  Structural Health Monitoring (SHM) systems are critical for monitoring aging
infrastructure (such as buildings or bridges) in a cost-effective manner. Such
systems typically involve collections of battery-operated wireless sensors that
sample vibration data over time. After the data is transmitted to a central
node, modal analysis can be used to detect damage in the structure. In this
paper, we propose and study three frameworks for Compressive Sensing (CS) in
SHM systems; these methods are intended to minimize power consumption by
allowing the data to be sampled and/or transmitted more efficiently. At the
central node, all of these frameworks involve a very simple technique for
estimating the structure's mode shapes without requiring a traditional CS
reconstruction of the vibration signals; all that is needed is to compute a
simple Singular Value Decomposition. We provide theoretical justification
(including measurement bounds) for each of these techniques based on the
equations of motion describing a simplified Multiple-Degree-Of-Freedom (MDOF)
system, and we support our proposed techniques using simulations based on
synthetic and real data.
