## 1 Introduction  
For concrete box-girder bridges, integral parts of the structural health monitoring (SHM) system include the structural state assessment system and the real-time warning system. A necessary prerequisite to achieve a reliable state assessment and real-time warning is the clear understanding of environmental load effects on the structure, especially the temperature related effects. In fact, the temperature effects have been investigated by many researchers. It is considered that the stress generated by the nonlinear temperature distribution is usually equivalent to the live load, and the temperature-induced stress is significant in the concrete structure [1]. [PERSON] et al. [2] studied the thermal characteristics of concrete under the influence of temperature variation on box-girder utilizing experiments and finite element simulation. Their work highlighted the distribution of thermal difference and its influencing factors. Besides, [PERSON] et al. [3] discovered that temperature effects possess an important impact on the reliability of full bridges by analyzing a vast amount of monitored data. In order to analyze the influence of temperature effects on structure assessment [4; 5], [PERSON] et al. [6] applied Kalman filtering and Kalman cointegration to identify the damage and recognized that external effects (e.g., temperature) may mask the changes induced by structural damage. Moreover, [PERSON] et al. and [PERSON] et al. [7; 8] carried a sensitivity study based on the structural fundamental frequencies in which it has been found that variations in ambient temperature might lead to the misjudgment of structural health conditions. Their work emphasized on temperature effects, but the observation and analysis of temperature distributions need to be further investigated. The temperature distribution is the state of temperature at various positions inside and outside a structure at a certain time [9]. Preliminary studies of the temperature effects only considered the general temperature effects. [PERSON] et al. [10] examined more than 8 years' temperature displacements using mean values of different temperatures sensors and obtained the statistical law of temperature change. [PERSON] et al. [11] studied the change of structural dynamic response using uniform temperature rise and fall models. Nevertheless, they all ignored the difference in temperature distribution. To further study the temperature stress, the nonlinear effect should be taken into consideration, when horizontal and vertical temperature gradients exist [12; 13]. The external factors affecting the temperature distribution of concrete structures are solar radiation, nighttime cooling, cold air flow, wind, rain, snow, and other meteorological factors [1]. The internal factors that affect the temperature distribution of the concrete are mainly determined by the thermophysical properties of the concrete and the geometrical dimensions of the components. The spatial heterogeneity and time-dependent nature of temperature distribution make it difficult to determine the exact relationship between temperature and structural response [14]. Considering the monitored response data of a real bridge inevitably includes the influences of live load and environmental factors, making the problem more complicated. To explore the temperature influences, separation of the temperature-induced part in data should be performed beforehand. For instance, [PERSON] al. [15] used the linear fitting method to determine the relationship between ambient temperature and temperature-induced strain while [PERSON] et al. [16] separated the time-dependent deformations from the temperature-related deformations by means of linear regression. They all achieved the purpose of separating the temperature-induced parts in the raw structural response data. Previously, some scholars have noticed discrepancies in different temperature history data of steel bridges. For example, [PERSON] et al.