Robust multi-fidelity optimization approach exploiting data-driven, non-linear model order reduction

A robust design optimization, which searches for an optimum that is insensitive to design uncertainties, is a multi-query analysis with high computational costs. To reduce the computational effort, surrogate models, such as reduced order approaches, are often necessary. For non-linear problems, model order reduction (MOR) techniques were only recently introduced as efficient simplification techniques. Hereby, a physical model can be combined with data-driven approaches in various ways to provide suitable surrogates for the contradicting requirements of accuracy and efficiency. In this work, a multi-fidelity robust optimization scheme exploiting data-driven model order reduction is proposed. Nested optimization loops based on the popular differential evolution (DE) algorithm are utilized to minimize both the objective and its variability. By means of Finite Element (FE) training simulations, a reduced subspace can be created via proper orthogonal decomposition (POD) as basis of the surrogate models. In this new subspace, two models with significantly lower numbers of unknowns are established: the non-intrusive reduced order model (ROM) as low-fidelity model and the intrusive ROM representing the high-fidelity model. With the non-intrusive MOR, an efficient data-driven approach exploits the coarse optimization loop. However, for the evaluation of the second loop, the more accurate intrusive MOR approach is utilized. Operating within the FE solver, the system of equations is first projected to the reduced subspace and then solved. The key aspects of the proposed multi-fidelity approach are illustrated by a robust design optimization for a non-linear structural problem.