*Article* **Modeling of Temperature Time-Lag E** ff**ect for Concrete Box-Girder Bridges**

#### **Kang Yang 1, Youliang Ding 1,\*, Peng Sun 2, Hanwei Zhao 1 and Fangfang Geng 3**


Received: 1 July 2019; Accepted: 7 August 2019; Published: 9 August 2019

**Featured Application: According to field research results, a time-lag between structural response and temperature load is commonly encountered in practice. Due to the fact that it cannot be neglected for accurate structure health monitoring, a phase-shifting method is proposed; with the method, the time-lag e** ff**ect can be e** ff**ectively reduced, leading to a sound understanding of temperature load and its e** ff**ect.**

**Abstract:** It is common to assume the relationship between temperature and temperature response is instantaneous in bridge health monitoring systems. However, a time-lag e ffect between temperature and thermal strain response has been documented by the analysis of monitored field data of concrete box-girder s. This e ffect is clearly reflected by the ring feature in the temperature-strain correlation curve. Inevitably, the time-lag e ffect has an adverse impact on the accuracy and reliability of state assessment and real-time warning for structural health monitoring (SHM) systems. To mitigate the influence of the time-lag e ffect, a phase-shifting method is proposed based on the Fourier series expansion fitting method. The time-domain signal is firstly converted into the frequency domain signal to compute the phase di fference between temperature data and response strain data at each decomposed order. Subsequently, the total phase di fference can be obtained by weighted summation. The signal processing e ffectively reduces the hysteresis loop area and enhances the correlation between the structural response data and the temperature data. When processing the daily data in di fferent seasons, it is found that after subtraction by the proposed method, the linear feature becomes dominant in the relationship between temperature and the strain during long-term observation.

**Keywords:** structural health monitoring; temperature e ffects; time-lag e ffect; Fourier series expansion; box-girder bridges
