A semi-analytical framework for structural reliability analysis

Estimation of the probability of failure of structural systems can often be computationally intensive and time consuming. Hence, alternative techniques for efficient computation of the probability of failure of complex structures while retaining the accuracy is of paramount importance to structural engineering community. This paper presents a semi-analytical approach for computing failure probability of structure. The proposed approach utilizes (i) polynomial correlated function expansion, a novel surrogate modelling technique, to determine the moments and (ii) maximum entropy method to determine an analytical expression for the response probability density function (PDF). Once the analytical expression for the PDF is obtained, failure probability is calculated by numerically integrating the PDF in the failure domain. As a special case, when only the first two moments of response are considered, an analytical formula for the probability of failure is also proposed. Four structural engineering problems are shown to illustrate the performance of the proposed approach. It is observed that the proposed approach outperforms other existing approaches.