Reconfigurable Model for Multi-leak Location in a Pipeline C Verde 1 Instituto de Ingenier´ ıa-UNAM, M´ exico verde@servidor.unam.mx Abstract A novel approach is presented for leaks detection and isolation in pipelines via the use of updating residual generators. To overcome the isolability problem for 2 leaks when only 2 sensors are used, the approach as- sumes a fluid model discretized in 3 sections in which their divisions depend on the unknown leaks posi- tions and they can be only identified when leaks are present. The key of the isolation scheme is the search of the positions z 1 and z 2 from a value set which satisfies physical constraints and at the same time minimizes the residual gain with respect to (z 1 ,z 2 ). Simulation examples with one and two leaks show the effectiveness of the leak diagnosis method. Keywords: Leak detection, updating residual gener- ator, model based approach for fault detection and isolation. 1 Introduction Safety and environmental issues associated with pipelines leaks are a growing concern. Leak detection can be performed either through occasional surveil- lance or a continuous monitoring. The latest tech- nique considers physical effects by direct measure- ments or by a diagnosis obtained from a mathemat- ical model using FDI for dynamic process [1]. A considerable amount of work has been done to de- velop model-based methods to locate continuously small leaks [2], [3], [4]. These papers assumed a fi- nite dimension model with fix space discretization. On the other hand, it has been recently shown [5] that if 2 sensors are used the existence conditions for a solution of the leak detection in a pipeline satisfy only if the line is divided in 3 sections and maximum 2 leaks are considered. To overcome this problem we introduce a model for the fluid discretizing the spacial variable in 3 non uniform sections with un- known boundaries which have be determined in such 1 Work supported by CONACyT-35402A, FIES-IMP, and ECOS-ANUIES a way that they match with the real leaks positions. Under this situation, subspaces sensitive only to a leak are calculated and they allow to reformulate the leak detection and isolation problem in a optimiza- tion algorithm framework, minimizing the gain of a residual with respect to the leaks positions and get- ting a residual sensitive to one of the leaks and in- sensitive to the position of them. In comparison with previous model, this eliminates the error introduced by the leak position deviation and solves the loca- tion problem for 2 leaks with a reduced number of observers. To match the unknown positions z 1 and z 2 , an ex- ternal low periodical triangular signal, that sweeps the plausible leak positions is injected in the residual generators. This allows to get the leak position and size from the residual, searching the position which achieves the minimal residual, and determining the size of the leak from the other residual when the min- imum is achieved. The paper is organized as follows: in Section 2 the nonlinear dynamic model together with the static relations assuming leaks non uniform distributed in the pipeline are given. Section 3 introduces the sub- spaces which are robust only to one leak with inlet and outlet flows as outputs and the associated ob- servers with these subspaces are given. In Section 4 the leak isolation problem is formulated and solved. Simulation results for a water pipeline are given in Section 5 and conclusions are given in Section 6. 2 Nonlinear Model of a Pipeline Assuming convective changes in velocity and com- pressibility to be negligible in a line of length L, and considering that the density and pipe cross-section area are constants, the equations governing one di- mensional transient flow are [6] ∂Q ∂ t + gA ∂ H ∂ z + µQ |Q| =0 (1) b 2 ∂ Q ∂ z + gA ∂ H ∂t =0 (2)