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Mathematics 2016, 4(2), 26; doi:10.3390/math4020026

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

1
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA
2
Advanced Computing, Mathematics and Data Division, Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA
3
Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Mohsen Zayernouri
Received: 12 January 2016 / Revised: 15 March 2016 / Accepted: 21 March 2016 / Published: 14 April 2016
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Abstract

It is shown in literature that sensor placement at the extrema of Proper Orthogonal Decomposition (POD) modes is efficient and leads to accurate reconstruction of the field of quantity of interest (velocity, pressure, salinity, etc.) from a limited number of measurements in the oceanography study. In this paper, we extend this approach of sensor placement and take into account measurement errors and detect possible malfunctioning sensors. We use the 24 hourly spatial wind field simulation data sets simulated using the Weather Research and Forecasting (WRF) model applied to the Maine Bay to evaluate the performances of our methods. Specifically, we use an exclusion disk strategy to distribute sensors when the extrema of POD modes are close. We demonstrate that this strategy can improve the accuracy of the reconstruction of the velocity field. It is also capable of reducing the standard deviation of the reconstruction from noisy measurements. Moreover, by a cross-validation technique, we successfully locate the malfunctioning sensors. View Full-Text
Keywords: proper orthogonal decomposition; sensor placement; uncertainty; anomaly detection proper orthogonal decomposition; sensor placement; uncertainty; anomaly detection
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, Z.; Yang, X.; Lin, G. POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study. Mathematics 2016, 4, 26.

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