Bayesian dynamic regression for reconstructing missing data in structural health monitoring

Massive data that provide valuable information regarding the structural behavior are continuously collected by the structural health monitoring (SHM) system. The quality of monitoring data is directly related to the accuracy of the structural condition assessment and maintenance decisions. Data missing is a common and challenging issue in SHM, compromising the reliability of data-driven methods. Thus, the accurate reconstruction of missing SHM data is an essential step for the reliable evaluation of the structural condition. Data recovery can be considered as a regression task by modeling the correlation among sensors. The Bayesian linear regression (BLR) model has been extensively used in probabilistic regression analysis due to its efficiency and the ability of uncertainty quantification. However, because of the fixed coefficients (refer to a static model) and linear assumption, the BLR model fails to accurately capture the relationship and accommodate the changes in related variables. Given this limitation, this study presents a Bayesian dynamic regression (BDR) method to reconstruct the missing SHM data. The BDR model assumes that the linear form is only locally suitable, and the regression variable varies according to a random walk. In particular, the multivariate BDR model can reconstruct the missing data of different sensors simultaneously. The Kalman filter and expectation maximum (EM) algorithms are employed to estimate the state variables (regressors) and parameters. The feasibility of the multivariate BDR model is demonstrated by utilizing the data from a building model and a long-span cable-stayed bridge. The results show that the multivariate BDR model exhibits excellent performance to rebuild the missing data in terms of both computational efficiency and accuracy. Compared to the standard BLR and linear BDR models, the quadratic BDR model owns better reconstruction accuracy.