Uncertainty Quantification of Transient-Based Leakage Identification: A Frequency Domain Framework

The leak detection methods in the frequency domain have presently become widely established among transient-based techniques. This study quantifies the uncertainty of the frequency domain multiple leak detection subjected to uncertain Gaussian, independent, and identically distributed measurements. The lower limit of the variances and covariances of the estimated leak locations and sizes are derived via the Cramer-Rao Lower Bound theory, whose derivation consistency with the Taylor expansion is also revealed. A systematic methodology based on the Monte Carlo simulations and probing waves is carried out to examine and verify the proposed formulations and corresponding outcomes, leading to an in-depth analysis of interactions between probing waves and leaks. The results justify the formation of points of minimum error in the pipeline corresponding to each specific harmonic wave, which has direct application in detectability using signals of limited bandwidth in actual practice. The findings resolve the reason behind localization failure for some test cases and success for others despite the same noise levels, as illustrated via numerical and experimental test cases. A workflow for efficient leak detection and the approach to estimating the corresponding localization uncertainty is proposed. According to the findings of this study, one may recommend the predicted error-location results to accompany the wave-based leak detection outputs to render a measure of accuracy in the identification process.