Frequency Co-integration-based damage detection for bridges under the influence of environmental temperature variation

Natural frequencies of structures are usually convenient to acquire with a high precision in engineering. However, it is still difficult and faces challenges to apply the frequencies in the area of structural health monitoring. One of the main reasons is the natural frequency's sensitivity to the variation of environmental conditions, such as temperature, which often disturbs the frequency based identification and even results in the false evaluation of the structural health condition. To overcome this problem, a novel frequency-based co-integration technique is proposed in this paper. The main principle is that the non-stationarity of the acquired frequencies caused by the variation of environmental temperature, can be transformed to stationary sequence by linear combining two non-stationary frequencies using the co-integration algorithm. The calculated stationary relationship between two frequencies series is insensitive to the influence of environmental variation, and can be employed to detect structural damage. In the study, ADF (Augmented Dickey-Fuller) test and EG (Engle-Granger) test are first introduced to check the non-stationary order and calculate the co-integration coefficients of the frequency series. Subsequently, the theoretical derivation of frequency co-integration based technique is developed using a simply supported beam as an example, and the procedure of damage detection based on frequency co-integration technique under the influence of environmental temperature is introduced in detail. At last, the validity and robustness of the proposed method are illustrated and verified through a numerical simulation of a steel truss bridge and a real cable-stayed bridge under the influence of changing environmental temperature. Both the numerical simulation and the practical application demonstrate that the proposed frequency co-integration technique can effectively eliminate the influence of the changing environmental temperature and identify the structural damage accurately.