Atomic norm minimization for modal analysis

Maintaining safely operable structures such as buildings and bridges requires periodic assessment of the health of the structure. We study the problem of identifying the characteristic modes and frequencies of a structure from small amounts of vibrational data collected from wireless sensors deployed across the structure. Using the recent technique of atomic norm minimization, we show that under certain conditions exact recovery of the mode shapes and frequencies is possible, and we survey several possible randomized sampling and compression schemes for minimizing the amount of data that is collected and transmitted by the sensors.