Sparse Measurements and Optimal Sensor Placement for Classification and State Estimation of Complex Systems
Technical Report,01 Sep 2015,31 Aug 2018
University of Washington Seattle United States
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Determining the optimal placement of sensors under a cost constraint is relevant to many fields of scientific research and industry. Indeed, such considerations are critical in evaluating global monitoring systems and characterizing spatio-temporal dynamics e.g. the brain, ocean and atmospheric dynamics, power grid networks, fluid flows, etc. For these applications, it is typical that only a limited number of measurements can be made of the system due to either prohibitive expense i.e. either sensors are expensive, or they are expensive to place, or both or the inability to place a sensor in a desired location inaccessibility. Additionally, there are a number of high-level objectives for sensor placement, most of which are well studied. Common objectives include classification, reconstruction, reduced-order modeling, and control. We develop a heuristic, greedy sampling strategy whereby the sensor placement optimization is formulated as a cost-constrained problem in a relaxed form. We further introduce a parameter representing the balance between the quality of the reconstruction and the cost, and thus can evaluate a cost-error curve. The simple algorithmic structure proposed provides an effective and scalable strategy for economical sensor placement for a wide range of scientific and engineering applications.
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