Objective Functions for Transient-Based Pipeline Leakage Detection in a Noisy Environment: Least Square and Matched-Filter

Abstract

This paper addresses leak detection in the presence of measurement noise using the inverse transient method (ITM). The unknown leak parameters are determined by optimizing a merit function, which fits the numerically modeled pressures to measurements. Traditionally, the fitting is accomplished by a least-square (LS) objective function that minimizes the L2 distance between the model and data. However, in practical problems where the environment is noisy, the minimum L2 distance may result in some fictitious leaks. This paper proposes an alternative objective function, known as matched-filter (MF) in the literature, which is expected to produce a more robust localization in a noisy environment because it maximizes the signal-to-noise ratio (SNR). This function is then compared with the conventional LS approach by assessment of leak-detection accuracy. It was proved that the MF estimator has smaller mean square error of leak localization than LS when signals have high noise level (SNR≤3 dB). For a low noise level, the two estimators converge to the same results. The conclusions were supported by numerical and experimental case studies.