Real-time leak diagnosis in water distribution systems based on a bank of observers and a genetic algorithm

The main contribution of this paper is to present a novel solution for the leak diagnosis problem in branched pipeline systems considering the availability of pressure head and flow rate sensors on the upstream (unobstructed) side and the downstream (constricted) side. This approach is based on a bank of Kalman filters as state observers designed on the basis of the classical water hammer equations and a related genetic algorithm (GA) which includes a fitness function based on an integral error that helps obtaining a good estimation despite the presence of noise. For solving the leak diagnosis problem, three stages are considered: (a) the leak detection is performed through a mass balance; (b) the region where the leak is occurring is identified by implementing a reduced bank of Kalman filters which localize the leak by sweeping all regions of the branching pipeline through a GA that reduces the computational effort; (c) the leak position is computed through an algebraic equation derived from the water hammer equations in steady-state. To assess this methodology, experimental results are presented by using a test bed built at the Tuxtla Gutiérrez Institute of Technology, Tecnológico Nacional de México (TecNM). The obtained results are then compared with those obtained using a classic extended Kalman filter which is widely used in solving leak diagnosis problems and it is highlighted that the GA approach outperforms the EKF in two cases whereas the EKF is better in one case.Peer ReviewedPostprint (published version

Online leak diagnosis in pipelines using an EKF-based and steady-state mixed approach

This paper proposes a methodology for leak detection and isolation (LDI) in pipelines based on data fusion from two approaches: a steady-state estimation and an Extended Kalman Filter (EKF). The proposed method considers only pressure head and flow rate measurements at the pipeline ends, which contain intrinsic sensor and process noise. The LDI system is tested in real-time by using an USB data acquisition device that is implemented in MATLAB environment. The effectiveness of the method is analyzed by considering: online detection, location as well as quantification of non-concurrent leaks at different positions. The leak estimation error average is less than 1% of the flow rate and less than 3% in the leakage position. Furthermore, the incorporation of a steady-state estimation shows that the solution of the LDI problem has improved significantly with respect to the one that only considers the EKF estimation. An experimental analysis was also performed on the effectiveness of the proposed approach for different sampling rates and for different leakage positionsPeer ReviewedPostprint (author's final draft

Pressure sensor placement for leak localization in water distribution networks using information theory

This paper presents a method for optimal pressure sensor placement in water distribution networks using information theory. The criterion for selecting the network nodes where to place the pressure sensors was that they provide the most useful information for locating leaks in the network. Considering that the node pressures measured by the sensors can be correlated (mutual information), a subset of sensor nodes in the network was chosen. The relevance of information was maximized, and information redundancy was minimized simultaneously. The selection of the nodes where to place the sensors was performed on datasets of pressure changes caused by multiple leak scenarios, which were synthetically generated by simulation using the EPANET software application. In order to select the optimal subset of nodes, the candidate nodes were ranked using a heuristic algorithm with quadratic computational cost, which made it time-efficient compared to other sensor placement algorithms. The sensor placement algorithm was implemented in MATLAB and tested on the Hanoi network. It was verified by exhaustive analysis that the selected nodes were the best combination to place the sensors and detect leaksPeer ReviewedPostprint (published version

Development of non-invasive monitoring approach to diagnose leaks in liquid pipelines

This paper presents a novel non-invasive monitoring method, based on a Liénard-type model (LTM) to diagnose single and sequential leaks in liquid pipelines. The LTM describes the fluid behavior in a pipeline and is given only in terms of the flow rate. Our method was conceived to be applied in pipelines mono-instrumented with flowmeters or in conjunction with pressure sensors that are temporarily unavailable. The approach conception starts with the discretization of the LTM spatial domain into a prescribed number of sections. Such discretization is performed to obtain a lumped model capable of providing a solution (an internal flow rate) for every section. From this lumped model, a set of algebraic equations (known as residuals) are deduced as the difference between the internal discrete flows and the nominal flow (the mean of the flow rate calculated before the leak). Once the residuals are calculated a principal component analysis (PCA) is carried out to detect a leak occurrence. In the presence of a leak, the residual closest to zero will indicate the section where a leak is occurring. Some simulation-based tests in PipelineStudio® and experimental tests in a lab-pipeline illustrating the suitability of our method are shown at the end of this article

