**5. Conclusions**

Temperature is the most common and critical environmental load acting on bridge structures. The non-uniformity distribution and time-dependent character of the temperature leads to the complexity of temperature response. The existence of a structural response lag behind a reference temperature was investigated by analyzing the monitored data of a small concrete box-girder bridge. This time-lag effect causes interference between temperature load and structural response, leading to difficulties in the real-time warning of the SHM system. To address this problem, this study proposed a phase difference subtraction method based on the Fourier series fitting algorithm. Then, the method was verified to be effective through a case study. The main conclusions are as follows:


**Author Contributions:** Original ideas K.Y. and Y.D.; data analysis, K.Y.; funding acquisition, Y.D.; methodology, K.Y. and H.Z.; writing—original draft preparation P.S.; writing—review and editing, P.S. and F.G.

**Funding:** This research was funded by the National Natural Science Foundation of China (51578138 and 51608258) and the Fundamental Research Fund for the Central Universities.

**Conflicts of Interest:** The authors declare no conflict of interest.
