Incremental Bayesian matrix/tensor learning for structural monitoring data imputation and response forecasting

There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. Recent development in Bayesian temporal factorization models for high-dimensional time series analysis has provided an effective tool to solve both imputation and prediction problems. However, for large datasets, the default Bayesian temporal factorization model becomes inefficient since the model has to be fully retrained when new data arrives. A potential solution is to train the model using a short time window covering only most recent data; however, by doing so, we may miss some critical dynamics and long-term dependencies which can only be identified from a longer time window. To address this fundamental issue in temporal factorization models, this paper presents an incremental Bayesian matrix/tensor learning scheme to achieve efficient imputation and prediction of structural response in long-term SHM. In particular, a spatiotemporal tensor is first constructed followed by Bayesian tensor factorization that extracts latent features for missing data imputation. To enable structural response forecasting based on long-term and incomplete sensing data, we develop an incremental learning scheme to effectively update the Bayesian temporal factorization model. The performance of the proposed approach is validated on continuous field-sensing data (including strain and temperature records) of a concrete bridge, based on the assumption that strain time histories are highly correlated to temperature recordings. The results indicate that the proposed probabilistic tensor learning framework is accurate and robust even in the presence of large rates of random missing, structured missing and their combination. The effect of rank selection on the imputation and prediction performance is also investigated. The results show that a better estimation accuracy can be achieved with a higher rank for random missing whereas a lower rank for structured missing.