Leak diagnosis in pipelines based on a Kalman filter for Linear Parameter Varying systems

Abstract

This paper proposes a new approach for the leak diagnosis problem in pipelines based on the use of a Kalman filter for Linear Parameter Varying (LPV) systems. Such a filter considers the availability of flow and pressure measurements at each end of the pipeline. The proposed methodology relies on an LPV model derived from the nonlinear description of the pipeline. For the Kalman filter design purposes, the LPV model is transformed into a polytopic representation. Then, using such a representation, the LPV Kalman filter is designed by solving a set of Linear Matrix Inequalities (LMIs) offline. In the online implementation, the observer gain is calculated as an interpolation of those gains previously computed at the vertices of the polytopic model. The main advantages of this approach are: a) the embedding of the nonlinearities in the varying parameters allows the quasi-LPV system to be obtained which is equivalent to the original nonlinear one, and; b) the use of the well-known LMIs to compute the Kalman gain allows the extension to the LPV case. Those aspects are the main advantages with respect to the classic design of the Extended Kalman Filter (EKF) that requires a linearization procedure and the solution of the Ricatti equation at each iteration. To illustrate the potential of this method, a test bed plant built at Cinvestav-Guadalajara is used. Additionally, the results presented are compared with those results obtained through the classical EKF showing that LPV Kalman observer outperforms the classical EKF.