Time-varying Multivariate Linear Regression Modeling of Temperature-induced Bearing Displacements of A Single Tower Cable-Stayed Bridge

Based on the monitoring temperature field and bearing displacement data of a single-tower cable-stayed bridge, the changing trends of temperatures, temperature differences and displacements are analyzed, and then the correlations between bearing displacements and temperatures as well as temperature differences are analyzed in long-term and short-term periods; furthermore, a time-varying multivariate linear regression model for simulation of temperature-induced displacements is put forward, and the Kalman filtering technique is employed to achieve the accurate values of time-varying coefficients in this model; Finally, the modeling accuracy is verified and compared with the traditional multiple linear model. The results show that the temperature-induced displacements are not only affected by uniform temperature but also affected by gradient temperatures, which should be fully considered during time-varying multiple linear regression modeling; the correlations between bearing displacements and temperatures shows a good linear relationship over a long period of time (such as in several months), and shows obvious nonlinear relationship over a short period of time (such as in one day), indicating that the correlation in different time scales is different; the time-varying multiple linear regression model considering not only the influence of uniform temperature and gradient temperature but also the linear and nonlinear correlations demonstrates better modeling accuracy, with errors of only 0.77%, 2.35%, and 2.58% for daily, monthly, and quarterly data, respectively, and the simulated values of bearing displacements are very close to the measured values, with the root mean square errors of only 0.8479 and 0.7149, indicating that the proposed time-varying multiple linear regression model has a good simulation accuracy of bearing displacements.