Surrogate model-based reliability analysis for structural systems with correlated distribution parameters

Uncertainties are usually modeled by random variables, and the values of distribution parameters are estimated from the collected samples. In practical engineering, point and interval samples are possibly available for the estimation of distribution parameters; then, their values are intervals instead of point values. In view of the fact that all distribution parameters are estimated from the same set of samples, they must be correlated rather than mutually independent. In this study, the correlation among interval distribution parameters is considered and modeled using ellipse models, and the Monte Carlo simulation (MCS)-based reliability method for correlated distribution parameters, denoted as D–MCS, is first proposed. Performance functions are usually implicit functions involving simulation that are expensive-to-evaluate evaluate in real applications; hence, an efficient adaptive surrogate model-based reliability method for structural systems with correlated interval distribution parameters is proposed to reduce computational burden. A new and efficient learning function based on the U function is developed to adaptively add the best new training samples at each iteration. The corresponding stopping criterion to terminate the proposed algorithm is also developed. The lower and upper bounds of probability of failure are calculated based on the final constructed surrogate model. The proposed method is effective because it can provide more accurate reliability results compared with traditional independence assumption reliability methods, and it can be used for structural systems with mixed variables. The proposed method is easy to code and understand. Three numerical examples are investigated to show the applicability of the proposed method.