Iterative Most Probable Point Search Method for Problems With a Mixture of Random and Interval Variables

To represent input variability accurately, an input distribution model for random variables should be constructed using many data. However, for certain input variables, engineers may have only their intervals, which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. To consider both input variability and uncertainty, inverse reliability analysis should be carried out considering both random and interval variables—mixed variables—and their mathematical correlation in a performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed-variable problem. The update procedures for MPP search are developed considering the features of mixed variables in the inverse reliability analysis. MPP search for random and interval variables proceed simultaneously to consider the mathematical correlation. An interpolation method is introduced to find a better candidate MPP without additional function evaluations. Mixed-variable design optimization (MVDO) has been formulated to obtain cost-effective and reliable design in the presence of mixed variables. In addition, the design sensitivity of a probabilistic constraint has been developed for an effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds an accurate MPP more efficiently than the generic optimization method does. In addition, it is verified that the developed method enables the MVDO process with a small number of function evaluations.