Sampling considerations for modal analysis with damping

Structural health monitoring (SHM) systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Wireless sensor networks that sample vibration data over time are particularly appealing for SHM applications due to their flexibility and low cost. However, in order to extend the battery life of wireless sensor nodes, it is essential to minimize the amount of vibration data these sensors must collect and transmit. In recent work, we have studied the performance of the Singular Value Decomposition (SVD) applied to the collection of data and provided new finite sample analysis characterizing conditions under which this simple technique also known as the Proper Orthogonal Decomposition (POD) can correctly estimate the mode shapes of the structure. Specifically, we provided theoretical guarantees on the number and duration of samples required in order to estimate a structure's mode shapes to a desired level of accuracy. In that previous work, however, we considered simplified Multiple-Degree-Of-Freedom (MDOF) systems with no damping. In this paper we consider MDOF systems with proportional damping and show that, with sufficiently light damping, the POD can continue to provide accurate estimates of a structure's mode shapes. We support our discussion with new analytical insight and experimental demonstrations. In particular, we study the tradeoffs between the level of damping, the sampling rate and duration, and the accuracy to which the structure's mode shapes can be estimated.