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Optimization and Engineering

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15-06-2018 | Research Article

Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics

Authors: Roland Herzog, Ilka Riedel, Dariusz Uciński

Published in: Optimization and Engineering | Issue 3/2018

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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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Title: Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics
Authors: Roland Herzog
Ilka Riedel
Dariusz Uciński
Publication date: 15-06-2018
Publisher: Springer US
Published in: Optimization and Engineering / Issue 3/2018
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI: https://doi.org/10.1007/s11081-018-9391-8

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