Time-lag effect of thermal displacement and its compensation method for long-span bridges

The time-lag effect between temperature and thermal displacement may induce the displacement-based safety assessment results of long-span bridges to derivate from the truth. In this paper, the typical characteristics of the time-lag effect between temperature and thermal displacement are firstly investigated by using the synchronously monitored temperature and displacement data from a long-span steel box-girder arch bridge. And then, the inherent reasons of the time-lag effect are found out by employing the Kendall correlation coefficient. Following that, a general method derived from the Bayesian function registration model and the Z-mixture preconditioned Crank-Nicolson algorithm is proposed to compensate the time-lag effect. Finally, the proposed compensation method is verified by data from three bridges and compared with the traditional method achieved through shifting a fixed time interval. The results show that thermal displacement may be ahead of or lag behind temperature, depending on the temperature and thermal displacement of concern. The lag time varies from a few minutes to several hours with temperature and displacement variables, as well as time instants. The time-lag effect between temperature and thermal displacement is caused by the asynchronous change of the dominant temperature for the specific thermal displacement and other temperatures because of different material thermodynamic parameters and geometric characteristics of different bridge components. The developed compensation method can completely eliminate the time-lag effect between temperature and thermal displacement of various long-span bridges without any pre-correlation analysis and prior knowledge. The correlation between temperature and thermal displacement compensated by the method proposed in this paper is much stronger than that compensated by the traditional method.