Sensor selection for hyper‐parameterized linear Bayesian inverse problems

PAMM, vol. 20

Abstract

Abstract Models of physical processes often depend on parameters, such as material properties or source terms, that are only known with some uncertainty. Measurement data can be used to estimate these parameters and thereby improve the model's credibility. When measurements become expensive, it is important to choose the most informative data. This task becomes even more challenging when the model configurations vary and the data noise is correlated. In this poster we summarize our results in [1] and present an observability coefficient that describes the influence of the sensors on the inverse solution. It can guide optimal sensor selection towards a uniformly good parameter estimate over all admissible model configurations. We propose a sensor selection algorithm that iteratively improves the observability coefficient, and present numerical results for a steady‐state heat conduction problem with correlated noise.

Authors 3

1. Nicole Aretz Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen University Schinkelstr. 2 52062 Aachen Germany

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany

2. Peng Chen

   The University of Texas at Austin

   Affiliation as printed

   Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th St Austin TX 78712 USA

   Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E 24th St, Austin, TX 78712 USA

3. Karen Veroy corresponding Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science · Eindhoven University of Technology

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen University Schinkelstr. 2 52062 Aachen Germany

   Centre for Analysis, Scientific Computing and Applications Eindhoven University of Technology Groene Loper 5 5612 AZ Eindhoven The Netherlands

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany

   Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, Groene Loper 5, 5612 AZ Eindhoven, The Netherlands

   Karen Veroy

   Telephone: +31 40 247 3181