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• A hybrid reliability-based heat dissipation structural design optimization model is established for the practical heat dissipation problem with the interval distribution parameters. • Two equivalent triple-loop hybrid reliability-based heat dissipation structural design optimization models are established. • An efficient single-loop method is proposed to solve hybrid reliability-based heat dissipation structural design optimization the model. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]