Accurate identification of the modal frequency of structures is an important task for structural health monitoring (SHM). The modal frequency, determined by the structural stiffness and mass, can be affected by different ambient factors, such as temperature, wind direction and wind power, and so on. Ambient factors, especially temperature, can cause changes in modal frequencies even greater than the changes caused by structural damage [

1].Since then, many researchers have studied temperature-induced variations in natural frequency of structures. In the past two decades, bridges have been paid more attention than other types of structures, possibly because bridges are directly exposed to the ambient environment. On the basis of two-year continuous dynamic monitoring data from two bridges under normal operating conditions, Hu et al. [

2] found that temperature has a primary effect on the variations of modal frequencies in a nonlinear manner. The annual maximum relative variation of frequency estimates is in the14–20.6% range for the 12 modes analyzed, which would mask the subtle changes induced by structural damage. Deng et al. [

3] monitored the Yunyang Suspension Bridge with a 1490-m main span for a period of 10 months. The first six modal frequencies experienced about 2% variation, as the ambient temperature of the steel bridge varied from −5 to +50 °C. In recent years, as more and more high-rise buildings have been built, variations in frequencies of high-rise structures have attracted more and more studies as extensively as bridge structures. In the field monitoring of a 17-story steel frame building, Nayeri et al. [

4] found that there is a strong correlation between and temperature and frequencies, whereas frequency variations lagged behind temperature variations by a few hours. Based on the one-year monitoring data of a 22-story reinforce concrete (RC) building, Yuen and Kuok [

5] found that the first three frequencies increased with an increase in ambient temperature, which was opposite to their analytical results. During a 24-h period of field monitoring, Faravelli et al. [

6] studied the variations in frequencies of the 600-m-tall Guangzhou New TV Tower. By monitoring the Shanghai Tower (with a height of 632 m) for 12 h, Zhang et al. [

7] found that the natural frequency has an ascending trend with increasing temperature, with slight decreases with an increase of humidity. Domarie and Sabia [

8] studied the variations of modal frequencies based on the continuous monitoring data over a year of a high bell tower. The frequency values tended to vary in different trend in different temperature period. Furthermore, such a variation was smooth for the bending modes, while it showed as abrupt for the torsional modes. Ni et al. [

9] carried out a field test to measure a tall building for 48 h to investigate the performance variance and the distribution of the modal parameters. Wu et al. [

10] conducted a long-term monitoring and condition evaluation of an office building. A crucial observation from this assessment is that the percentages of frequency variation in three months for most of the identified modes were beyond 10%.Although in the normal temperature range, the change of frequency is usually at the level of a few percentages, which can be more severe than the change caused by structural damage. In order to avoid false condition evaluation, the relation between temperature and structural modal parameters should be established so that the temperature effect can be eliminated in condition evaluation.

In eliminating the effect of ambient factors on modal parameters, the key is to build a mathematical model that can accurately reflect the intrinsic relation between modal parameters and ambient factors. Many methods have been applied to eliminate the influence of ambient factors on modal parameters. The commonly used methods are the Bayesian framework [

11,

12], time series analysis [

13,

14,

15] and artificial neural network (ANN) [

16,

17,

18]. Behmanesh et al. [

11] presented a hierarchical Bayesian framework in the absence of noise or model discrepancies to accurately identify parameters subjected to external actions. Jesus et al. [

12] applied the Bayesian framework to the structural identification of a long suspension bridge by considering temperature and traffic load effects. Liu et al. [

15] established a structural health monitoring (SHM) benchmark database for a prestressed concrete box girder bridge, and a linear regression model between the first three modal frequencies and temperatures was built based on the monitored data. Li et al. [

16] studied the dependence of the modal frequency, modal shape and damping ratio on temperature and wind speed. For certain modes, temperature was the most significant environmental factor that accounted for the variation of damping ratios, while for other modes, wind velocity was the significant factor. Shan et al. [

17] applied three regression-based numerical models, including multiple linear regression (MLR), back-propagation neural network (BPNN), and support vector regression (SVR) to capture the relations between modal frequencies and temperature distributions from measurements of a concrete beam during a period of 40 days. Teng et al. [

18] conducted the continuous dynamic monitoring of a bridge and applied ANN to remove the temperature effect on modal frequencies so that a health index can be constructed under operational conditions.