Reliability-based optimization design for structures with stochastic and bounded parameter uncertainties

In the reliability analysis and design of structures, it is unreasonable to describe all the uncertain parameters as stochastic variables when the probabilistic distribution characteristic for some of them is unavailable and only their variation bounds are known. Based on the probabilistic model description and the multi-ellipsoid model description for different types of uncertainties, a reliability-based optimization model of structures combining stochastic and bounded uncertainties is mathematically formulated with constraints on mixed reliability indices defined in standard U-space. The performance measure approach is employed to transform the original model into its equivalent form for improving the convergence and the stability. Then the reformulated nested optimization problem is simplified into a series of deterministic ones by using the sequential approximate programming approach, which greatly facilitates the efficient solution. Two examples, a mathematic optimization problem and a design of missile wing structure, are given to illustrate the validity of the proposed model as well as the efficiency of the presented numerical techniques.