Autoregressive matrix factorization for imputation and forecasting of spatiotemporal structural monitoring time series

Reconstruction and prediction of spatiotemporal time series data has been a classic problem in structural health monitoring (SHM) in civil engineering applications. However, due to the explosive growth of sensing data, traditional time series analysis approaches fail in handling large-scale data with missing values. To this end, two autoregressive (AR) based matrix factorization (MF) methods are presented for missing sensor data imputation and structural response forecasting. The first model integrates the standard MF formulation with an innovative graph-based temporal regularizer, which can effectively model the nonlinear dynamics of SHM data and is computationally efficient, while the second approach introduces an additional AR based matrix to better simulate the temporal factor thanks to its capability of learning the details of temporal evolution. Finally, the proposed methods are evaluated by using a field-recorded SHM dataset of a municipal concrete bridge, considering various missing scenarios (i.e., random, structured and mixed). The results demonstrate excellent performance of the methods which accurately recover missing entries in the time series and forecast future response. Additionally, the parametric analysis on model parameters indicates that reasonably higher rank and longer time lag improve the estimation accuracy while saving computational cost.