A single-loop method for reliability-based design optimization with interval distribution parameters

The Reliability-Based Design Optimization (RBDO) provides an effective way to obtain the optimum design in the presence of random uncertainties which follow the precise probability distribution function in the structural optimization design. However, in many practical engineering problems, the probability distribution which describes the stochastic nature of the uncertainties cannot be precisely obtained due to limited information. To quantify this kind of imprecise uncertainties, a probability-interval hybrid model emerged, where all uncertain variables are treated as random variables while some distribution parameters can only be given variation intervals. For such kind of uncertainties, this paper establishes a hybrid reliability-based design optimization model and proposes a single-loop solution algorithm. The interval parameters lead to an interval of reliability for each constraint function, thus giving rise to a triple-loop optimization problem for the hybrid RBDO, which is difficult to solve due to the unaffordable computational effort and the hinder of convergency. In this paper, the Karush–Kuhn–Tucker (KKT) optimality conditions of the inner loops are imposed as equivalent deterministic equality constraints. The original triple-loop optimization is thus converted into an equivalent single-loop problem, which alleviates the computational demand significantly. The efficiency and accuracy of the proposed Single-Loop Method (SLM) is verified through several practical engineering problems.