Sequential approximate reliability-based design optimization for structures with multimodal random variables

For practical engineering design problems, random variables tend to follow multimodal probability distributions when working at multiple operating conditions. For example, the structural fatigue stress of a steel bridge carrying both highway and railway traffic obeys the bimodal distribution. The existing popular reliability-based design optimization (RBDO) methods are mainly used to treat random variables with only unimodal distributions, which, therefore, tends to result in relatively large computational errors when multimodal random variables are involved. In this paper, a sequential approximate RBDO method is firstly proposed for engineering design involving multimodal random variables. The probability density function (PDF) of the response function is firstly calculated to assess the reliability of each probabilistic constraint, due to the existence of multimodal random variables. Then, a deterministic optimization problem is established to calculate candidate design points, based on the approximation that the response PDF demonstrates only transitional deformation in the optimization process. Three numerical examples and one engineering application of a thermal laptop design are presented to demonstrate the effectiveness of the proposed method.