A robust study of reliability-based optimization methods under eigen-frequency

Nowadays, the search in reliability-based design optimization is becoming an important engineering design activity. Traditionally for these problems, the objective function is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure. This paper focuses on the study of a particular problem with the failure mode on vibration of structure. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large-scale multidisciplinary systems which are likewise computationally intensive. With this in mind research, we propose in this paper a new method to treat reliability-based optimization methods under frequencies constraint. The goal of this development has resolved just one problem of optimization and reduced the cost of computation. Aircraft wing design typically involves multiple disciplines such as aerodynamics and structure; this numerical example demonstrated the different advantages of the proposed method.