## 5 EKF-Based Approach for AE Source Localization during Quasi-Static Tensile Test  
### Mechanical Test and AE Monitoring  
Tensile test experiments were performed on the above presented aluminum plate at the Acoustics Laboratory of Le Mans University. For these experiments, we used the same data acquisition system with the same settings and the same AE sensors as well. The latter were synchronized and triggered by one of them once the first detected signal exceeds the predefined threshold. A properly calibrated tensile test INSTRON hydraulic machine was used with a constant displacement rate. The load cell capacity of the test machine is 100 kN, where specimens were loaded at 1 mm/min. It is naturally expected that cracks will be generated from the notch and propagate through the specimen. The acoustic activity is simultaneously recorded with mechanical test data until the overall failure of the specimen. The acquired AE signals are processed following the EKF-based localization procedure described in Section 3. Figure 8a shows the aluminum plate mounted on the testing machine as well as the distribution of the AE sensors. Before the application of the tensile load, preliminary tests were performed in order to determine the AE acquisition threshold. Indeed, the latter was set at 45 dB in order to avoid the detection of signals emitted by the noisy environment. Once the quasi-static test is over, we obtain the results shown on Figure 8b. The latter shows that the cumulative AE events are in accordance with the different stages which characterize the evolution of the load as a function of time. We first note that in the elastic domain (1), where the load is between 0 kN and \(\sim\)31 kN, the AE is almost absent and only few AE signals are detected. Damage is initiated beyond the yield point (2), where a sudden increase in the AE activity is observed. Within the uniform plastic strain domain which extends between the yield point and the ultimate strength \(\sim\)34.5 kN, strong AE peaks become visible. These relatively high energy signals are associated with the initiation and propagation of crack. The failure domain of the specimen begins as \begin{table}
\begin{tabular}{c c c c c c c c} \hline AE Source & \begin{tabular}{c} **X Coordinate** \\ **of Source** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Estimated** \\ **X Coordinate** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Error in X** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Y Coordinate** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Estimated** \\ **Y Coordinate** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Error in X** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Group** \\ **Velocity** \\ **(m/s)** \\ \end{tabular} \\ \hline _PLB 1_ & 15 & 17.2 & 14.67 & 30 & 28.12 & 6.26 & 3635 \\ _PLB 2_ & 30 & 30.04 & 0.16 & 30 & 30.08 & 0.27 & 3264 \\ _PLB 3_ & 20 & 18.95 & 5.25 & 40 & 41.82 & 4.56 & 3575 \\ _PLB 4_ & 20 & 19.92 & 0.39 & 55 & 54.94 & 1.92 & 3470 \\ _PLB 5_ & 30 & 30.90 & 3.01 & 55 & 56.04 & 1.92 & 3461 \\ _PLB 6_ & 45 & 43.71 & 2.86 & 55 & 55.27 & 0.49 & 3526 \\ _PLB 7_ & 55 & 53.89 & 2.00 & 55 & 57.59 & 4.71 & 3562 \\ _PLB 8_ & 65 & 65.63 & 0.97 & 70 & 71.12 & 1.60 & 3.551 \\ _PLB 9_ & 65 & 64.17 & 1.27 & 45 & 45.91 & 1.94 & 3417 \\ _PLB 10_ & 30 & 31.63 & 5.44 & 40 & 42.54 & 6.17 & 3124 \\ _PLB 11_ & 40 & 42.62 & 6.55 & 55 & 56.00 & 1.61 & 3547 \\ _PLB 12_ & 50 & 52.70 & 5.41 & 55 & 56.90 & 5.13 & 3071 \\ _PLB 13_ & 55 & 55.46 & 0.84 & 45 & 44.31 & 1.51 & 3506 \\ _PLB 14_ & 50 & 52.73 & 5.47 & 70 & 68.01 & 2.64 & 3167 \\ _PLB 15_ & 40 & 40.95 & 2.38 & 45 & 43.28 & 3.92 & 3631 \\ _PLB 16_ & 30 & 31.89 & 6.31 & 70 & 68.73 & 1.73 & 3462 \\ _PLB 17_ & 45 & 43.15 & 4.10 & 70 & 68.18 & 2.52 & 3501 \\ _PLB 18_ & **40** & **40.21** & 0.53 & 30 & 32.66 & 8.56 & 3213 \\ \hline \end{tabular}
\end{table} 
Table 1: Location data of the AE sources based on the EKF method and their corresponding group velocities. soon as the stress begins to drop, until the final rupture.