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

Alireza Keramat, Xun Wang, Moez Louati, Silvia Meniconi, Bruno Brunone, Mohamed S. Ghidaoui

Research output: Journal article publicationJournal articleAcademic researchpeer-review

35 Citations (Scopus)


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.

Original languageEnglish
Article number4019042
JournalJournal of Water Resources Planning and Management
Issue number10
Publication statusPublished - 1 Oct 2019
Externally publishedYes


  • Inverse transient analysis
  • Leak detection
  • Least square
  • Matched field
  • Matched-filter
  • Noise
  • Water hammer

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geography, Planning and Development
  • Water Science and Technology
  • Management, Monitoring, Policy and Law


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