Bayesian Update and Method of Distributions: Application to Leak Detection in Transmission Mains

Abstract

AbstractWater‐hammer equations are used to describe transient flow in pipe networks. Uncertainty in model parameters, initial and boundary conditions, and location and strength of a possible leak renders deterministic predictions of this system untenable. When deployed in conjunction with pressure measurements, probabilistic solutions of the water‐hammer equations serve as a tool for detecting leaks in pipes. We use the method of distributions to obtain a probability density function (PDF) for pressure head, whose dynamics are described by the stochastic water‐hammer equations. This PDF provides a prior distribution for subsequent Bayesian data assimilation, in which data collected by pressure sensors are combined with this prior to obtain a posterior PDF of the leak location and size. We conduct a series of numerical experiments with uncertain initial velocity and measurement noise to ascertain the robustness and accuracy of the proposed approach. The results show the method's ability to identify the leak location and strength in a water transmission main.