# Flaw Size Quantification for Cable Flaw Inspection System with Inductive Search Coil Sensor
## 5 Discussion and Conclusions  
This paper presents a non-destructive inspection method for bridge cables based on the self-induction phenomenon, which utilizes a single self-induction coil search sensor. The self-induction coil of the proposed method offers various advantages that make it a potentially effective alternative for flaw detection. It requires less data processing and exhibits real-time responsiveness. Moreover, its lightweight design enables easy integration with robotic systems. Another advantage is its ability to provide a relative quantification of flaw size, which is a crucial factor for evaluating the condition of bridge cables. In this regard, Table 4 presents a comparative analysis of various cable flaw detection methodologies. To evaluate the effectiveness of the proposed method, this study examines the impact of various factors, including excitation frequency, flaw location, flaw axial length, and cross-sectional area on the inductance response. Firstly, a positive linear relationship is established between flaw axial length and the peak-valley distance of the response. This suggests that the method has the potential to assess the axial length of flaws based on the measured response. Secondly, a positive proportional correlation is observed between the self-inductance response amplitude and the cross-sectional area of flaws. This indicates that the proposed method can estimate the flaw's cross-sectional area. The experimental results  
Figure 16: Diagram of the relationship between flaw cross—sectional area and response amplitude (**a**) Compensated response comparison of a 10 mm flaw at 2500 Hz excitation frequency (**b**) Graph of the relationship between the flaw cross-sectional area and the corresponding absolute response amplitude at 2500 Hz excitation frequency. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Flaw Position** & **Excitation** & **Flaw Length** & **Flaw Cross-Sectional Area** \\ \hline \(P_{d}=2\) & 2500 Hz & 10–40 mm & 1/19 to 6/19 PLA on Layer 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The restricted experimental condition. obtained in this study provide supporting evidence for the validation and effectiveness of the proposed method in flaw detection and assessment. While the proposed method has some limitations, such as the current experimental focus on three-layer cables, future research aims to expand the testing to include more layers. Additionally, feasibility assessments of the measurement system will be performed, and the method will be validated and calibrated on a larger scale to enable its practical implementation in real-life bridge assessments. Despite these considerations, the proposed method offers a optional solution for evaluating the condition of bridge cables, with the potential to enhance the safety and reliability of bridge structures. Conceptualization, Z.F. and M.Z. ; methodology, Z.F. and M.Z. ; software, Z.F. ; validation, Z.F. and M.Z. ; formal analysis, Z.F. ; investigation, M.Z. ; resources, M.Z., N.D. and H.Q. ; data curation, Z.F. and M.Z. ; writing--original draft preparation, Z.F. ; writing--review and editing, M.Z. and H.Q. ; supervision, N.D. and H.Q. ; project administration, N.D. All authors have read and agreed to the published version of the manuscript. This research was funded by AIRS-SWET-Cooperation Engineering Center, the Guangdong Basic and Applied Basic Research Foundation under Grant No. 2019A1515111119 and No. 2021A1515010926 and the Shenzhen Science and Technology Program under Grant No. JSGG20210802154539015. Not applicable. The data presented in this study are available on request from the corresponding author. The author would like to thank [PERSON] and [PERSON] for their kindly suggestions in the scenario requirements definition and experiments method. The authors declare no conflict of interest.