Optimal estimation of the roughness coefficient and friction factor of a pipeline

This work addresses the estimation of two interrelated parameters of the fluid flow in pipes. First, a numerical and experimental evaluation of some proposed methods to compute the friction factor in turbulent regime is presented. Special attention is given to an explicit solution obtained through the Lambert W-function. Subsequently, a method to estimate the roughness coefficient using nonlinear optimization techniques is proposed, which then allows determining the friction factor from it. Numerical tests were performed for a wide range of operating points of a pipeline. In order to validate the proposed approach, experimental analysis was carried out on a pipeline pilot-plant. The results show the applicability and effectiveness of the proposed method.Postprint (author's final draft

Localización de fugas en redes de distribución de agua mediante k-NN con distancia cosenoidal

Se propone la localización de fugas en redes de distribución de agua medianteclasificadores basados en el método de los vecinos más cercanos (k-NN) con métrica de distanciacosenoidal. El uso de distancias cosenoidales mejora la respuesta del clasificador, con relaciónal que usa métrica Euclidiana. Comparado con las técnicas de localización de fugas basadasen la máxima correlación de los residuos, se consigue una mayor robustez en condicionesaltamente ruidosas, y una menor dependencia del modelo hidráulico de la red, lo que facilita suimplementación, pues no requiere del cálculo de la matriz de sensibilidad. La técnica propuestase programó en MATLABR©y se probó con datos sintéticos obtenidos de simulaciones conEPANET. La evaluación del desempeño reportada se basa en el índice de pérdidas (la fracciónde fugas localizadas erróneamente) y en una medida del error de localización obtenida de ladistancia topológicaPeer ReviewedPostprint (published version

Diagnosis of fluid leaks in pipelines using dynamic PCA?

In this paper, a data-driven system based on PCA is described to detect and quantify fluid leaks in an experimental pipeline. A dynamic PCA implementation (DPCA) was used to capture the process dynamics because the system variables are time-correlated. To detect leaks online, the Hotelling’s T2 statistic and the squared prediction error (SPE) were used as residuals, which are compared against statistically defined thresholds from a set of training data. To determine the number of delays to be included in the DPCA model as well as the number of principal components to be used, a tuning process was executed to find the residual with the optimal number of delays and components that showed the best correlation between the residuals and the leakage size. This allowed the construction of a regression model to estimate the flow rate of the leaks directly from the residual.Peer ReviewedPostprint (author's final draft

Diagnosis of fluid leaks in pipelines using dynamic PCA?

In this paper, a data-driven system based on PCA is described to detect and quantify fluid leaks in an experimental pipeline. A dynamic PCA implementation (DPCA) was used to capture the process dynamics because the system variables are time-correlated. To detect leaks online, the Hotelling’s T2 statistic and the squared prediction error (SPE) were used as residuals, which are compared against statistically defined thresholds from a set of training data. To determine the number of delays to be included in the DPCA model as well as the number of principal components to be used, a tuning process was executed to find the residual with the optimal number of delays and components that showed the best correlation between the residuals and the leakage size. This allowed the construction of a regression model to estimate the flow rate of the leaks directly from the residual.Peer Reviewe

Simultaneous optimal estimation of roughness and minor loss coefficients in a pipeline

This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook–White equation for an operating interval of the pipeline from the flow and pressure measurements at the pipe ends. The proposed method has been implemented in MATLAB and validated in a serpentine-shaped experimental pipeline by contrasting the theoretical friction for the estimated coefficients obtained from the Darcy–Weisbach equation for a set of steady-state measurements.Peer ReviewedPostprint (published version

Leak-Diagnosis Approach for Water Distribution Networks based on a k-NN Classification Algorithm

International audienceThis paper proposes an approach based on a k-Nearest Neighbour classification algorithm (k-NN) to identify regions in a water distribution network (WDN) that are affected under presence of leaks. The classification algorithm is trained with numerical data coming from a MATLAB simulator based on a dynamic model of the WDN that involve leaks in its formulation. Concretely, the training is done by using the numerical solutions of a dynamic model of the WDN under several leak cases. The dynamic model is formulated by taking into account typical assumptions of the rigid water column (RWC) theory and using the graph theory. The proposed approach was evaluated in a hydraulic pilot plant