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## Über dieses Buch

This book focuses on the analysis and design of advanced techniques for on-line automatic computational monitoring of pipelines and pipe networks. It discusses how to improve the systems’ security considering mathematical models of the flow, historical flow rate and pressure data, with the main goal of reducing the number of sensors installed along a pipeline. The techniques presented in the book have been implemented in digital systems to enhance the abilities of the pipeline network’s operators in recognizing anomalies. A real leak scenario in a Mexican water pipeline is used to illustrate the benefits of these techniques in locating the position of a leak. Intended for an interdisciplinary audience, the book addresses researchers and professionals in the areas of mechanical, civil and control engineering. It covers topics on fluid mechanics, instrumentation, automatic control, signal processing, computing, construction and diagnostic technologies.

## Inhaltsverzeichnis

### Chapter 1. Introduction

This chapter serves as a background of monitoring systems for pipeline networks by applying software-based fault diagnosis tools and briefly describes each contribution of this monograph. The term computational pipeline monitoring (CPM) refers to algorithmic monitoring tools that are used to enhance the abilities of the pipeline network’s operators in recognizing anomalies which may be indicative of products’ loss. The presented advanced methods and issues associated with models and features of pipeline networks are limited to scenarios of leaks and blockages in a single pipeline and pipeline networks. The framework of the procedures considers the physical variables associated with the flow process as measurements. In particular, pressure, flow, and temperature sensors are assumed to be located only at specific points of the pipeline networks. Thus, this chapter introduces the reader to the main theme of the monograph which is the analysis and design of advanced online automatic monitoring systems for pipeline networks by considering leaks and blocks as abnormal events. To simplify the understanding of the specific topics, the general fault detection and isolation (FDI) background is roughly presented in this chapter by citing tutorial books related to the FDI issues.

Cristina Verde

### Chapter 2. An Overview of Transient Fault Detection Techniques

This chapter overviews the theory and strategies of transient fault detectionFault detection, considering both active and passive systems, and contrasting the more common frequent approaches with time-domain methodologies. The chapter contends that real complex systems may have mimics, where one characteristic can locally impersonate another. The chapter seeks to examine the “state of play” in these areas, providing a factual summary of what has been shown and demonstrated to date, along with a more speculative set of reflections about challenges and about which methods appear to the authors to have the greatest promise for deployment and commercialization.

Xinge Xu, Bryan Karney

### Chapter 3. Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines

The chapter concerns numerical issues encountered when the pipeline flowPipeline flow process is modeled as a discrete-time state-space modelDiscrete-time state-space models. In particular, issues related to computational complexityComputational complexity and computability are discussed, i.e., simulation feasibility which is connected to the notions of singularitySingularity and stabilityStability of the model. These properties are critical if a diagnostic systemDiagnostic system is based on a discrete mathematical model of the flow process. The starting point of the study is determined by the partial differential equations obtained from the momentum and mass conservation laws by using physical principles. A realizable computational model is developed by approximation of the principal equations using the finite differenceFinite difference method method. This model is expressed in terms of the recombinationRecombination matrix matrix A which is the key of the analysis by taking into account its possible singularitySingularity and stabilityStability. The nonsingularity of the matrix A for nonzero and finite, time and spatialTime and spatial discretization steps is proven by the Lower–Upper decomposition. A feature of the discrete model allows the derivation of a nonsingular aggregated model, whose stabilityStability can be analyzed. By considering the Courant–Friedrichs–Lewy conditionCourant–Friedrichs–Lewy condition and data from experimental studies, numerical stability conditions are derived and limitations for the feasible discretized grid are obtained. Moreover, the optimal relationship between the time and space steps which ensures a maximum stability margin is derived. Because the inverse of matrix A, composed of four tridiagonal matrices, is required for the main diagnosis methods, two analytical methods for the inversion are discussed which reduce the system’s initialization time and allow designing an accurate and fast diagnosis algorithm. By considering that each inversion method generates its particular structure, two different flow models are generated: one based on auxiliary variables and the other suitable if the stabilityStability condition of A is satisfied. The applicability of the two models is shown by considering the norm of the difference between their behaviors for a finer discretization gridDiscretization. A similarity measure is proposed which considers the number of pipeline segments as well as the ratio between the time and spatial stepsTime and spatial discretization. Thus, the system’s computational efficiency is improved and satisfactory results are shown with respect to the base model, if a highly dimensional model with the approximated diagonal matrix is considered.

