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Erschienen in: Optimization and Engineering 4/2015

01.12.2015

Sequentially optimal sensor placement in thermoelastic models for real time applications

verfasst von: Roland Herzog, Ilka Riedel

Erschienen in: Optimization and Engineering | Ausgabe 4/2015

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Abstract

Optimal sensor placement problems are considered for a thermoelastic solid body. The main motivation is the real-time capable prediction of the displacement of the tool center point (TCP) in a machine tool by temperature measurements. A reduced order model based on proper orthogonal decomposition is used to describe the temperature field. The quality of the TCP displacement estimation is measured in terms of the associated covariance matrix. Based on this criterion, a sequential placement algorithm is described which stops when a certain prediction quality is reached. Numerical tests are provided.

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Fußnoten
1
\(L^2(\varOmega )\) is the Lebesgue space of square integrable functions, and \(H^1(\varOmega )^3\) stands for the Sobolev space of vector valued square integrable functions whose weak first-order derivatives are also square integrable.
 
2
To be precise, (2.19) is valid only for \(i \ge n_{{\text {POD}}}\ge 3\), i.e., one needs at least as many sensors as one has output quantities.
 
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Metadaten
Titel
Sequentially optimal sensor placement in thermoelastic models for real time applications
verfasst von
Roland Herzog
Ilka Riedel
Publikationsdatum
01.12.2015
Verlag
Springer US
Erschienen in
Optimization and Engineering / Ausgabe 4/2015
Print ISSN: 1389-4420
Elektronische ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-015-9275-0

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