Data-Driven Sensor Placement Methods
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The scalable optimization of sensor placement remains an open challenge in engineering and physical sciences. Optimal placements can only be determined in general using a brute-force combinatorial search over the domain. This explosion in complexity presents a major challenge for high-dimensional domains in oceanography, fluid dynamics, manufacturing, and biology. Fortunately, high-dimensional data generated by these systems often possess reproducible, low-rank structure that can be exploited to drastically reduce the amount of measurements required for global inference. In this thesis, we exploit data-driven learning to optimize sensor placement for signal reconstruction. Dimensionality reduction methods including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to obtain low-rank representations from data. We exploit empirical interpolation methods (EIMs), initially pioneered in reduced order modeling, to efficiently optimize the placement of sensors for high-dimensional reconstruction, estimation and control. This work connects our EIM-based method to related placement criteria in optimal experimental design, and extends our method to obtain an arbitrary number of optimal sensors. The superior performance and accuracy of our method is demonstrated on a variety of high-dimensional data from facial images, ocean temperatures, fluid dynamics, aircraft manufacturing and insect flight. Finally, an extension to sensor and actuator placement for optimal closed-loop control is proposed, which similarly leverages balanced model reduction of observability and controllability Gramians for speedy sensor and actuator optimization.
- Applied mathematics