YMack_et_al_2007 - 14 Surrogate Model-Based Optimization...

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14 Surrogate Model-Based Optimization Framework: A Case Study in Aerospace Design Yolanda Mack 1 , Tushar Goel 1 , Wei Shyy 2 , and Raphael Haftka 1 1 Mechanical and Aerospace Engineering Department, 231 MAE-A, P.O. Box 116250, University of Florida, Gainesville, FL 32611-6250, USA { tiki,tusharg,haftka } @ufl.edu 2 Department of Aerospace Engineering, Fran¸cois-Xavier Bagnoud Building, 1320 Beal Avenue, University of Michigan, Ann Arbor, MI 48109-2140, USA weishyy@umich.edu Summary. Surrogate-based optimization has proven very useful for novel or ex- ploratory design tasks because it offers a global view of the characteristics of the design space, and it enables one to re±ne the design of experiments, conduct sensi- tivity analyses, characterize tradeoffs between multiple objectives, and, if necessary, help modify the design space. In this article, a framework is presented for design op- timization on problems that involve two or more objectives which may be conflicting in nature. The applicability of the framework is demonstrated using a case study in space propulsion: a response surface-based multi-objective optimization of a radial turbine for an expander cycle-type liquid rocket engine. The surrogate model is com- bined with a genetic algorithm-based Pareto front construction and can be effective in supporting global sensitivity evaluations. In this case study, due to the lack of established experiences in adopting radial turbines for space propulsion, much of the original design space, generated based on intuitive ideas from the designer, violated established design constraints. Response surfaces were successfully used to de±ne previously unknown feasible design space boundaries. Once a feasible design space was identi±ed, the optimization framework was followed, which led to the construc- tion of the Pareto front using genetic algorithms. The optimization framework was effectively utilized to achieve a substantial performance improvement and to reveal important physics in the design. 14.1 Introduction With continuing progress in computational simulations, computational-based optimization has proven to be a useful tool in reducing the design process duration and expense. Numerous methods exist for conducting design opti- mizations. Popular methods include gradient-based methods [4, 14], adjoint methods [6, 10], and surrogate model-based optimization methods such as the response surface approximation (RSA) [9]. Gradient-based methods rely on a Y. Mack et al.: Surrogate Model-Based Optimization Framework: A Case Study in Aerospace Design , Studies in Computational Intelligence (SCI) 51 , 323–342 (2007) www.springerlink.com c ± Springer-Verlag Berlin Heidelberg 2007
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324 Yolanda Mack, Tushar Goel, Wei Shyy, and Raphael Haftka step by step search for an optimum design using the method of steepest de- scent on the objective function according to a convergence criterion. Adjoint methods require formulations that must be integrated into the computational simulation of the physical laws. For a new design or a computationally expen-
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YMack_et_al_2007 - 14 Surrogate Model-Based Optimization...

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