Solving the Pipe Network Analysis Problem Using Optimization Techniques

Collins, Michael A.; Cooper, Leon N.; Helgason, Richard V.; Kennington, Jeffery L.; LeBlanc, Larry J.

doi:10.1287/mnsc.24.7.747

Cited by 182 publications

(106 citation statements)

References 28 publications

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“…After the local linearization method proposed by Cross (1936), the work by Collins et al (1978) gave rise to a number of global linearization techniques (i.e., characterized by the simultaneous solution of all the network equations) (e.g. Martin and Peters, 1963;Shamir and Howard, 1968;Epp and Fowler, 1970;Hamam and Brammeller, 1971;Kesavan and Chandrashekar, 1972;Wood and Charles, 1972;Isaacs and Mills, 1980;Wood and Rayes, 1981;Carpentier et al, 1987) culminating with the work by Todini and Pilati (1988).…”

Section: Introductionmentioning

confidence: 99%

Computationally Efficient Modeling Method for Large Water Network Analysis

et al. 2012

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Nowadays, unprecedented computing power of desktop personal computers and efficient computational methodologies, such as the global gradient algorithm (GGA), make large water distribution system modeling feasible. However, many network analysis applications, such as optimization models, require running numerous hydraulic simulations with modified input parameters. Therefore, a methodology that could reduce the computational burden of network analysis, and still provide the required model accuracy, is needed. This paper presents a matrix transformation approach to convert the classic GGA, which is implemented within the widely

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Section: Introductionmentioning

confidence: 99%

Computationally Efficient Modeling Method for Large Water Network Analysis

et al. 2012

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“…(72) is sparse and symmetric for the Darcy-Weisbach head loss formulation used in this paper, but can be a difficult to invert or decompose. A more efficient way to deal with the Jacobian was shown by Todini and Pilati (1988), which was originally based on the Content Model (Collins et al 1978). Todini and Pilati developed an efficient approach to the inversion of the Jacobian by partitioning as…”

Section: Steady-state Qh-formulationmentioning

confidence: 99%

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

et al. 2011

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Applications of frequency-domain analysis in pipelines and pipe networks include resonance analysis, time-domain simulation and fault detection. Current frequency-domain analysis methods are restricted to series pipelines, single-branching pipelines and single-loop networks and are not suited to complex networks. This paper presents a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size. The formulations focus on the topology of arbitrary networks and do not consider any complex network devices or boundary conditions, other than head and flow boundaries. The frequency-domain equations are presented for node elements and pipe elements, which correspond to the continuity of flow at a node and the unsteady flow in a pipe, respectively. Additionally, a pipe-node-pipe and reservoir-pipe pair set of equations are derived. A matrix-based approach is used to display the solution to entire networks in a systematic and powerful way. Three different formulations are derived based on the unknown variables of interest that are to be solved for, being the head-formulation, flow-formulation and the head-flow-formulation. These hold significant analogies to different steady-state network solutions. The frequencydomain models are tested against the method of characteristics (a commonly used timedomain model), with good result. The computational efficiency of each formulation is discussed with the most efficient formulation being the head-formulation.

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“…The problem of determining flows and heads in a general pipeline system (such as in municipal water systems) with reservoirs, pumps, gate and check valves, given fixed inputs and withdrawals has been shown [Collins et al 1978] to be equivalent to a convex transshipment problem under the assumption of convex head losses. Such problems are easily solved as ordinary transshipment problems using a piecewise linear approximation of the convex function.…”

Section: Applications Of Pure Network Problemsmentioning

confidence: 99%

Netform Modeling and Applications

Glover¹,

Klingman²,

Phillips³

1990

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Many real-world applications have profited from netform innovations in both modeling and solution strategies. Practical experience shoves that advances in netform modeling and solution strategies overcome many of the difficulties in conceptual design and problem solving of previous approaches to system optimization. Moreover, they provide the type of technologies required of truly useful decision-planning tools, technologies that facilitate modeling, solution, and implementation. The ultimate test and worth of computer-based planning models, however, depends on their use by practitioners. In this tutorial, we show how certain algebraic models can be viewed graphically using netform modeling and describe several large practical problems we have solved. Some of our insights can make it easier for practitioners to take advantage of these technologies.

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Solving the Pipe Network Analysis Problem Using Optimization Techniques

Cited by 182 publications

References 28 publications

Computationally Efficient Modeling Method for Large Water Network Analysis

Computationally Efficient Modeling Method for Large Water Network Analysis

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

Netform Modeling and Applications

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