Design optimization using reduced order modeling

Within optimization, a model or analysis is analyzed numerous times and more so when stochastic analyses are imposed within optimization such as reliability based design optimization (RBDO). For large models, deterministic, constraint and RBDO becomes infeasible due to the computational costs and the number of function calls needed. This work seeks to alleviate the computational costs of analyzing dynamic systems through employing a surrogate model in place of the full model analysis. Two types of surrogate models are used. Response surface techniques, which are black box approximations and a Galerkin projection approach which is a physical based approximations which significantly reduces the number of degrees of freedom in the system. For the Galerkin approximation, proper orthogonal decomposition and method of snapshots will be used as a basis. The key to utilizing the surrogate models in a optimization and stochastic analyses lies in making them accurate for the design space of interest. These two methods will be tested on a nonlinear MEMs bandpass filter, where the objective is to maximize the amplitude of the device using two design parameters, length and thickness of the beam. Further studies will be performed on a connecting rod, where the latter of the two methods will be explored by a multi-point approximation of the design space which will increase the accuracy for a larger design change.