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2012 | Buch

Modeling and Numerical Simulation of Pipe Flow Problems in Water Supply Systems Kapitel lesen Erstes Kapitel lesen

Mathematical Optimization of Water Networks

herausgegeben von: Alexander Martin, Kathrin Klamroth, Jens Lang, Günter Leugering, Antonio Morsi, Martin Oberlack, Manfred Ostrowski, Roland Rosen

Verlag: Springer Basel

Buchreihe : ISNM International Series of Numerical Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other.

The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics.

The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems.

Most of the presented research has been supported by the joint project „Discret-continuous optimization of dynamic water systems“ of the federal ministry of education and research (BMBF).

Inhaltsverzeichnis

Frontmatter

Optimization of Water Supply Networks

Frontmatter
Chapter 1. Modeling and Numerical Simulation of Pipe Flow Problems in Water Supply Systems
Abstract
In this chapter the simulation of a water supply system on a mesoscale abstraction level is considered. The water network consists of storage tanks, pipes, pumps and valves. It is operated by the characteristics of the water supplier, the consumer and the pumps. For all network elements the modeling equations are given. They include mass and momentum conservation for pressurized pipe flow. For their numerical solution the method of lines is proposed. The discretization in space is based on a finite volume approach together with a local Lax-Friedrich splitting and central WENO reconstruction. Boundary and coupling conditions are implemented as algebraic equations. This leads to a system of differential-algebraic equations in time which is solved by a special Rosenbrock method. The paper ends with some typical simulation results of the network.
Gerd Steinebach, Roland Rosen, Annelie Sohr
Chapter 2. Simulation and Continuous Optimization
Abstract
In this chapter we consider the solution of the model equations of water supply networks and continuous optimal control tasks. We begin with the description of our simulation tool in Sect. 2.1, in particular the numerical treatment of the water hammer equations. This includes the description of the implemented discretization scheme together with a stability and convergence analysis. As we will see, the applied scheme perfectly matches with the properties of the water hammer equations and thus builds a useful foundation for the solution of the entire model equations as well as optimal control tasks.
In Sect. 2.2 we consider the computation of sensitivity information, which is necessary for the application of gradient-based optimization techniques. Here, we follow a first-discretize approach to derive adjoint equations. Due to the special structure of the considered problems, very efficient algorithms can be applied.
Finally, Sect. 2.3 deals with the problem of singularities in the model equations of water supply networks. Here, a physically motivated regularization approach is applied and also extended to be applicable in an adjoint calculus.
Oliver Kolb, Jens Lang
Chapter 3. Mixed Integer Optimization of Water Supply Networks
Abstract
We introduce a mixed integer linear modeling approach for the optimization of dynamic water supply networks based on the piecewise linearization of nonlinear constraints. One advantage of applying mixed integer linear techniques is that these methods are nowadays very mature, that is, they are fast, robust, and are able to solve problems with up to a huge number of variables. The other major point is that these methods have the potential of finding globally optimal solutions or at least to provide guarantees of the solution quality. We demonstrate the applicability of our approach on examples networks.
Antonio Morsi, Björn Geißler, Alexander Martin
Chapter 4. Nonlinear and Mixed Integer Linear Programming
Abstract
In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming. We combine the continuous nonlinear and the mixed integer approach introduced in Chap. 3 to incorporate the solution quality. Finally, we show results for a real municipal water supply network.
Oliver Kolb, Antonio Morsi, Jens Lang, Alexander Martin

