Leak Detection, Isolation and Estimation in Pressurized Water Pipe Networks Using LPV Models and Zonotopes

In this paper, a leak detection, isolation and estimation methodology in pressurized water pipe networks is proposed. The methodology is based on computing residuals which are obtained comparing measured pressures (heads) in selected points of the network with their estimated values by means of a Linear Parameter Varying (LPV) model and zonotopes. The structure of the LPV model is obtained from the non-linear mathematical model of the network. The proposed detection method takes into account modelling uncertainty using zonotopes. The isolation and estimation task employs an algorithm based on the residual fault sensitivity analysis. Finally, a typical water pipe network is employed to validate the proposed methodology. This network is simulated using EPANET software. Parameters of LPV model and their uncertainty bounded by zonotopes are estimated from data coming from this simulator. A leak scenario allows to assess the effectiveness of the proposed approach.

[1]  F. Schmid,et al.  A New Fault Diagnosis Algorithm that Improves the Integration of Fault Detection and Isolation , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 2002 .

[3]  Vicenç Puig,et al.  Robust Fault Detection with Unknown-Input Interval Observers using Zonotopes , 2008 .

[4]  Vicenç Puig,et al.  Identification for Passive Robust Fault Detection of LPV Systems using Zonotopes , 2009 .

[5]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .

[6]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[7]  Didier Henrion,et al.  GloptiPoly 3: moments, optimization and semidefinite programming , 2007, Optim. Methods Softw..

[8]  Giuseppe Carlo Calafiore,et al.  Identification of Reliable Predictor Models for Unknown Systems: a Data-Consistency Approach based on Learning Theory , 2002 .

[9]  Vicenç Puig,et al.  OBSERVER GAIN EFFECT IN LINEAR INTERVAL OBSERVER-BASED FAULT DETECTION , 2006 .

[10]  J. Bokor,et al.  Failure detection for quasi LPV systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[11]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[12]  Giuseppe Carlo Calafiore,et al.  Interval predictor models: Identification and reliability , 2009, Autom..

[13]  Jeff S. Shamma,et al.  Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations , 1993 .

[14]  Stéphane Ploix,et al.  Parameter uncertainty computation in static linear models , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).