# Temperature Effects on Vibration-Based Damage Detection of a Reinforced Concrete Slab
## 1 Introduction
[PERSON] and [PERSON] [23] found that changes in dynamic characteristics of the bridge due to damage in girders or cables may be smaller than changes in dynamic characteristics due to variations in temperature. [PERSON] et al. [24] investigated the variation of wind, temperature and acceleration of the Braga Stadium suspension roof during a period of 8 months and analyzed the influence of wind and temperature on the variation of modal parameters. To distinguish the modal parameter change caused by structural damage and temperature change, many methods are adopted to identify the structural damage considering temperature variations. [PERSON] et al. [25] proposed a non-destructive global damage identification method based on a genetic algorithm (GA) to identify the damage location and severity of the structure under the influence of temperature variation and noise, which is verified by a number of damage scenarios using a three-span continuous beam. It shows good robustness under random noise levels with a lab steel grid experiment. [PERSON] et al. [26] developed an extended Kalman filter-based artificial neural network (EKFNN) method to eliminate the temperature effects and detect damage for structures equipped with long-term monitoring systems, and the correlations between natural frequencies and temperature are analyzed to select proper input variables for the neural network model. [PERSON] et al. [27] proposed a fuzzy neural network-based damage assessment method, in which uniform load surface curvature is used as damage indicator. Under the assumption that the elasticity modulus of concrete is temperature dependent, the algorithm can distinguish the damage from the temperature effect. The relationship between frequency and temperature variations are constructed to study the influence of temperature on frequency. The purpose is to quantify the relationship between temperature and natural eigenfrequency. [PERSON] et al. [28] adopted support vector machine (SVM) to analyze the monitoring data and quantify the influence of temperature on modal frequency, the results obtained by the SVM models are compared with those produced by a multivariate linear regression model, and it is shown that the SVM models exhibit good capabilities for mapping between the temperature and modal frequencies. [PERSON] et al. [29] monitored the natural variability of the frequencies and mode shapes of the Alamosa Canyon Bridge that result from changes in time of day considering the amount of traffic and environmental conditions. [PERSON] and [PERSON] [21] monitored the Z24 Bridge and proposed a black-box model to describe the variations of eigenfrequencies as a function of temperature, and new data are compared with the models to discriminate the reason that induced the changes of eigenfrequency. [PERSON] et al. [30] proposed a linear adaptive model to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. [PERSON] et al. [31] monitored the influence of temperature and humidity on the vibration characteristics of the structure, and linear regression models between modal properties and environmental factors were built. [PERSON] et al. [32] established a multiple linear regression model (MLRM) to describe the relationship between modal frequency and non-uniform temperature distribution to raise the accuracy of quantified temperature and frequency. [PERSON] et al. [33] obtained the correlation between temperature and frequency by comparing the test data of a simply supported beam under the effect of temperature. Few researches focus on the damage identification based on the established relationship model, such as the linear regressive model and the autoregressive with exogenous (ARX) model. When the damage causes the nonlinear response of the structure, it is expected that the residual damage will increase. Therefore, the standard deviation of residual damage is predicted as the damage characteristic quantity by using ARX model.