## 2 Model and Test Setup
### Localization Algorithm of AE Events: Simplex Method  
The time difference in the determined onset times at two different accelerometers can be computed and the set of these time differences enables the estimation of AE source location with a given wave  
Figure 4: The two-stage Akaike information criterion (AIC) method for estimation of an onset time of an acoustic emission signal: (**a**) the first-round estimation, (**b**) the second-round estimation. The vertical (voltage) resolution and the horizontal (time) interval in the 8-bit A/D converter were approximately 19.5 mV and 60 ns for this acquired signal.  
velocity of the medium. For AE source localization, we used the Simplex method, which is a kind of time-of-arrival localization method. This method is widely used due to its robust convergence characteristic. The Simplex method searches the minimum value of the mathematical functions by comparing the function value at each vertex in the space, taking advantage of specific iterative rules [11, 12, 34, 35].  
The error \(E\) can be calculated for an arbitrary point within the medium by comparing the computed onset time differences with the AIC-based onset time differences. Accordingly, the error value \(E\) is computed at every point in space, which is called error space. Herein, we determined the mean square error (or L2 norm error) as the error value \(E\). Finally, the point with the minimal error is localized as the source location of the AE event [35]. The L2 norm error was calculated every 1 mm interval in the x-y plane, as follows:  
\[E=\sqrt{\frac{\sum\limits_{i}\left(\left(t_{i}-\frac{\sum t_{i}}{n}\right)- \left(t_{i}-\frac{\sum t_{i}}{n}\right)\right)^{2}}{m-q}}, \tag{2}\]  
where \(E\) is the L2 norm error, \(t_{i}\) and \(tt_{i}\) are the onset time determined by AIC picker and the calculated arrival time at \(i\)th accelerometer, respectively, \(n\) is the number of accelerometers, \(m\) is the number of equations, and \(q\) is the degree of freedom. Meanwhile, the z-coordination for the AE source, or the depth \(z\), was fixed according to the artificial AE signal location. This simplified the source localization as the 2-D problem. In this study, we used the constant, pre-determined depth value: z = 4 cm, which is the middle depth of the raft thickness for all the cases.  
The source localization requires the medium wave velocity \(V\) as an input. Therefore, the representative wave velocity values for the RT, RB, and PM cases were found by using the Hsu-Nielsen (H-N) pencil-lead break and the accelerometers in the scaled PRF model. With four accelerometers attached to the top surface of the PRF, the artificial AE sources were generated on the raft top, the raft bottom, and the pile middle. For the RT and RB cases, the first arrival captured in the accelerometers corresponded to P-wave. Therefore, the RT and RB cases used the P-wave velocity \(V_{P}\) of 2450 m/s. Herein, the P-wave velocity \(V_{P}\) was determined with the time-difference-of-arrival (TDOA) method. For the PM case, the wave propagates through a pile with no confinement, which corresponds to the rod wave propagation. Therefore, the rod wave velocity \(V_{R\omega}\) of a cylindrical HDPE rod was determined using the free-free resonant column (FFRC) method, and this \(V_{R\omega}\) value of 1600 m/s was used for the PM case.  
We evaluated the accuracy of source localization by two approaches: Euclidean distance error and zonation based on the Voronoi diagram. First, the Euclidean distance error (EDE) was determined by calculating a distance from the estimated source location to the exact source location. Second, tessellated zones were produced by the Voronoi diagram to assign one pile to each zone. The accuracy was determined by comparing the estimated zone and the actual pile zone. Herein, the accuracy was expressed as a percentage point, based on 20 trials.