Variable-fidelity optimization with design space reduction

• Published in: Chinese journal of aeronautics 2013-08, Vol.26 (4), p.841-849
• Main Authors: Zahir, Mohammad Kashif, Gao, Zhenghong
• Format: Article
• Language: English
• Subjects: Aircraft; Airfoil optimization; Algorithms; Computational efficiency; Construction; Curse of dimensionality; Design engineering; Design space reduction; Genetic algorithms; Kriging; Mathematical models; Optimization; Reduction; Shape optimization; Surrogate models; Surrogate update strategies; Variable fidelity; 优化问题; 可变; 工程系统; 感兴趣区域; 真模型; 设计空间; 高保真; 高逼真度
• ISSN: 1000-9361
• DOI: 10.1016/j.cja.2013.06.002

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.