Greedy Sensor Placement with Cost Constraints

The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments. We consider a relaxation of the full optimization formulation of this problem and then extend a well-established QR-based greedy algorithm for the optimal sensor placement problem without cost constraints. We demonstrate the effectiveness of this algorithm on data sets related to facial recognition, climate science, and fluid mechanics. This algorithm is scalable and often identifies sparse sensors with near optimal reconstruction performance, while dramatically reducing the overall cost of the sensors. We find that the cost-error landscape varies by application, with intuitive connections to the underlying physics. Additionally, we include experiments for various pre-processing techniques and find that a popular technique based on the singular value decomposition is often sub-optimal.