (i) expressing the component functions in term of extended bases, (ii) determination of actual responses at quasi-random sample points, (iii) determination of the unknown coefficients associated with the bases by employing homotopy algorithm and (iv) Monte Carlo simulation. PCFE decouples the stochastic computations and finite element (FE) computations, and consecutively the FE code can be treated as a black box, as in the case of a commercial software. Six numerical problems, involving explicit performance functions and real-life problems described by implicit limit-state functions, have been solved to illustrate the performance of the proposed approach. It is observed that PCFE outperforms the existing approaches.