# Flaw Size Quantification for Cable Flaw Inspection System with Inductive Search Coil Sensor
## 1 Introduction  
Cable-stayed bridges are crucial for economic development due to their practical and economical features. The cables play an irreplaceable role in providing loading and bearing capacity in the stay-cable bridge system. Since bridges are important national assets, proper maintenance is necessary to ensure public safety. To maintain a safe service status and avoid accidents and economic losses, structural health monitoring of the system structure is significant [1]. In general, cable damage factors can be divided into two categories: external and internal. External damage factors include corrosion due to sunlight or moisture from damaged wrapping or caulking. Internal damage factors are caused by fatigue due to vibrations, overload, and small corrosion cracks, which can be considered as deterioration arising from external damages. There are currently two mainstream approaches for detecting the two types of cable damage mentioned above. The first approach is manual flaw detection, which involves visual inspection of cables, splay castings, cable strands, and associated hardware in the anchorages. However, visual testing has limitations for sheathed cables, as damages may occur inside the wrapping, which can make the results subjective and inaccurate. Furthermore, the detecting process involves aerial work with lifting equipment, which increases the risks to workers. The second approach relates to non-destructive testing (NDT) [2; 3; 4] with sensors, which have been extensively studied for their ability to detect flaws without damaging the material under test. Several studies have been conducted on NDT techniques. Dye Penetrant (DP) testing [5] is a simple and easy method for detecting shallow cracks in steel cable surfaces using liquid dye, which is easily combined with a visual inspection. [PERSON] et al. [6] specially analyzed the effects of temperature variations and mechanical vibrations on the performance and accuracy of the liquid penetrant inspection techniques. However, it is costly when assessing quality at multiple locations. Optical Fiber Sensing [7; 8] is a stable and precise method. [PERSON] et al. [9] proposed an approach for monitoring cable force using optical fiber Bragg grating (FBG) sensors and time domain analysis sensing technique. [PERSON] et al. [10] developed an inclination sensor based on \"pendulum-equal strength beam\" utilizing Fiber Bragg grating technology to monitor the deflection. But optical fiber sensing is still challenged by issues such as the complexity of the detection process and excessively high sensitivity. Radio-graphic Testing (RT) is a non-destructive testing method that uses either x-rays or gamma rays to examine the internal structure of manufactured components to identify any flaws or defects. [PERSON] et al. [11] used faster R-CNN to realize automated damage detection. However, it should be noted that RT can be costly and may pose health risks due to the potential hazards associated with radiation exposure. Ultrasonic Testing (UT) [12] uses ultrasonic transmission and reception to quickly detect defects with strong penetration ability and defect positioning capacity. Recent studies have proposed various techniques to enhance UT accuracy and efficiency. [PERSON] et al. [13] utilized a semi-analytical finite element (SAFE) technique to identify guided wave modes for multi-wire bridge cables. [PERSON] et al. [14] employed the matching pursuit algorithm for ultrasonic guided wave detection. Other research efforts have focused on combining UT with other techniques to achieve improved defect visualization, such as the synthetic aperture focusing technique with a remote laser signal and laser-based ultrasonic signal proposed by [PERSON] et al. [15]. Additionally, [PERSON] et al. [16] utilized the ultrasonic coda wave interferometry technique to study the influence of temperature and load on the bridge. However, UT has certain limitations, such as its poor intuitiveness of the detection results.