## 5 Conclusions  
Aiming to address the problems of low detection rate and serious artifacts of branch fillet weld defects, a regional wavelet denoising method based on FMC-TFM imaging is proposed. At the same time, the minimum rectangle method is used to extract the defect feature of the full-focus image. The inspection of a fillet weld of a narrow diameter branch pipe (branch pipe diameter \(\leq\) 50 mm) has always been a difficult problem in industrial inspections. In this paper, a real-time imaging detection system was developed based on the principle of FMC-TFM ultrasonic detection, and the fillet welds with a main pipe diameter of 90 mm and branch pipe diameter of 25 mm-45 mm were scanned and detected. At the same time, the images containing artifacts were saved. Then, regional wavelet denoising and adaptive denoising algorithms were used to denoise different regions of the image. Finally, the minimum rectangle method was used to extract the image features, and the location and size of weld defects were analyzed and combined with the welding process and pipe size information. The effective detection rate of various defects was 100%, the sensitivity of size quantization was 0.1 mm, and the sensitivity of angle quantization was 1\({}^{\circ}\). The length range of various defects was 2.3 mm\(-\)6.3 mm, the width range was 0.6 mm\(-\)0.8 mm, and the angle range was 52\({}^{\circ}\)-75\({}^{\circ}\). The defect location was highly consistent with the welding area. The subregion fusion denoising method eliminated the artifacts in the weld and non-weld center region, while the artifact elimination rate at the edge was relatively low. The work in this paper effectively reduces the interference of complex surface artifact features, further supports the defect recognition and intelligent classification of fmc-tfm images, and improves the detection rate and classification accuracy. However, there is the problem that the artifact elimination rate at the edge of the image was low, so it is necessary to eliminate the edge artifact further in order to realize the intelligent and accurate identification of branch fillet weld defects. In addition, the feature extraction method based on the minimum rectangle has the disadvantage of having a limited envelope. It is necessary to improve the envelope performance of the feature region further in order to more efficiently assist the risk assessment of the fillet weld of the branch pipe. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pipe Type** & **Defect Type** & **Length (mm)** & **Width (mm)** & **Center Position** & **Angle (\({}^{\circ}\))** & **Effectiveness** \\ \hline \multirow{2}{*}{T-90-25-B} & incomplete fusion & 3.90 & 0.70 & (43.90,15.10) & 72.0 & 100\% \\  & slag inclusion & 3.20 & 0.70 & (42.60,14.20) & 69.0 & 100\% \\ \hline \multirow{2}{*}{T-90-35-B} & root crack & 2.70 & 0.60 & (39.30,14.10) & 69.0 & 100\% \\  & incomplete fusion & 4.80 & 0.70 & (39.80,13.10) & 71.0 & 100\% \\ \hline \multirow{2}{*}{T-90-40-B} & lack of penetration & 3.80 & 0.80 & (45.00,13.90) & 73.0 & 100\% \\  & undercut & 4.50 & 0.70 & (45.40,14.90) & 73.0 & 100\% \\ \hline \multirow{2}{*}{T-90-45-DC} & lack of penetration & 6.30 & 0.70 & (43.90,19.40) & 72.0 & 100\% \\  & incomplete fusion & 4.90 & 0.70 & (45.50,17.00) & 74.0 & 100\% \\ \hline \multirow{2}{*}{T-90-45-B} & incomplete fusion & 5.60 & 0.70 & (44.40,16.80) & 75.0 & 100\% \\  & incomplete fusion & 4.70 & 0.60 & (45.20,16.50) & 71.0 & 100\% \\ \hline \multirow{2}{*}{Y-90-25-NB} & slag inclusion & 2.30 & 0.60 & (26.80,22.60) & 52.0 & 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Defect characteristics of welds. **Author Contributions:** Conceptualization, Y.W. ; methodology, Y.L. ; software, Y.B. and J.C.; validation, Y.W. ; formal analysis, Y.L. ; investigation, S.D. ; resources, S.D. ; data curation, Y.L. ; writing--original draft preparation, Y.W. ; writing--review and editing, Y.W. ; visualization, Y.L. ; supervision, S.D. ; project administration, H.W. ; funding acquisition, S.D.