Leak detection using parameter identification L. Torres * G.Besan¸con ** C. Verde * * Instituto de Ingenier´ ıa, UNAM, 04510 DF, M´ exico, Mexico (ftorreso@iingen.unam.mx, verde@unam.mx). ** Control Systems Dep., Gipsa-lab, Grenoble INP, BP46, 38402 Saint-Martin d’H` eres, France (Gildas.Besancon@gipsa-lab.inpg.fr) Institut Universitaire de France. Abstract: This work proposes an approach to detect single and multiple leaks. The task is carry out by identifying the parameters of finite models associated with the leak events. The identification problem is attacked by using the Prediction Error Method (PEM). In addition, a frequency evaluation is realized to check the conditions for implementing the PEM or any other method which require an excitation condition. Keywords: Leak detection, parameter estimation, hydraulic systems. 1. INTRODUCTION Water is the most precious resource on the earth, reason by which leak detection methods have become issues of primary relevance in modern hydraulic networks. The pur- pose of the detection methods is to obtain information in time on the leak location to avoid undesirable conse- quences. There are some classic approaches based on well-known di- agnostic algorithms which have been presented in Billman and Isermann (1984), Allidina and Benkherouf (1988). These approaches are adequate for the detection of a unique leak. Another relevant detection methods use the characteristics of the pressure wave when a leak occurs, see Brunone and Ferrante (2001); Wang (2002). In general, these mentioned methods require an adequate quantity of sensors along the pipeline. However, they can not be used to detect more than one leak in a pipe section delimited by a pair of (flow or pressure) sensors at each end. The reason is the lack of information when the pipeline is in steady state. Additionally, the bandwidth of sensors limit the measuring of transients generated by the presence of leaks. One way to obtain detectability for every leak position in the case of multiple leaks, is to provide some excitation to the system. This allows to recover a frequency response diagram with the additional information. Frequency re- sponse analysis have shown to be well-liked for use in leak detection. The frequency response describes how the pipeline responds at various frequencies by relating the amplitude and phase of the system input and output at each frequency. The characteristics of the pipeline can be extracted by using any frequency sweeping technique. The unique re- quirement is that the frequency content of the input signal should be as high as possible such that maximum infor- mation is extracted from the pipeline. An example of a wide bandwidth signal is a single sharp pulse that can be generated through the fast perturbation of a valve as is suggested by Lee et al. (2008), or sinusoidal oscillations at various frequencies as is proposed in Covas et al. (2005), Sattar and Chaudhry (2008). Summarizing, there are many other ways to extract the frequency response of a pipeline as well as many other relevant frequency approaches not discussed here. They are at hand in Ferrante and Brunone (2003); Lee et al. (2005b,a), or in the surveys Ghidaoui et al. (2005) and Colombo et al. (2009). Most of these frequency approaches utilize some signatures in the frequency response diagram to estimate the position or the magnitude of leaks. We propose in this work, to handle the leak detection issue as a problem of parameter identification, such that we can use efficiently the frequency information provided by the excitation of the system at certain frequencies. The principal advantage of our approach over the other frequency-sweep-based methods is that the estimations of the positions and magnitudes of the leaks are obtained directly, avoiding the interpretation of signatures or pat- terns. Fault detection via parameter identification relies in the principle that possible faults in a monitored system are associated with specific parameters and states of the mathematical model of the system given in the form of an input-output relation. For a better understanding of the concept is recommended to read the books written by Isermann (2011) and Isermann and M¨ unchhof (2011). Leaks in a pipeline can be seen as fault events associated to certain parameters to be considered in a model, such as the positions and magnitudes of the leaks. As an option, a finite model can be obtained by solving approximately the Water Hammer equations. Once obtained the finite model, leak equations and their associated parameters can be included in it. Preprints of the 8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SAFEPROCESS) August 29-31, 2012. Mexico City, Mexico Copyright © 2012 IFAC. All rights reserved. 910