Collaborative Optimization Framework Based on the Interaction of Low- and High-Fidelity Models and the Moving Least Squares Method

Abstract

This paper aims at the development of efficient approximation model building techniques to reduce computational costs associated with the collaborative optimization (CO) for handling multidisciplinary design optimization problems based on high-fidelity simulation models. Multilevel optimization approaches such as CO have received considerable attention as an approach to solving large-scale complex MDO problems, however the CO methodology has not become a mainstream design optimization tool in industry. Some of the main reasons for this are: high computational cost and the system level convergence difficulties. These issues result in limiting real-life applications of CO based on high-fidelity simulation models. To address these issues, this paper proposes two levels of approximation model building techniques: Approximations in the disciplinary optimization are based on multi-fidelity modeling (interaction of low-and high-fidelity models) and for the system level optimization a combination of global approximation and trust region strategy is introduced. The multifidelity modeling consists of computationally efficient simplified numerical models (lowfidelity) and expensive detailed (high-fidelity) models. The use of approximation models at the system level is more complex due to the peculiar characteristics of equality constraints, which hinder the direct use of conventional response surface modeling techniques. To overcome this difficulty, the construction of approximation models at the system level is based on the moving least squares method and trust region strategy. The proposed method is demonstrated on a test “composite beam” problem. The effectiveness of the method for modeling and collaborative optimization using high-fidelity models is studied. Overall results show the methods introduced in this paper provide an effective way of improving system level convergence and computational efficiency of a CO based on high-fidelity simulation models.