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Backward uncertainty propagation in shape optimization
Author(s) -
Mohammadi Bijan
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4077
Subject(s) - mathematical optimization , computer science , inversion (geology) , covariance matrix , optimization problem , quantile , inverse , cma es , inverse problem , covariance , mathematics , algorithm , covariance function , paleontology , mathematical analysis , statistics , geometry , structural basin , biology , econometrics
Summary We aim at quantifying the impact of state uncertainties in shape optimization. This provides confidence bounds for the optimal solution. The approach is presented for inverse designs where the target is assumed uncertain. No sampling of a large dimensional space is necessary, and the approach uses what is already available in a deterministic gradient‐based inversion algorithm. Our proposal is based on the introduction of directional quantile‐based extreme scenarios knowing the probability density function of the target data. We use these scenarios to define a matrix having the structure of the covariance matrix of the optimization parameters. We compare this construction to another one using the gradient of the functional by an adjoint method. The paper goes beyond inverse design and shows how to apply the method to general optimization problems. The ingredients of the paper are illustrated on a model problem with the Burgers equation and on the optimization of the shape of an aircraft. Overall, the computational complexity is comparable with the deterministic case. Copyright © 2015 John Wiley & Sons, Ltd.