Bayesian Multiple Linear Regression and New Modeling Paradigm for Structural Deflection Robust to Data Time Lag and Abnormal Signal

Long-span bridges are the lifeline throats of urban transportation network. Deflection (i.e., deformation) behavior of long-span bridges is complex. It can be found from long-term monitoring data that there is an obvious time-lag effect between the quasi-static behavior of deflection and environmental temperature, and abnormal signals, such as drift and jump-point, appear sporadically in the deflection data. In order to deal with the interference from the data time lag and abnormal signal, this article adopts the Bayesian multiple linear regression (BMLR) method to establish the mathematical model of bridge deflection based on temperature, other points’ deflection, or cable force data. A new paradigm of the recursive modeling strategy of BMLR for bridge deflection based on short-term data is proposed, which truly realizes the dynamic update ability of Bayes’ theorem in multiple regression modeling. Under the same conditions of modeling, the proposed paradigm performs higher accuracy of prediction and lower space of data storage occupied than the traditional multiple linear regression method and is less time taken than methods of deep learning. The whole process was validated to be robust to the data time lag and abnormal signal. When faced with the situation of sparse sensing points and not enough long time of monitoring, it is possible to fast predict deflection of new-added/adjusted sensing points using short-term observation data.