## 5 Verification of the Proposed Scheme by Parametric Study  
In order to test and verify the performance of the proposed pile defect identification scheme based on wavelet packet transform (Method 1), a parametric study using ABAQUS/Explicit [33] was performed on various FEM models of defective piles by varying the parameters and conditions of the simulated pile cases shown in Figure 8b-j into six datasets, as shown in Table 4. The range of the input parameters shown in Table 4 covered various extent and location or position of the defects shown in Figure 8, from small to large, narrow or wide, and long or short. In Table 4, \(E_{1}\) and \(E_{2}\) refer to the modulus of elasticity values for the intact and defective pile, respectively, \(D_{\text{n}}\) is the maximum diameter of the neck defect, \(D_{\text{b}}\) is the maximum diameter of the bulge imperfection, while the rest of the material parameters are as described in Section 4. Similarly, the depths \(z_{1}\) and \(z_{2}\) in Table 4 indicate the variations of the position of the geometric defects in reference to Figure 8. The objective of the parametric study was to compare with the conventional method of evaluation by nonlinear amplification of the original signal without WPT applied (Method 2), as described in Figure 11, as well as to determine if there were any limitations of the proposed method presented. Table 5 shows a comparison of the detection ratio between the two methods of pile defect diagnosis from the parametric study, in which the detection ratio was rated as high = 1.0, medium = 0.5, and low = 0, as shown. In most cases, the low-frequency components of WPT applied to the signals at the third level of decomposition had yielded a clear resolution and identification of the feature parameters. As shown in Table 5 and Figure 12, the superiority of the identification scheme based on the WPT method was seen for the detection ratings of 1 against 0 using the conventional evaluation method without WPT applied. As shown, method 2 contained more dark colors on the contour plot, indicating lower detection ratios, especially at cases c, d, e, and f. This means that method 2 had difficulty in detecting segments with weak concrete, neck defects, bulge imperfections, cracks, and notches in comparison to method 1. Using method 2, segments with weak concrete were hardly detected if \(E_{2}\) was almost the same as  
Figure 11: Amplification and WPT decomposition of the signal. and were moderately detected if the length and area of the very weak segment (e.g., \(E_{2}\) = 7, 10, 15 GPa) were short and small. In addition, neck defects and bulge imperfections were hardly detected if the defects were small (\(D_{\text{n}}\geq 0.8D\), \(D_{\text{b}}\leq 1.1D\)) and if the segment with the defect was long. Moreover, notches and cracks were hardly detected if it was located nearer to the top of the pile and if the depth of the defect was shallow. A comparison was made for the velocity waveform of the amplified signals shown in Figures 13-18 with and without WPT applied, which clearly showed the identified feature parameters and noise suppression of the signal with WPT. Based on the observations of the velocity waveforms for pile defects due to reduction in the area of the pile section, it was not possible to distinguish among a neck, crack, and void when the length of the neck or void was short, as shown in Figures 14, 17 and 18. Similarly, a very short extent of a weak pile segment might be misinterpreted to be a defect due to a reduction in cross-section area, as shown in Figure 13, especially when the measured reflection time at the pile tip \(T\) was almost equal to the reference time \(T_{r}\). On the other hand, the reflections from a reduced pile area defect could be distinguished from a notch or crack if the extent of the defect was long, as shown in Figure 15, although it might be difficult to distinguish it from being a long necking or a long and narrow void.