Multifidelity design guided by topology optimization

• Published in: Structural and multidisciplinary optimization 2020-03, Vol.61 (3), p.1071-1085
• Main Authors: Yaji, Kentaro, Yamasaki, Shintaro, Fujita, Kikuo
• Format: Article
• Language: English
• Subjects: Accuracy; Computational fluid dynamics; Computational Mathematics and Numerical Analysis; Design of experiments; Design optimization; Design parameters; Engineering; Engineering Design; Nonlinearity; Research Paper; Theoretical and Applied Mechanics; Topology optimization; Turbulent flow
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-019-02406-4

In this study, we present a framework based on the concept of multifidelity design optimization with the purpose of indirectly solving complex—computationally heavy and/or unstable—topology optimization problems. Our primary idea is to divide an original topology optimization problem into two types of subproblems for low-fidelity optimization and high-fidelity evaluation. To realize this idea, artificial design parameters, which we refer to as seeding parameters, are incorporated into the low-fidelity optimization problem for generating various patterns of topology-optimized candidates. The low-fidelity optimization problem is deliberately formulated as an easily solvable one by decreasing the nonlinearity of the original physical phenomena. Notably, selecting valid seeding parameters in the low-fidelity optimization problem is essential for employing the proposed framework. The aim of high-fidelity evaluation is to obtain a satisfactory solution using a high-fidelity analysis model, which considers the nonlinearity of the original physical phenomena, from the data set of the topology-optimized candidates, via the design of experiments. We apply the proposed framework to two case studies of isothermal and thermal turbulent flow problems, and discuss its efficacy as an alternative strategy for solving complex topology optimization problems.