Zdzisław Kowalczuk, Marek Tatara

### Chapter 4. One-Dimensional Modeling of Pipeline Transients

This chapter summarizes the one-dimensional modeling of transients in a pipeline, commonly used for detection and location of faults (such as leaks and obstructions) by means of model-based methods. The modeling starts with the discretization via finite-difference method of classical water hammer equations. The result of such a discretization is a system of ordinary differential equations, which is considered together with boundary conditions that represent faults and pipeline accessories. Some illustrative results are finally given based on a test bench.

Jean François Dulhoste, Marcos Guillén, Gildas Besançon, Rafael Santos

### Chapter 5. Observer Tools for Pipeline Monitoring

This chapter discusses how the problem of fault monitoring in pipelines can be addressed by state observer tools. In short, the approach relies on a dynamical modeling of water flow dynamics in the pipeline subject to fault effects, and on this basis fault parameters are directly estimated by observer techniques. Motivated by typical pipeline models and faults, possible observer tools are recalled and illustrated with some application examples.

Gildas Besançon

### Chapter 6. Auxiliary Signal Design and Liénard-type Models for Identifying Pipeline Parameters

This chapter presents the implementation of optimization algorithms to build auxiliary signals that can be injected as inputs into a pipeline in order to estimate—by using state observers—physical parameters such as the friction or the wave speed. For the design of the state observers, we propose to incorporate the parameters to be estimated into the state vector of Liénard-type models of a pipeline such that the observers can be constructed from the modified models. The proposed optimization algorithms guarantee a prescribed observability degree of the modified models by building an optimal input for the identification. The optimality of the input is defined with respect to the minimization of the input energy, whereas the observability through a lower bound for the observability Gramian, which is constructed from the Liénard-type models of the pipeline. The proposed approach to construct auxiliary inputs was experimentally tested by using real data obtained from a laboratory pipeline.

Javier Jiménez, Lizeth Torres, Ignacio Rubio, Marco Sanjuan

### Chapter 7. Recursive Scheme for Sequential Leaks’ Identification

This chapter deals with the problem of detection and identification of multi-leaks in a single, horizontal pipeline assuming that only flow and pressure sensors at the ends of the pipeline are available. A characteristic of this monitoring scenario with simultaneous leaks is that the events are undistinguishable in steady state. This means the leaks could only be identified during transient behaviors. A monitoring problem, close to the simultaneous leaks’ issue, is the leaks’ scenario appearing in sequence. It is shown here that the isolation task is feasible with this scenario in the framework of model-based methods. Thus, a general recursive scheme which is formatted with three coupled nonlinear input–output equivalent models in steady state is proposed. Since the scheme is based on the equivalence model condition between one and multiple leaks’, previous to the presentation of the scheme, the static relation between equivalent models for one and multiple leaks is derived by considering the friction as a function of the flows. The interrelated three input-output models have the property to retain the data of the past leaks’, which allows an on-line identification of the new event during a time window for any arbitrary number of leaks. In particular the identifiers are implemented by using extended Kalman filters. The algorithm is tested with synthetic data simulated with Pipeline Studio software for a sequential set of three leaks, and it shows successful results.

Cristina Verde, Jorge Rojas

### Chapter 8. Simulation of Gas Networks and Leak Detection Using Quadripole Models

A cost-effective, accurate, and robust leak detection method is essential in gas network management in order to reduce inspection time and to increase reliability in the system. This work presents a model-based leakage detection method; the gas dynamics are described by a linearized system of partial differential equations that is further reduced to a one-dimensional spatial model. By using an electrical analogy, a pipeline can be represented by a two-port network, where mass flow behaves like current and pressure like voltage. Four transfer function quadripole models are then established to describe the gas pipeline dynamics, depending on the variables of interest at the pipeline boundaries. A leak detection method is devised by employing mass flow data at boundaries and pressure data at some point of the pipeline, as well as by assessing the effects of the leakage on the pressure and mass flow along the pipeline. A case study has been built from operational data supplied by REN Gasodutos (the Portuguese gas company) to show the advantages of the proposed models.

