HUT‐based method for structural reliability considering the non‐normal and unknown distributions

Abstract

AbstractStructural reliability analysis involving the non‐normal random variables are commonly encountered in practical engineering. Furthermore, some random variables are often unknown probability distributions, and the probabilistic characteristic of these variables may be expressed using only statistical moments. In this contribution, an efficient algorithm for structural reliability analysis considering the random variables with non‐normal and unknown probability distributions is proposed, in which high‐order unscented transformation (HUT) and fourth‐moment methods are adopted to efficiently evaluate the structural reliability index. By introducing the Rosenblatt transformation and third‐order polynomial transformation (TPT) techniques, random variables with non‐normal or unknown distributions are transformed into standard normal distributions. Accordingly, the performance functions can be reconstructed using standard normal random variables, and HUT is then employed to efficiently estimate the first four moments (i.e., mean, standard deviation, skewness, and kurtosis) of the performance function. Based on the Hermite polynomial model, the complete expression of fourth‐moment reliability index is derived for estimating the reliability index using the first four moments of the performance function. The efficiency and accuracy of the proposed algorithm are demonstrated through six numerical examples. The results show that the proposed algorithm is applicable to estimating reliability index of both static and dynamic reliability problems involving explicit and implicit performance functions.