# Flaw Size Quantification for Cable Flaw Inspection System with Inductive Search Coil Sensor
## 1 Introduction
Magnetic particle Testing (MT) [17] detects surface or near-surface flaws in steel structures by analyzing the magnetic flux leakage. It is a method that requires little training for inspectors before practical operation. [PERSON] et al. [18] integrated convolutional neural networks (CNNs) into an automated vision system for magnetic particle inspection. [PERSON] et al. [19] proposed a thermography-based dry MT method that identifies cracks during the magnetic particle testing process. However, MT methods often have shallow depth measurement capabilities, which limits their application scope. Magnetic Flux Leakage (MFL) is a magnetic-based detection technique for cable damage. The MFL technique has been shown to be highly effective in locating flaws by monitoring the variance of magnetic flux leakage [20; 21]. Recent studies have introduced novel techniques to enhance the MFL signal denoising algorithm and improve defect identification. [PERSON] et al. [22] introduced kernel principal component analysis to enhance the MFL signal denoising algorithm and identify the defects. [PERSON] et al. [23] used the magnetic flux variation to quantify the defect size. However, despite its effectiveness, the MFL technique suffers from certain limitations, including high sensitivity to the distance between the defect and the sensor, insufficient excitation intensity, and overweight problems. These limitations make it challenging to quantitatively evaluate defects on the cable using MFL. Acoustic Emission (AE) testing [24] is widely used technique for monitoring steel bridge elements, where changes in cable force and vibration frequency during dynamic material processes are monitored. [PERSON] et al. [25] proposed a status-driven acoustic emission monitoring method that combines wavelet analysis and transfer learning through convolutional neural networks. [PERSON] et al. [26], on the other hand, presented an AE signal segmentation algorithm that facilitates the extraction of AE signal characteristics by setting segmentation parameters. However, the accuracy of AE detection tends to decrease with increasing distance. In addition, vibration-based methods [27; 28] have also been utilized for cable condition assessment by monitoring changes in cable tension. [PERSON] et al. [29] proposed a cable tension estimation framework based on an artificial neural network using parameters such as cable length, mass per unit length, axial stiffness, bending stiffness, cable tension, and corresponding natural frequenciesobtained from a comprehensive cable model, enabling accurate estimation of cable tension. [PERSON] et al. [30] used the Shannon entropy index to characterize cable vibration signals and employed a fuzzy logic classifier for pattern recognition to detect and locate cable structural damage affected by environmental vibrations. [PERSON] et al. [31] proposed a long-term condition assessment method for monitoring stay cables based on the concept of the influence surface and the linear relationship between the matching cable tensions of two adjacent cables. [PERSON] et al. [32] introduced a new approach for detecting and locating cable losses using statistical time features (STF) obtained through auto-correlation function (ACF), principal component analysis (PCA), and Mahalanobis distance (MD). [PERSON] et al. [33] developed a Damaged Cable Identification Machine (DCIM) and a Damage Severity Identification Machine (DSIM) based on support vector classification to determine cable damage and its severity. While the aforementioned methods offer comprehensive solutions for cable flaw-detection, they often involve complex operations, ponderous detection structures and relative non-intuitive representation of detection results. In this paper, a portable non-destructive inspection method for bridge cables is proposed, by leveraging the self-induction phenomenon.