Structural reliability analysis based on random distributions with interval parameters

In this paper, a new reliability analysis technique is developed for uncertain structures based on a hybrid uncertain model. Random distributions are used to deal with the uncertainty, while some key parameters in the distribution functions are given variation intervals instead of precise values. Two kinds of hybrid reliability models are constructed based on the reliability index approach (RIA) and the performance measurement approach (PMA), in which the reliability index interval and the target performance interval are employed to evaluate the reliability degree of an uncertain structure, respectively. A monotonicity analysis is conducted for the probability transformation process, which indicates that the extreme values of the limit-state function generally correspond to the bound combinations of the interval parameters. Based on the monotonicity analysis, two efficient algorithms are then formulated to solve the suggested RIA-based and PMA-based hybrid reliability models, in which the outer-layer optimization in terms of random variables and the inner-layer optimization in terms of interval parameters are executed by turns. Three numerical examples are presented to demonstrate the effectiveness of the present method, which include two simple problems with explicit expressions and one complex engineering application.