# Enhancing Impact Localization from Fluid-Pipe Coupled Vibration under Noisy Environment
## 1 Introduction  
Water transmission mains are crucial parts of water utilities and important assets in the infrastructure of a country. Transmission mains are designed to move large quantities of water from the supply source and to provide water to the smaller distribution mains. The transmission main are usually almost straight with few branches for long distances. The likelihood of a transmission main failure is actually lower than for other piping systems because they are typically more substantial in design. However, when they do occur, the consequences of failure for a transmission main are much greater than those for a smaller distribution main. There is a greater chance of flooding and infrastructure failure due to the larger volume of water that would be expected to escape from a leaking or ruptured main. Pipeline failure is typically attributed to aging infrastructure, severe environmental conditions, and third-party damage [1, 2]. Pressure monitoring has served as one of the most popular management interventions [3], and recently, unsteady pressure patterns [4] have been examined to improve the detectability of pressure transients by vibration sensing. Some frequency contents of vibration have distinguishable features that are not within the range measured by conventional pressure sensors. The dynamic oscillation of structures tells much about their own structural integrity and status, non-destructively [5, 6, 7, 8]. The dynamic response is generally induced by broad-band excitation, such as that which occurs from impacts. From water hammers (pressure transients) to unpredictable strikes, abruptexcitations often happen to pipelines: sudden body-to-body contacts of pipe structures, including valve-related issues, pipe bursts due to an abrupt crack opening, third-party damages, and so on. Such impacts generate structural resonance, and various waves propagate through the water and along the pipe from the excitation point. Cylinders that are filled with liquid produce and develop particular waves that are different from those without liquid [9; 10]. Water transmission mains have enough pressure inside the pipe to move large amounts of water, and this often completely fills the pipe with water. The interaction between water and the cylindrical shell makes a coupled motion in the cylindrical section, and one predominant axisymmetric wave propagates along the axial direction of the pipe. Such waves, also known as quasi-longitudinal waves, are predominantly fluid-based waves with some radial motion associated with the shell compliance [11]. The coupled waves can reach farther than elastic shear waves can because most of the energy of the coupled waves is in a lower frequency range than that for elastic waves [9; 12]. This certainly allows for longer-range monitoring with vibration signals for water transmission mains. When applying additional sensors to monitor the buried pipe structure, it might be highly desirable to use non-destructive sensing techniques [13; 14]. The coupled waves are axisymmetric dilatational waves, predominately in the form of longitudinal waves in the pipe wall with some radial motion, thanks to Poisson coupling [15; 16]. Vibration sensors are a kind of non-intrusive sensor that is able to detect the coupled behavior of a pipe structure with high sensitivity. The vibration sensors have a flat frequency response and are generally more sensitive than pressure sensors; therefore, noise easily contaminates vibration signals. The noise from many sources is transferred through the ground to a pipeline and is certainly measured by the vibration sensors. This may prevent us from observing signals of interest. Therefore, it is inevitable to remove or reduce noise to make a stable and reliable test and evaluation. Many researchers have long sought ways to manage noise to improve signal detectability in various fields. Wavelet analysis has been a promising way to reduce noise and extract singular features of signals [17].