# Enhancing Impact Localization from Fluid-Pipe Coupled Vibration under Noisy Environment
## 3 Results and Discussion  
### Data Preparation and System Characterization  
The methodology proposed here was tested using real vibration data, which were measured by the data acquisition system shown in Figure 6b, and the data were filtered with a low-pass filter with a cut-off frequency of 300 Hz. This is because frequencies above 300 Hz are very dispersive, as we can see in the dispersion curves of the coupled waves in Figure 1.  
An example of a vibration signal measured is shown in Figure 7a. The upper figure is the signal measured at S1, and the coupled wave can be identified around 0.16 s. The vibration signal measured at S2 is the lower one in Figure 7a. It also contains the wave that propagates through the pipe around 0.45 s, but the waveform looks quite different from that in the upper figure. It has a smaller magnitude and fewer oscillations than the above one. The latter parts of the signals after 0.5 s can be regarded as just background noise of the pipeline system. The frequency responses of the signals were obtained by taking a Fourier transform, as shown in Figure 7b, of which the magnitudes are in the vibration acceleration  
Figure 6: Schematics for experiments; (**a**) pipeline layout on map, (**b**) measurement setup at each sensing point, (**c**) pipeline and locations of sensors and impact hammer (the sensors and hammer are exaggerated). level (VAL, dB re 1 [\(\mu\)m/s\({}^{2}\)]) [40]. The frequency spectra of the signals are in black and the background noises of the system are in red. By comparing them, the characteristics of signals are clearly observable at each place. Specifically, the dominant frequency range of the signal at S1 is 70-120 Hz and 30-60 Hz for S2. As we can see in this figure, the two frequency responses are different, even if they are in the same transmission main. This might be because they have different transfer functions due to different boundary and environmental conditions. This led us first to identify the frequency characteristics of the system to be monitored before applying the proposed procedure. Figure 7: Vibration signals measured at S1 and S2 and their frequency responses; (**a**) vibration accelerations, (**b**) frequency responses of the acceleration signals in black and background noises in red (VAL: Vibration Acceleration Level, dB re 1 \(\mu\)m/s\({}^{2}\)). To find out the location of the impact inducing the coupled waves, the wave speed should be identified a priori. The wave speeds in water pipes are highly dependent on the pipe wall and water properties, as indicated in Equation (1). The wave is dispersive with respect to frequency and also varies according to the pipe dimensions, as shown in Figure 1. The vibration induced by water-pipe coupled waves are predominantly low-frequency waves [32], and it is noteworthy that they are almost non-dispersive in the low-frequency range. A separate experiment for estimating wave speed was performed in the pipe section. In this experiment, impact events were caused at one location, then measurements were done at the various locations available within this testbed (Figure 6a). Thirty impacts were caused to estimate the speed with a mean value and standard deviation. The results from the experiments are given in Figure 8, where we plotted the wave speed, estimated as a function of the distance of the measurement points from the impact location. The wave speed tends to gradually increase and saturate as the distance goes up, which well corresponds to the dispersion curve in Figure 1. Therefore, it may be tightly associated with the dispersive features regarding frequency. In other words, it is certainly possible to have faster wave speed over a longer distance because waves at low frequencies are apt  
has the maximum peak around 0.142 s in time and 700 in scale, and the ridge of the peak does not extend to a high scale. There are also a couple of burst noises followed by the coupled signal, and the noises have larger value as the scale increases.