Separation of pressure signals caused by waves traveling in opposite directions

Hydraulic transient analysis allows the condition assessment of pipeline systems by the measurement of a system's transient pressure response subject to input pressure excitations. The detection of a pressure wave's arrival time and amplitude at one or more sections can be used to detect unexpected anomalies, such as leaks, blockages, or corroded sections. Wave separation approaches, based on signal processing techniques involving two sensors, enable a directional attribution to any measured pressure perturbations. Being able to determine the direction of origin of a perturbation through a signal-splitting approach greatly facilitates anomaly detection through the resolution of this ambiguity. The signal-splitting procedure can be sensitive to the analysis conditions (i.e. the signal processing procedure used, the presence of noise within the signal, and the spacing of the sensors) and, as a result, produce spurious results. This paper explores this issue and proposes, and analyses, a range of strategies to improve the signal-splitting results. The strategies explored involve the consideration of alternative time and frequency-domain formulations; the use of filters and wavelet to condition the signal; and processing the time-shifted differenced signal as opposed to the original raw signal. Results are presented for a range of numerical and laboratory systems.