An efficient single-loop method for heat dissipation structure design under random uncertainties with interval distribution parameter

Abstract

The conventional reliability-based heat dissipation structural design optimization, which fully considers the influence of the random uncertainties in the optimization procedure, can provide an optimum design satisfying the reliability requirements of the heat radiating device. However, in practical heat dissipation design problems, especially in the early stage of structural design which lacks the corresponding experimental data, some crucial distribution parameters of the random uncertainties, may not be determined precisely. This paper establishes a hybrid reliability-based heat dissipation structural design optimization model for the problem with limited information based on a kind of probability-interval hybrid quantification model and proposes a single-loop method to solve this model efficiently. In this optimization model, the interval parameters coupled to the random uncertainties lead to an interval of reliability for each constraint function, thus giving rise to a triple-loop optimization problem. The proposed single-loop method firstly converts the original nested triple-loop optimization model into an equivalent double-loop optimization model through monotonic analysis. Then, the Karush-Kuhn-Tucker (KKT) optimality conditions of the inner loop are enforced to convert the double-loop model into an equivalent single-loop optimization model. Through this treatment, the original triple-loop optimization model can be then solved by a series of design deterministic optimization and the computational demand can be alleviated significantly. The efficiency and accuracy of the proposed single-loop method are verified through several numerical problems.