Optimal Design of Water Distribution Networks with GIS

John W. Labadie
Margaret T. Herzog

ABSTRACT

To assist water engineers to utilize an advanced water distribution system optimizer, a user-friendly interface, database support, and mapping utilities have been integrated into ArcView 3.1 GIS using AVENUE and the Dialog Designer extension. This decision support system (DSS) is developed into an ArcView extension called WADSOP - Water Distribution System Optimizer. WADSOP optimizes pipe sizing and layout, as well as pump station sizing and layout, to improve cost-effectiveness and reliability over most existing water distribution models based on less effective pipe simulation algorithms. GIS provides functions for development and preparation of accurate spatial information for input into the network design optimization model, which include network layout, connectivity, pipe characteristics and cost, pressure gradients, demand patterns, cost analysis, network routing and allocation, and effective color graphic display of results.

INTRODUCTION

Municipal water distribution systems represent a major portion of the investment in urban infrastructure and a critical component of public works. The goal is to design water distribution systems to deliver potable water over spatially extensive areas in required quantities and under satisfactory pressures. In addition to these goals, cost-effectiveness and reliability in system design are also important.

Municipal water distribution systems are inherently complex because they are:

large-scale and spatially extensive
composed of multiple pipe loops to maintain satisfactory levels of redundancy for system reliability

governed by nonlinear hydraulic equations
designed with inclusion of complex hydraulic devices such as valves and pumps
impacted by pumping and energy requirements
complicated by numerous layout, pipe sizing, and pumping alternatives
influenced by analysis of tradeoffs between capital investment and operations and maintenance costs during the design process.

Traditional methods of design of municipal water distribution systems are limited because system parameters are often generalized; spatial details such as installation cost are reduced to simplified values expressing average tendencies; and trial and error procedures are followed, invoking questions as to whether the optimum design has been achieved. Even with use of hydraulic network simulation models, design engineers are still faced with a difficult task.

The optimal design of municipal water distribution systems is a challenging optimization problem for the following reasons:

the system optimization requires an imbedded hydraulic simulation model for pressurized, looped pipe networks
the discrete decision variables are discrete, since pipe sizes must be selected from commercially available sets [e.g., 8", 10", 12", 15",.]; combinatorial problems involving discrete variables are considered NP-hard in optimization theory
the optimization problem can be highly nonlinear due to nonlinear hydraulic models and pump characteristic curves
the optimization problem should be regarded as stochastic due to uncertain demand loadings and system reliability issues
one way of considering uncertain demands is to include multiple demand loading scenarios in the optimization, which increases problem size and complexity
pressure constraints must be directly included in the optimization.

The optimal design of municipal water distribution systems involves numerous characteristics which carry significant spatial dependencies. These include:

topography and its influence on pressure distribution in a pipe network

street network characteristics, since most water distribution systems are installed in existing and planned road systems
right of way issues
congestion problems during installation due to buried utilities
land use and development issues impacting installation costs, such as increased costs of pipe excavation in commercial districts due to business disruption and the need for traffic rerouting
spatially distributed soil characteristics impacting excavation costs, such as loose, sandy soils requiring more costly reinforcement of the site.

With the wide range of optimization models available, it is interesting to speculate as to why these models are not routinely being used by practicing design engineers. Goulter [1992] believes that the primary reason for this is the lack of "suitable packaging" for optimal design models. It is clear that a spatial decision support system [DSS] is needed to aid design engineers, which would include the following components:

data base management system for both spatial and non-spatial data
user friendly dialog interfaces for data manipulation and output display
models subsystem including both simulation and optimization.

Modern geographic information systems [GIS] alone are capable of fulfilling many of these requirements for a spatial DSS.

STATE-OF-ART IN WDS OPTIMAL DESIGN MODELS

The current focus in optimal design models is on improving the efficiency and realism of the optimization techniques, with little attention given to spatial database requirements and dialog interfaces to enhance practical usage. A wide variety of techniques have been proposed, with one of the most oft studied being the Linear Programming Gradient (LPG) method and its extensions (Alperovits and Shamir, 1977; Eiger, et al., 1994). However, Bhave and Sonak (1992) claim that the LPG method is inefficient compared with other methods.

Some approaches attempt to employ efficient combinatorial methods to the optimal design problem. Gessler (1982) linked a network hydraulic simulation model to a filtering subroutine to efficiently enumerate all feasible solutions in pipe network design. This model selects both the optimal design, as well as several near-optimal solutions for tradeoff analysis, and is perhaps the most widely used optimization model. Other authors have formulated the optimal design problem as a nonlinear programming problem with discrete pipe sizes treated as continuous variables. Chiplunkar, et al. (1986) employed the Davidon-Fletcher-Powell method to design a water distribution under a single demand loading scenario. Lansey and Mays (1989) coupled the generalized reduced gradient (GRG) algorithm with a water distribution simulation model to optimally size pipe network, pump stations, and tanks. The primary disadvantage of these NLP methods is the required rounding off of optimal continuous decision variables to commercially available sizes, which can lead to network infeasibilities as well as raise questions as to optimality of the adjusted solution.

