Transient wave-based method with Bayesian MCMC Metropolis-Hastings for leak localization in water pipes under α -stable noise

Transient wave-based techniques for leak detection have garnered significant attention due to their high efficiency and accuracy. However, they are yet to be effectively applied to practical pipe systems, primarily due to their inability to adequately handle the various complexities and uncertainties encountered in real-world applications. Among these challenges is the presence of noise within the pipe system and measurement devices, where recent studies indicate significant portion of this noise largely follows a α-stable distribution model. To address this practical challenge, the study introduces a robust Bayesian framework for transient-based leak detection that overcomes a critical limitation arising from the reliance on Gaussian noise assumptions; while traditional methods often fail when faced with impulsive, heavy-tailed noise characteristics, this research explicitly incorporates an α-stable distribution to model non-Gaussian ambient and measurement noise in the pipe system, and simultaneously quantify leak parameters, including key water-pipe uncertainties, such as wave speed and friction factor. Using the transient wave-based method as a forward approach, an inverse Bayesian Markov Chain Monte Carlo approach is formulated, specifically with the Metropolis-Hastings algorithm, to process observed signals contaminated by α-stable noise, and estimate the posterior probability densities of the unknown parameters; while eliminating the need for signal pre-processing or filtering. Despite the challenges posed by noise, the proposed algorithm successfully estimates (1) leak location and magnitude for small leaks under differentα values, even for signal-to-noise-ratios as low as SNRα=−4dB; and (2) uncertainties in both water-pipe wave speed and friction factor. Numerical tests are performed in scenarios involving single and multiple leaks; finally, the proposed approach is validated by recent laboratory experiments, where unfiltered signals are processed within symmetric and asymmetric α-stable likelihood frameworks, through which unknown leaks and pipe parameters are successfully estimated, leading to conclusions based on the key findings and their implications.