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Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information

Bhattacharyya, Pinaky and Beck, James (2020) Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information. Structural Control and Health Monitoring, 27 (10). Art. No. e2605. ISSN 1545-2255. doi:10.1002/stc.2605.

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Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference. Equivalently, the expected information entropy of the posterior of the model parameters is minimized over all possible sensor configurations for a given sensor budget. In the context of structural dynamical systems, this minimization is computationally expensive because of the large number of possible sensor configurations. Here, a very efficient convex relaxation scheme is presented to determine informative and possibly optimal solutions to the problem, thereby bypassing the necessity for an exhaustive, and often infeasible, combinatorial search. The key idea is to relax the binary sensor location vector so that its components corresponding to all possible sensor locations lie in the unit interval. Then, the optimization over this vector is a convex problem that can be efficiently solved. This method always yields a unique solution for the relaxed problem, which is often binary and therefore the optimal solution to the original problem. When not binary, the relaxed solution is often suggestive of what the optimal solution for the original problem is. An illustrative example using a 50‐story shear building model subject to sinusoidal ground motion is presented, including a case where there are over 47 trillion possible sensor configurations. The solutions and computational effort are compared with greedy and heuristic methods.

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Bhattacharyya, Pinaky0000-0003-3773-0392
Additional Information:© 2020 John Wiley & Sons. Issue Online: 02 September 2020; Version of Record online: 03 August 2020; Manuscript accepted: 03 June 2020; Manuscript revised: 12 February 2020; Manuscript received: 12 July 2019.
Subject Keywords:Bayesian model updating; convex optimization; mutual information; optimal sensor location; structural dynamics
Issue or Number:10
Record Number:CaltechAUTHORS:20200819-121109344
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Official Citation:Bhattacharyya, P, Beck, J. Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information. Struct Control Health Monit. 2020; 27:e2605.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105030
Deposited By: George Porter
Deposited On:19 Aug 2020 19:41
Last Modified:16 Nov 2021 18:39

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