## 6 Conclusions  
This paper proposes a novel joint localization method of AE source based on TDOA method and beamforming method. By using the AE signal from finite element simulation, the performance of TDOA method and beamforming method of four sensors arranged on the plate are studied in detail. Aiming at the advantages and disadvantages of the performance of the two methods, a joint localization method is proposed. The performance of joint localization method is verified by simulation and experiment. Both simulation and experimental results show that the joint localization method not only improves the accuracy of the TDOA method, but also greatly reduces the localization calculation cost of the beamforming method.  
Conceptualization, T.H., X.W. and X.L.; Methodology, X.W. and T.H.; Validation, X.W.; Writing--Original Draft Preparation, X.W.; Writing--Review and Editing, X.W., X.L., T.H., J.T. and Y.S.; Supervision, T.H.; Project Administration, T.H.; Funding Acquisition, T.H. All authors have read and agreed to the published version of the manuscript.  
This work was finally supported by the National Natural Science Foundation of China (Grant No. 51675023), the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Actual Location**} & \multicolumn{1}{c}{**TDOA Localization**} & \multicolumn{1}{c}{**Beamforming**} & \multicolumn{1}{c}{**Beamforming**} \\ \hline x (mm) & y (mm) & Result (mm) & Scanning Region & Localization Result (mm) \\ \hline
100 & 600 & (\(-42\), N.A.) & \(<\)1\(>\) & (\(100,560\)) \\
160 & 600 & (\(113\), N.A.) & \(<\)1\(>\) & (\(160,590\)) \\ \hline
220 & 210 & (\(215\), \(71\)) & & (\(220\), \(200\)) \\
220 & 450 & (\(220\), N.A.) & & (\(220\), \(440\)) \\  & 510 & (\(196\), N.A.) & \(<\)2\(>\) & (\(220\), \(500\)) \\
280 & 270 & (\(280\), \(390\)) & & (\(280\), \(260\)) \\  & 390 & (\(283\), \(598\)) & & (\(280\), \(390\)) \\ \hline
340 & 330 & (\(343\), N.A.) & & (\(340\), \(330\)) \\  & 500 & (\(344\), N.A.) & \(<\)3\(>\) & (\(340\), \(500\)) \\
400 & 270 & (\(402\), \(224\)) & & (\(400\), \(250\)) \\  & 390 & (\(403\), \(253\)) & & (\(410\), \(400\)) \\ \hline
560 & 210 & (\(460\), \(169\)) & & (\(560\), \(190\)) \\  & 450 & (\(467\), \(229\)) & \(<\)4\(>\) & (\(570\), \(450\)) \\  & 510 & (\(454\), \(212\)) & & (\(570\), \(530\)) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Experimental localization results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Localization Accuracy (mm)** & **Beamforming Method (s)** & **Joint Localization Method (s)** \\ \hline
10 & 2.03 & 0.53 \\
5 & 8.49 & 2.46 \\
2 & 49.16 & 12.08 \\
1 & 193.26 & 50.67 \\
0.5 & 780.19 & 198.16 \\
0.2 & 4887.19 & 1234.80 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The comparison of the average calculation time between the beamforming method and the joint localization method under different localization accuracy.  
Education, Northeastern University (VCAME201904) and the Academic Excellence Foundation of BUAA for PhD Students.  
**Acknowledgments:** We thank other members of our lab who provided valuable and constructive suggestions.  
**Conflicts of Interest:** The authors declare no conflict of interest.