## 3 Examination of 3D SIBIE Procedure
### 3D SIBIE Procedure Improved with Signal Amplification  
As explained in this study, the 3D SIBIE procedure is developed based on 3D model with the use of the multiple-sensor array. The procedure is successfully applied for the case studies of the targeted concrete specimen for the laboratory test by employing the accelerometer array unit and the laser doppler vibrometer for detecting signals as well as the case of the existing RC deck in service. As the results, the extension of the 2D computation process for the conventional SIBIE procedure to 3D coordinates enables to visualize the interior damage. The 3D SIBIE procedure has a great promise for on-site and non-contact measurement and potentially could be used to operate remote and rapid damage inspection and material assessment for concrete structures. The 3D SIBIE procedure do not consider the attenuation of propagation in elastic waves so that the results described above in Figures 14-17, relatively high reflection intensity is found even in the intact area of interest. Since the amplitude in frequency domain of the signal detected at the receiving point with the accelerometers or LDV by reflection of elastic wave becomes smaller as its propagation distance becomes longer, it is considered that the deeper the detection depth in the targeted volume, the smaller the reflection intensity mathematically in the result of signal computing process of the SIBIE procedure. Pile Integrity Test (PIT) utilizes a simple principle of elastic wave characters to assure the quality of the concrete pile. When elastic waves are excited at the pile head, it is assumed that elastic waves travel at the speed of \(C\) inside the concrete pile shaft, and the pile length can be determined by measuring the time lapse of \(T\). Based on the detected signal waveform between the time of hammering and the time of receiving reflections on pile head, as shown in Figure 18, the amplitude of the reflected wave is attenuated due to the effect of geometrical or internal damping of the materials during the propagation. Thus, in the applied technique for in-situ measurement, an exponential amplification function is applied across the recorded waveform to amplify the low energy reflection peaks from the pile toe and other internal defects such as voids and cracks [16; 17; 18]. In the same manner as in the signal amplification method of PIT principle, the method is also introduced for the 3D SIBIE procedure to correct the reflection intensity in the visualization results. Figure 19 shows some examples of actually recorded signals with the accelerometer sensor array, explained in Figure 13, followed by hammering at concrete surface. In order to define an exponential function for signal amplification in consideration with the signal attenuation through the targeted concrete, an exponential function is derived for each data set from the obtained waveforms as in Figure 20.  
Figure 17: 3D SIBIE result with LDV signal detection for intact concrete specimen. The respective functions for each recorded data can be used to calibrate the attenuation of the detected signals. By using the calibrated data according to the signal amplification function, as shown in Figures 21-24, the visualization images of reflection intensity are modified by the 3D SIBIE procedure. The results indicate that the visualized images are changed due to the improved signal processing. Figure 19: Detected signals at accelerometers with a hammer strike. Figure 20: Signal attenuation along wave propagation in sensor distance. Figure 18: Principle of PIT (Pile Integrity Test). This means that reflection intensities at the damage-simulated part with styrofoam is sufficiently high compared to those at an intact part without the consideration of the attenuation effect during elastic waves propagation. On the other hand, as for intact cases, the relatively high reflection intensities expressed in the intact part are perfectly removed and only the high reflection at 400-mm depth corresponding to the boundary of the specimen is obtained.