# Damage Identification of Stay Cables Based on a Small Amount of Deflection Monitoring Data
In the early stage of the development of structural damage identification, most studies on structural damage identification are carried out with the change in natural frequency as the starting point [6; 7]. After slight damage occurred to the cable, the natural frequency was a small variable [8]; therefore, it was difficult to identify the damage of the cable through frequency change. [PERSON] et al. [9] decomposed the dynamic response of the cable into evanescent wave component and propagating wave component, and judged the local damage of the cable by the reflection coefficient of the blanking wave. [PERSON] et al. [10] used bridge deck strain combined with support vector machine to identify cable damage. [PERSON] et al. [11] proposed a cable damage identification method based on Kalman filtering and co-integration. However, the dynamic response of the bridges is prone to the interference of the external environment. Due to the complexities of the actual bridge structures and the field environment, as well as the incomplete measured data, the uncertainty of the structural dynamic responses leads to the unsatisfactory practical application effect of the existing research results. The method based on static parameters has attracted the attention of scholars. After the cable is damaged, the damage cable force decreases while the nearby cable force increases. The damage of the cable can be identified through the change in cable force [12]. In practical engineering, the cable force testing methods include jack hydraulic method, pressure sensor measurement method, frequency method, magnetic flux detection method [13; 14], etc. These detection methods will be more or less affected by various factors in the practical application process so that the accuracy will be reduced. Compared with the dynamic response of the structure, the signal of the bridge deflection response is more stable, which can not only represent the overall performance of the structure, but also reflect the local stress state of the structure, and is less affected by the external environment interference. Many scholars have studied the method of cable damage identification based on the deflection data of the main beam. Taking an arch bridge as the research background, [PERSON] et al. [15] deduced the relationship between the deflection difference of the tie beam and the change in the cable force of the damaged hangers by using the relevant principles of structural mechanics, accurately identified the location of the damaged hangers by using the third derivative of the deflection difference of the tie beam, and verified the reliability of the method with laboratory models. Taking an arch bridge as the background as well, [PERSON] et al. [16] proposed a derrick damage identification method based on the influence matrix of the deflection difference of the tie beam in the arch bridge by deducing the relationship between the deflection difference of the tie beam and the change in cable force, and verified the feasibility of the method in the laboratory. [PERSON] et al. [17] identified the damage of the stay cable by using the particularity of a few non-zero coefficients in the residual force and static load vector of the stay cable. [PERSON] et al. [3] suggested a method for detecting hanger damage based on the fluctuation of the displacement difference between measuring points. [PERSON] et al. [18] introduced one new method to localize and quantify the partial cable damage using the abnormal variation in temperature-induced girder deflection caused by cable damage. For a cable-stayed bridge with hundreds of cables, installing sensors at the anchorage point of each cable to measure the beam deflection is costly and workload-heavy. How to obtain the deflection distribution curve of the girder through the deflection of a few monitoring points is an urgent problem to be solved in cable damage identification based on the deflection of the girder.