Optimal Control of Sewer Networks

Frontmatter
Chapter 5. Optimal Control of Sewer Networks Problem Description
Abstract
This chapter gives an overview of optimal control of sewer networks with dynamic process models. After introducing the method of model predictive control (MPC) and its requirements for optimization and process modeling a focus is set on practical applications and the industrial viewpoint. An up-to-date sewer management system is introduced and used to illustrate industrial requirements and the mathematical challenges involved in it.
Steffen Heusch, Holger Hanss, Manfred Ostrowski, Roland Rosen, Annelie Sohr
Chapter 6. Modeling of Channel Flows with Transition Interface Separating Free Surface and Pressurized Channel Flows
Abstract
In practical application open-channel or free-surface channel flow under the influence of gravity in sewers has traditionally been modeled with mathematical models based on one-dimensional governing equations of continuity and momentum—the so-called Saint Venant equations. High volumetric flow rates or strong rains may lead to the transition from partial to fully filled cross sections in a sewer net, i.e. a free surface flow is not guaranteed any more. Hence the mathematical model of the Saint Venant equations loses its validity in whole or in parts of the channels and a transition occurs to the pressurized pipe equations. The main goal of this work is to bring forward our knowledge about the process of changing the governing regime of the fluid equations in the channel flow and to attempt to perform a general modeling tracking the movement of the transition interface between a free surface flow and the pressurized flow in one-dimensional channels. Various flow cases with or without a moving transition are numerically investigated by means of the high-precision Discontinuous Galerkin Finite Element method. An exact knowledge of this event allows to optimize the controlling of equipment and the operation in a sewer or design a new sewer correctly and effectively.
Saeid Moradi Ajam, Yongqi Wang, Martin Oberlack
Chapter 7. Optimal Control of Sewer Networks Engineers View
Abstract
This chapter introduces a software tool for MPC of sewer networks with a dynamic process model which is based on an interative approach. A flexible optimizer, which implements local and global optimization methods, is connected to a dynamic sewer network model to evaluate the objective function values. Numerical results for a simple urban drainage network are presented, illustrating the functionality of the approach.
Steffen Heusch, Manfred Ostrowski
Chapter 8. Real-Time Control of Urban Drainage Systems
Abstract
A hydrodynamic process model based on shallow water equations is discretized on 1D-networks with the method of finite volumes. Based on the finite volumes we replace algebraic coupling conditions by a consistent finite volume junction model. We use discrete adjoint computation for one step Runge-Kutta schemes to generate fast and robust gradients for descent methods. We use the descent methods to generate an optimal control for an example network and discuss the computational results.
Johannes Hild, Günter Leugering
Chapter 9. Performance and Comparison of BlueM.MPC and Lamatto
Abstract
We compare the quality and generation performance of the optimal control sequence produced by the software frameworks BlueM.MPC and Lamatto.
Steffen Heusch, Johannes Hild, Günter Leugering, Manfred Ostrowski
Chapter 10. Multicriteria Optimization in Wastewater Management
Abstract
In this chapter we consider the goals and objectives arising in wastewater management in the context of a multiobjective analysis. This allows, among others, the individual consideration of (1) the overflow volume (i.e., the total amount of released water), (2) the pollution load in the released water, and (3) the cost of the generated control. Given a specific sewage network and data of typical inflow scenarios, a multiobjective offline analysis of the problem and, in particular, of the trade-off between the different goals provides the decision maker with valuable information of the problem characteristics. This information can then be used to specify a suitable scalarized, single-objective optimization problem for the real-time optimal control that represents the decision makers preferences in a best possible way. If an efficient solver for such scalarizations is available (which is the case for the problems considered here), this leads to an efficient online procedure that is justified by an extensive offline problem analysis.
Even though the methods presented in this chapter were tailored for wastewater management problems, they are also applicable in the context of the other applications mentioned in this volume.
Kerstin Dächert, Kathrin Klamroth
Metadaten
Titel
Mathematical Optimization of Water Networks
herausgegeben von
Alexander Martin
Kathrin Klamroth
Jens Lang
Günter Leugering
Antonio Morsi
Martin Oberlack
Manfred Ostrowski
Roland Rosen
Copyright-Jahr
2012
Verlag
Springer Basel
Electronic ISBN
978-3-0348-0436-3
Print ISBN
978-3-0348-0435-6
DOI
https://doi.org/10.1007/978-3-0348-0436-3

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