Distributed modal identification using restricted auto regressive models

Advances in Wireless Sensor Networks (WSN) technology have provided promising possibilities in detecting a change in the state of a structure through monitoring its features estimated using sensor data. The natural vibration properties of the structure are a set of features commonly used for this purpose and are often estimated using a multivariate autoregressive model (AR model) for the measured structure's response to ambient vibrations. Fitting a multivariate AR model to the observed acceleration requires the computation of the lagged covariance between the measurements in all nodes. The resulting volume of data transmission causes significant latency due to the low data bandwidth of WSNs in addition to having a high transmission energy cost. In this paper, a set of restrictions to the estimation of the AR model is introduced. Such restrictions significantly reduce the volume of data flowing through the WSN thus reducing the latency in obtaining modal parameters and extending the battery lifetime of the WSN. A physical motivation is given for the restrictions based on a linear model for a multi-degree of freedom vibrating system. Stabilization diagrams are compared for the restricted and full AR models fitted using data simulated from linear structures and real data collected from a WSN deployed on the Golden Gate Bridge. These stabilization diagrams show that the estimated modes using the restricted AR models are of comparable quality to that of the full AR model while substantially reducing the volume of transmitted data.