Modal Identification of Bridges Using Mobile Sensors with Sparse Vibration Data

Dynamic sensor networks have the potential to significantly increase the speed and scale of infrastructure monitoring. Structural health monitoring (SHM) methods have been long developed under the premise of utilizing fixed sensor networks for data acquisition. Over the past decade, applications of mobile sensor networks have emerged for bridge health monitoring. Yet, when it comes to modal identification, there remain gaps in knowledge that have ultimately prevented implementations on large structural systems. This paper presents a structural modal identification methodology based on sensors in a network of moving vehicles: a large-scale data collection mechanism that is already in place. Vehicular sensor networks scan the bridge's vibrations in space and time to build a sparse representation of the full response, i.e., an incomplete data matrix with a low rank. This paper introduces modal identification using matrix completion (MIMC) methods to extract dynamic properties (frequencies, damping, and mode shapes) from data collected by a large number of mobile sensors. A dense matrix is first constructed from sparse observations using alternating least-square (ALS) then decomposed for structural modal identification. This paper shows that the completed data matrix is the product of a spatial matrix and a temporal matrix from which modal properties can be extracted via methods such as principal component analysis (PCA). Alternatively, an impulse-response structure can be embedded into the temporal matrix and then natural frequencies and damping ratios are determined using Newton's method with an inverse Hessian approximation. For the case of ambient vibrations, the natural excitation technique (NExT) is applied and then structured optimization (Newton's method) is performed. Both approaches are evaluated numerically, and results are compared in terms of data sparsity, modal property accuracy, and postprocessing complexity. Results show that both techniques extract accurate modal properties, including high-resolution mode shapes from sparse dynamic sensor network data; they are the first to provide a complete modal identification using data from a large-scale dynamic sensor network.