Missing point estimation in models described by proper orthogonal decompositions

P. Astrid, S. Weiland, K. Willcox, A.C.P.M. Backx

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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.
Original languageEnglish
Pages (from-to)2237-2251
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 2008


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