High Resolution Bridge Mode Shape Identification via Matrix Completion Approach

Abstract

Mathematical platforms that are able to estimate modal characteristics from mobile sensors are not much investigated. Mobile sensors collect spatially dense data compared to limited spatial density of fixed sensor networks. This feature potentially enables to refine the identified natural mode shapes as well as more robust estimations of other modal characteristics, e.g., natural frequencies and damping ratios. In this paper, highresolution natural mode shape identification of a simple-span bridge using mobile data is investigated. A recent methodology developed by authors is used to reconstruct a full bridge response matrix from mobile data. Matrix completion technique approximates unobserved signals at many virtual stationary locations via a convex optimization procedure. This reconstructed data is then fed in batches into available output-only system identification algorithms to extract modal properties. Mode shape refinement then is performed by superimposing identified results of all considered batches. The accuracy of the matrix completion for signal reconstruction was shown before, however, the performance of the estimated signal for modal identification has not been demonstrated yet. In this study, a numerical case study is examined to compare identification results from this procedure compared to a conventional sensing network consists of fixed sensors.