An efficient uncertainty propagation method for parameterized probability boxes

In the response analysis of uncertain structural models with limited information, parameterized p-boxes are used to quantify the uncertain variables. In this study, a new technique is developed to compute the probability bounds of the structural response. Monotonicity analysis is performed on probability transformations of the random variables, revealing the relations between the interval distribution parameters and probability bounds of the structural response. Based on the monotonicity analysis, an algorithm for parameterized p-boxes is developed for computing the structural response. Three numerical examples are investigated to demonstrate the effectiveness of the proposed method.