Bayesian Experimental Design for Linear Elasticity

Thumbnail Image

Access rights

openAccess
CC BY
publishedVersion

URL

Journal Title

Journal ISSN

Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)

Authors

Date

2024-12

Department

Department of Mathematics and Systems Analysis

Major/Subject

Mcode

Degree programme

Language

en

Pages

26

Series

Inverse Problems and Imaging, Volume 18, issue 6, pp. 1294-1319

Abstract

This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of the examined body in order to maximize the value of the resulting boundary deformations as data for the inverse problem of reconstructing the Lamé parameters inside the object. We resort to a linearized measurement model and adopt the framework of Bayesian experimental design, under the assumption that the prior and measurement noise distributions are mutually independent Gaussians. This enables the use of the standard Bayesian A-optimality criterion for deducing optimal positions for the pressure activations. The (second) derivatives of the boundary measurements with respect to the Lamé parameters and the positions of the boundary pressure activations are deduced to allow minimizing the corresponding objective function, i.e., the trace of the covariance matrix of the posterior distribution, by gradient-based optimization algorithms. Two-dimensional numerical experiments are performed to test the functionality of our approach: all introduced algorithms are able to improve experimental designs, but only exhaustive search reliably finds a global minimizer.

Description

Keywords

A-optimality, Bayesian experimental design, Lame<acute accent> parameters, Inverse problem, Linear elasticity

Other note

DOI

10.3934/ipi.2024015

Citation

Eberle-Blick, S & Hyvönen, N 2024, 'Bayesian Experimental Design for Linear Elasticity', Inverse Problems and Imaging, vol. 18, no. 6, pp. 1294-1319. https://doi.org/10.3934/ipi.2024015

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-202412318189

Collections

[article-cris] Perustieteiden korkeakoulu / SCI