A density-matching approach for optimization under uncertainty
Computer Methods in Applied Mechanics and Engineering
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Seshadri, P., Constantine, P., Iaccarino, G., & Parks, G. (2016). A density-matching approach for optimization under uncertainty. Computer Methods in Applied Mechanics and Engineering, 305 562-578. https://doi.org/10.1016/j.cma.2016.03.006
Modern computers enable methods for design optimization that account for uncertainty in the system - so-called optimization under uncertainty (OUU). We propose a metric for OUU that measures the distance between a designer-specified probability density function of the system response (the target) and the system response's density function at a given design. We study an OUU formulation that minimizes this distance metric over all designs. We discretize the objective function with numerical quadrature, and we approximate the response density function with a Gaussian kernel density estimate. We offer heuristics for addressing issues that arise in this formulation, and we apply the approach to a CFD-based airfoil shape optimization problem. We qualitatively compare the density-matching approach to a multi-objective robust design optimization to gain insight into the method.
optimization under uncertainty, design under uncertainty, density-matching
This research was funded through a Dorothy Hodgkin Postgraduate Award, which is jointly sponsored by the Engineering and Physical Sciences Research Council (EPSRC) (UK) and Rolls-Royce plc. The first author would like to acknowledge the financial assistance provided by the Center for Turbulence Research at Stanford University and St. Edmund's College, Cambridge. The authors would like to thank Shahrokh Shahpar of Rolls-Royce plc for his advice on various aspects of this work. The authors also thank the reviewers for their suggestions and comments, which improved the overall quality of this manuscript. The second author's work is supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.
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External DOI: https://doi.org/10.1016/j.cma.2016.03.006
This record's URL: https://www.repository.cam.ac.uk/handle/1810/254252
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