# Enhancing Impact Localization from Fluid-Pipe Coupled Vibration under Noisy Environment
## 1 Introduction
There has also been much work on wavelets of water pipelines [18; 19; 20; 21; 22]. In particular, most of the work done to detect burst or leaks has been dedicated to pressure transients with intrusive pressure sensors [23]. However, the pressure sensors have low sensitivity and therefore do not easily detect impact signals, except for big ones, such as a water hammer or pipe rupture. To cope with catastrophic damage earlier on, it is necessary to pick up relatively small but indispensable impact or burst signals with high accuracy. In this study, signals from impacts to a pipeline or caused by exterior strikes, such as inattentive third-party digging, were taken into account. Considerably more often, damage is caused by people: accidental events from careless digging or those related to building or repair work in the proximity of the pipeline [24]. Compared to pressure transients, impact signals are small and hard to detect by pressure sensors due to their low sensitivity to structural vibration. It is noteworthy that detecting small impact signals is becoming more important for finding degradation in the forms of small leaks, structural degradation, cracks, and so on, for effective monitoring and protective management of assets. Dynamic wave modes of pipelines are able to provide fertile information for detecting events that could do more harm than good to the pipe structures. It is also of particular importance to find where a failure is. Identifying the exact position of a pipe failure is vital to hasten pipeline repairs and maintenance [25]. Knowing the time difference of arrival (TDOA) between sensors must be known to localize an event along the pipelines. Large diameter pipelines, such as water transmission mains, are regarded as one-dimensional (1D) structures for low-frequency wave propagation, which means that source localization can be done adequately with just two sensors. Nevertheless, in practice, TDOA is hard to obtain precisely due to other general noises. Even though various methods have been proposed and developed to estimate TDOA in noisy (including reverberations in a space) environments [26; 27; 28; 29], it is still challenging to estimate accurately time differences buried in noise. These motivated us to develop a way to detect the coupled waves propagating through pipelines by reducing noise and also by localizing the impact sources that induce the waves. Thus, the first problem is associated with how to lessen noise effectively and then how to estimate a time difference accurately between a pair of sensors. To obtain a time difference embedded in noise, we have to know the distinctive characteristics of the noise and of the signal that contains the time difference. Noise can be assumed to be inherently random and uncorrelated (such as white noise) or to be part of a banded spectrum. The latter has decreasing energy because the frequency is contained within a band, such as pink noise, which is known to be ubiquitous in daily life [30], and traffic noise [31]. The waves we want to pick up generally have a specific band-limited characteristic in its own frequency range with respect to each piping system. Based on the distinguishable features, many methods have been proposed and developed. In particular, wavelet analysis has been widely adopted as an effective way to reduce noise and detect specific temporary features of target signals. We propose a methodology that is able to detect fluid-pipe structure-coupled waves propagating through pipelines, using a wavelet-based algorithm in a noisy environment, and then localize where the impact sources are. Clearly, the objectives of this work were to (a) employ quasi-longitudinal waves, which propagate via coupling between liquid and the pipe structure, (b) propose wavelet-based signal processing for noise reduction and for improving signal detectability, and (c) estimate precisely the arrival times at each sensor and then quantitatively compare the results of the proposed approach to those achieved using the conventional cross-correlation algorithm.