Abstract
We consider large-scale dynamical systems in which both the initial state and some parameters are unknown. These unknown quantities must be estimated from partial state observations over a time window. A data assimilation framework is applied for this purpose. Specifically, we focus on large-scale linear systems with multiplicative parameter-state coupling as they arise in the discretization of parametric linear time-dependent partial differential equations. Another feature of our work is the presence of a quantity of interest different from the unknown parameters, which is to be estimated based on the available data. In this setting, we employ a simplicial decomposition algorithm for an optimal sensor placement and set forth formulae for the efficient evaluation of all required quantities. As a guiding example, we consider a thermo-mechanical PDE system with the temperature constituting the system state and the induced displacement at a certain reference point as the quantity of interest.
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The authors would like to thank four anonymous reviewers for their constructive criticism which helped improve the paper.
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Appendix: Specific Form of \(N'(0)\)
Appendix: Specific Form of \(N'(0)\)
We refer the reader to Herzog and Riedel (2015) for more details.
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Herzog, R., Riedel, I. & Uciński, D. Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics. Optim Eng 19, 591–627 (2018). https://doi.org/10.1007/s11081-018-9391-8
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DOI: https://doi.org/10.1007/s11081-018-9391-8