Sara T. Baltazar, Paulo Lopes dos Santos, Teresa P. Azevedo Perdicoúlis

### Chapter 9. Features of Demand Patterns for Leak Detection in Water Distribution Networks

This chapter presents a data-driven based approach for detection of leaks in water distribution networks in which the demand is formed by a known periodic pattern plus a stochastic variable. The leak detection method is based on an adaptation of the dynamic principal component analysis (DPCA), and it is assumed that only pressures at selected consumption nodes are measured. Since the variables of water distribution networks (WDNs), even in normal conditions, are nonstationary and time-correlated the data are preprocessed with a periodic transformation previous to the application of DPCA. The proposed approach is validated with the Hanoi network model. The performance is evaluated with three indexes: the leak detection rate, the false alarm rate, and the delay of the detection with respect to the leak’s occurrence time. All of them are satisfactory for diverse leaks’ scenarios, and the proposed approach presents an improvement in the leak detection rate of approximately $$70\%$$70% as compared with the traditional PCA and DPCA methods.

Marcos Quiñones-Grueiro, Cristina Verde, Orestes Llanes-Santiago

### Chapter 10. Leak Localization in Water Distribution Networks Using Pressure Models and Classifiers

This chapter proposes an architecture and an associate methodology for leak localization in Water Distribution Networks (WDN) that are based on pressure models and classifiers. In a first stage of the proposed architecture, residuals are obtained by comparing available pressure measurements with the estimations provided by a WDN model. In a second stage, a classifier is applied to the residuals with the aim of determining the leak location. The classifier is trained with data generated by simulation of the WDN under different leak scenarios and uncertainty conditions. Several classification approaches are considered and compared. The proposed methodology is tested both using synthetic and experimental data with real WDNs of different sizes. The comparison with the current approaches shows a performance improvement.

Adrià Soldevila, Sebastian Tornil-Sin, Joaquim Blesa, Rosa M. Fernandez-Canti, Vicenç Puig

### Chapter 11. Sensor Placement for Classifier-Based Leak Localization in Water Distribution Networks

This chapter presents a sensor placement method for the classifier-based approaches for leak localizationLeak localization in water distribution networksWater distribution networks introduced in the previous chapter. The proposed approach formulates the sensor placement problem as a binary optimization problem. Because of the complexity of the problem, it is solved by applying genetic algorithms. In order to reduce the number of sensor configurations to test, a binary matrix that identifies pairs of sensors providing similar information is added as a constraint. The sensors are placed in an optimal way, which maximizes the accuracy of the leak localizationLeak localization. The proposed approach is first illustrated by means of the application to an academic example based on the reduced version of the Hanoi water distribution networkWater distribution networks. A more realistic case study is then proposed based on the Limassol district metered area.

Adrià Soldevila, Joaquim Blesa, Sebastian Tornil-Sin, Rosa M. Fernandez-Canti, Vicenç Puig

### Chapter 12. Water Leak Diagnosis in Pressurized Pipelines: A Real Case Study

This chapter presents a successful leak diagnosis for a real pipeline. The diagnosis was performed on the water pipeline West 5 located in Guadalajara City, Mexico, which is supervised by Inter-Municipal System of Potable Water and Sewage (SIAPA). Herein, the authors try to highlight those difficulties that arise when facing a real leak problem, especially if the fluid line is not monitored online or records of the flow rate and pressure are not available. By considering that only one leak is present in the system and by using the pipeline configuration information provided by the SIAPA staff, a discrete-time extended Kalman filter, used as a state observer, was designed in order to isolate the leak. The final decision about the leak location was based on the results of four different database analyses in which three showed a similar tendency.

### Backmatter

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