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Missing Point Estimation in Models Described by Proper Orthogonal Decomposition

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4 Author(s)
Patricia Astrid ; Shell Global Solutions Int. B.V., Amsterdam ; Siep Weiland ; Karen Willcox ; Ton Backx

This paper presents a new method of missing point estimation (MPE) to derive efficient reduced-order models for large-scale parameter-varying systems. Such systems often result from the discretization of nonlinear partial differential equations. A projection-based model reduction framework is used where projection spaces are inferred from proper orthogonal decompositions of data-dependent correlation operators. The key contribution of the MPE method is to perform online computations efficiently by computing Galerkin projections over a restricted subset of the spatial domain. Quantitative criteria for optimally selecting such a spatial subset are proposed and the resulting optimization problem is solved using an efficient heuristic method. The effectiveness of the MPE method is demonstrated by applying it to a nonlinear computational fluid dynamic model of an industrial glass furnace. For this example, the Galerkin projection can be computed using only 25% of the spatial grid points without compromising the accuracy of the reduced model.

Published in:

IEEE Transactions on Automatic Control  (Volume:53 ,  Issue: 10 )