7. Signal Reconstruction from Mobile Sensors Network Using Matrix Completion Approach

Bridge system identification is recently studied using mobile sensing network data. As one possible solution, the data collected by moving sensors are to be mapped to some predefined virtual stationary locations and then, using estimated stationary data, various system identification methods can be applied. The mapping function, however, has not been studied thoroughly so far. STRIDEX, which is a recently proposed platform for bridge SID using mobile sensing, assume sinc function as an estimator for the mapping function. Despite its effectiveness under certain conditions, the function cannot accurately estimate stationary time responses from mobile data in more realistic cases of moving sensors with random presence over the bridge. In this paper, an alternative solution based on low-rank matrix completion problem is proposed and motivations for this choice are discussed. This method attempts to complete the matrix as accurate as possible by convex optimization, given a sparse matrix of acceleration values with various time and space coordinates. A comprehensive comparison between sinc and matrix completion approaches is performed and the results are evaluated in terms of the response prediction accuracy in both time and frequency. Results show that the proposed matrix completion signals are a very good match to the actual signals, while the reconstructed signals using sinc are sometimes not as accurate.