# Edge Effect Analysis and Edge Defect Detection of Titanium Alloy Based on Eddy Current Testing
## 4 Conclusions  
This study proposed a methodology to optimize coil parameters for edge defect detection. Two responses (\(D_{half},D_{30\%}\)) were defined to describe edge effect and another two responses (\(DIS\) and \(RATIO\)) were defined to evaluate the defect detecting capability. Coil parameters which were truly significant to the responses were selected using screening experiments. Regression models were then obtained for \(D_{half},D_{30\%}\), \(DIS\) and \(RATIO\) responses. A new response \(SPA\) was defined with a combination of \(D_{half},D_{30\%}\), and \(DIS\). It turned out that the larger the \(SPA\), the lower the possibility that the dip caused by defect is affected by edge effect. The larger the \(RATIO\), the easier the dip caused by defect is identified. An approach making use of desirability functions to both maximize \(SPA\) and \(RATIO\) was applied, and the best set of coil parameters in detecting edge defect was found. The proposed methodology can be extended to other sensor parameters and crack parameters analysis.  
There is still some follow-up work to investigate in the future. Firstly, the scanning path parallel to the edge might be less sensitive to edge effect, so it might provide better results in detecting edge defect. Secondly, other kinds of sensor including a differential sensor or absolute sensor with a transmitter and a receiver will be investigated. Thirdly, deep learning will be used to estimate the location and size of edge defect. In addition, more simulations and experiments at a relatively higher excitation frequency such as 500 kHz, 1 MHz, and 2 MHz will be conducted to investigate the excitation frequency effect for edge defect detection, especially the small edge defect detection.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Lower Limit** & **Upper Limit** & **Unit** \\ \hline Coil height & 1 & 2 & mm \\ Lift-off & 0.1 & 0.5 & mm \\ Excitation frequency & 50 & 100 & kHz \\ Outer diameter & 1 & 5 & mm \\ \(SPA\) & 4.51 & 5.89 & mm \\ \(RATIO\) & 0.12 & 0.41 & none \\ \hline \hline \end{tabular}
\end{table}
Table 13: Settings for optimization.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **Height** & **Lift-off** & **Frequency** & **Diameter** & **DIS** & **RATIO** & **Desirability** \\ \hline
1 & 1 & 0.1 & 100 & 1 & 5.72899 & 0.394245 & 0.92 \\
2 & 1 & 0.1 & 99.77 & 1 & 5.7273 & 0.393994 & 0.919 \\
3 & 1 & 0.1 & 98.81 & 1 & 5.72142 & 0.393337 & 0.916 \\
4 & 1.03 & 0.1 & 100 & 1 & 5.73143 & 0.391007 & 0.915 \\
5 & 1 & 0.1 & 99.99 & 1.03 & 5.72501 & 0.391539 & 0.914 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Solutions with the highest overall desirability.  
**Author Contributions:** Conceptualization, Y.X., Y.T., W.Y. and L.X.; methodology, Y.X., J.L., Y.T., W.Y. and L.X.; software, J.L.; validation, J.L.; writing--original draft preparation, J.L.; writing--review and editing, J.L., S.W. and Y.X.; visualization, J.L.; supervision, Y.X. and W.Y.; project administration, Y.X. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded in part by the National Natural Science Foundation of China under Grant number 61901022 and the Fundamental Research Funds for the Central Universities KG12-1124-01.  
**Conflicts of Interest:** The authors declare no conflict of interest.