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Fault detection using PDE-based observer in transport flow.

Hermine Som Judith Idellette1, Vincent Cocquempot2, Abdel Aitouche3

  • 1National Higher Polytechnic School of Douala- University of Douala, P.O. BOX 2701, Douala, Cameroon; University of Lille - UMR 9189 - CRIStAL, Lille, France.

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|September 9, 2023
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Summary

This study introduces a robust observer for detecting faults in water distribution systems (WDS). The method accurately estimates unmeasured signals, enabling effective leakage detection with adaptive thresholds.

Keywords:
Fault detectionHyperbolic systems of balance lawsLeakage detectionPDE-based observerTransport flow element

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Area of Science:

  • Control Systems Engineering
  • Fluid Dynamics
  • Network Analysis

Background:

  • Distribution flow networks face challenges with continuously varying boundary conditions.
  • Accurate state fault detection is crucial for operational efficiency and safety in water distribution systems (WDS).
  • Existing methods may struggle with the dynamic and complex nature of WDS.

Purpose of the Study:

  • To design a robust state fault detection scheme for distribution flow networks.
  • To develop a partial differential equation (PDE) observer for transport flow systems.
  • To enable on-line estimation of unmeasured signals for improved fault diagnosis.

Main Methods:

  • Design of a PDE detection observer based on nonlinear hyperbolic systems of balance laws.
  • Utilizing backstepping theory for observer construction in an anti-collocated setup.
  • Proving the stability of the error equation for observer reliability.

Main Results:

  • The observer provides on-line estimation of unmeasured signals.
  • Fault detection is achieved using estimation and observability time with an adaptive threshold.
  • Validation on real water distribution system (WDS) data demonstrated effective leakage detection.

Conclusions:

  • The proposed PDE observer and fault detection method are effective for WDS.
  • The approach enables timely and accurate leakage detection.
  • The method confirms the practical applicability of advanced control techniques in WDS management.