Information theoretic-based optimal sensor placement for virtual sensing using augmented Kalman filtering

doi:10.1016/j.ymssp.2022.110031

2023-04-01

PRE

Tulay Ercan

Omid Sedehi

Lambros S. Katafygiotis

DOI：10.1016/j.ymssp.2022.110031

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摘要

En 中文

An optimal sensor placement (OSP) framework for virtual sensing using the augmented Kalman Filter (AKF) technique is presented based on information and utility theory. The framework is applicable to input and response reconstruction when output-only vibration measurements are available. Using information theory, a utility function is built to quantify the expected information gained from the data for reducing the uncertainty of unmeasured quantities of interest (QoI). Taking into account the AKF equations and exploiting the Gaussian nature of the response QoI arising from linear dynamic systems, useful and informative analytical expressions are derived for the utility function. Subsequently, the utility function is extended to make the OSP design robust to uncertainties in the structural model and modelling error parameters, resulting in a multidimensional integral of the expected information gain over all possible values of the uncertain parameters, weighted by their assigned probability distributions. The proposed OSP framework maximizes this utility function through heuristic sequential sensor placement (SSP) strategies (forward and backward SSP) and genetic algorithms (GA) to optimize the type and location of sensors. A new modified SSP strategy is proposed that exploits the computational efficiency of the less accurate forward SSP algorithm and the accuracy of the computationally expensive backward SSP algorithm. A thorough study of the effect of measurements, modelling, input, and prediction uncertainties on the selection of the optimal sensor configuration is presented using a Finite Element (FE) model of a plate loaded by a single concentrated input force, highlighting the importance of accounting for robustness to errors and other uncertainties.

Keyword:

Kalman filtering

Virtual sensing

Response reconstruction

Information gain

Kullback-Leibler divergence

Utility theory