Reliability analysis with correlated random variables based on a novel transformation, adaptive dimension-reduction and maximum entropy method

In this paper, structural reliability analysis including correlated random variables is implemented based on a novel transformation and fractional exponential moments-based maximum entropy method (FEM-MEM) with a new adaptive dimension reduction. First, a novel transformation, which does not require the computation of correlation matrix in correlated standard normal space, is first presented to transform correlated random variables to be independent standard normal ones, which is quite easy and simple to implement. Then, an adaptive dimension-reduction model is developed for efficient FEMs estimation, where the contribution-degree analysis is performed and a hybrid integration formula is established accordingly. Further, the FEM-MEM, in which the proposed transformation and hybrid integration formula are embedded, is applied to derive the unknown probability distribution of the performance function with correlated random variables, which overcomes the shortcomings of traditional fractional moments-based MEM and significantly enhances the robustness, accuracy and efficiency. Four numerical examples including both the explicit and practical implicit performance functions are investigated to validate the proposed method, where pertinent Monte Carlo simulation and Nataf transformation are employed for comparisons.