Working Paper Article Version 1 This version is not peer-reviewed

Optimal Sensor Placement for Reliable Virtual Sensing using Modal Expansion and Information Theory

Version 1 : Received: 14 April 2021 / Approved: 15 April 2021 / Online: 15 April 2021 (09:38:20 CEST)

A peer-reviewed article of this Preprint also exists.

Ercan, T.; Papadimitriou, C. Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory. Sensors 2021, 21, 3400. Ercan, T.; Papadimitriou, C. Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory. Sensors 2021, 21, 3400.

Journal reference: Sensors 2021, 21, 3400
DOI: 10.3390/s21103400

Abstract

A framework for optimal sensor placement (OSP) for virtual sensing using the modal expansion technique and taking into account uncertainties is presented based on information and utility theory. The OSP maximizes a utility function that quantifies the expected information gained from the data for reducing the uncertainty of quantities of interest (QoI) predicted at the virtual sensing locations. The utility function is extended to make the OSP design robust to uncertainties in structural model and modelling error parameters, resulting in a multidimensional integral of the expected information gain over all possible values of the uncertain parameters and weighted by their assigned probability distributions. Approximate methods are used to compute the multidimensional integral and solve the optimization problem that arises. The Gaussian nature of the response QoI is exploited to derive useful and informative analytical expressions for the utility function. A thorough study of the effect of model, prediction and measurement errors and their uncertainties, as well as the prior uncertainties in the modal coordinates on the selection of the optimal sensor configuration is presented, highlighting the importance of accounting for robustness to errors and other uncertainties.

Subject Areas

Modal expansion; Information theory; Kullback-Leibler divergence; Utility theory; virtual sensing; response reconstruction; Structural Dynamics

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