Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.
A Combinatorial Optimization Problem for High Order PODs with Few Sensors
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Mohanty, A. K., Chakraborty, K., and Chatterjee, A. (November 17, 2006). "A Combinatorial Optimization Problem for High Order PODs with Few Sensors." ASME. J. Vib. Acoust. April 2007; 129(2): 252–255. https://doi.org/10.1115/1.2424983
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