Methods based on the use of linear programming (LP) have been developed which are capable of maintaining the constraint on discrete pipe sizes without the need for rounding off solutions. Morgan and Goulter (1985) modified the procedure of Kally (1972) to link a Hardy-Cross network solver with linear programming model. The model is designed to optimize both the layout and design of new systems and expansion of existing systems. It is a highly efficient method, with the main disadvantage being the generation of split pipe solutions (i.e., with some pipe sections requiring two pipe sizes). The latter indeed reduces system costs, but may not be attractive to design engineers.

More recent literature emphasizes reliability issues in water distribution system design, with consideration of the probabilities of satisfying system flow and pressure requirements. Lansey, et al. (1989) employed a chance constrained model to consider uncertainties in demands, pressure head, and pipe roughness. Bao and Mays (1990) applied Monte Carlo simulation methods to measure system reliability. Although reliability-based water distribution system models are useful for analysis of the problem, they may be impractible for designing large-scale systems. The use of multiple demand loading scenarios may be a means of indirectly including system reliability issues at more practical computational expense.

Recent studies have attempted to apply a variety of heuristic programming methods to the optimal design of water distribution systems. These include the application of genetic algorithms (Savic and Walters, 1997) and simulated annealing (Cunha and Sousa, 1999). The advantages of these methods are that they allow full consideration of system nonlinearity and maintain discrete design variables without requiring split pipe solutions. The disadvantages include:

cannot guarantee generation of even local optimal solutions, particularly for large-scale systems
require extensive fine-tuning of algorithmic parameters, which are highly dependent on the individual problem
can be extremely time consuming computationally
current applications have not included use of multiple demand loadings because of computational difficulties.

Presented herein is WADSOP (WAter Distribution System Optimizer) which improves on the method of Morgan and Goulter (1985) by

employing an efficient NLP technique as the hydraulic network solver which offers distinct advantages over traditional methods such as Hardy-Cross, Newton-Raphson, and linear system theory solvers
allows simultaneous inclusion of multiple demand loading scenarios in the optimization
includes the optimal location and sizing of pump stations
is linked with ArcView GIS for spatial and nonspatial data base requirements, effective display of results, and dialog interfacing for practicing engineers.

WADSOP applies an NLP-based network solver and an LP-based optimal design model interactively in a convergent scheme with the following advantages:

spatially-referenced cost functions are developed through the GIS for network layout and sizing
discrete, commercially available pipe sizes are utilized for any size ranges specified by the user
multiple demand loading scenarios are efficiently input into the GIS
inclusion of pump station sizing and layout decision variables to allow efficient analysis of tradeoffs between capital and energy costs.

The goals of WADSOP are to:

combine GIS with pipe network design and analysis models
encourage greater use of optimization models by design engineers
provide a flexible tool for engineers for:

Details on the optimization techniques employed in WADSOP can be found in Taher, et al. (1998). The purpose here is to present the WADSOP extension developed for implementation in ArcView 3.1. The spatial and nonspatial data requirements are described, as well as the ability to edit network characteristics. The WADSOP extension builds the database, prepares formatted ASCII files which are read by the design optimization model, executes the design model, and then displays results as color coded maps of the optimal pipe network characteristics, flows and pressures. Network routing and allocation routines are also available as part of the GIS.

WADSOP GIS APPLICATION DEVELOPMENT

The WADSOP application was developed exclusively in ArcView GIS (3.1) as an extension using AVENUE programming and ArcView project customization capabilities. All dialogs were developed using the Dialog Designer extension to ensure that the application could be used on any platform. The CAD Reader extension was used to permit CAD drawing input, mapping, and conversion, and the Spatial Analyst extension was used for digital elevation model input and usage. One of the most useful extensions incorporated was the Network Analyst for routing new pipes and rerouting old ones, allocating water supply to demand zones, and for developing pressure zones.

WADSOP Menu System
The figure below depicts the WADSOP menu system which functionality can also be accessed through a toolbar that can be activated from the WADSOP button in the button bar or toggle on or off from the menu system. Modules include data development, optimization, results, route, allocate, and help. The development of each of these modules will be discussed in detail in the following sections.

Pipe Edit Dialog

Upon selecting data development from the WADSOP menu or input from the WADSOP toolbar, the Data Development Switchboard is produced for developing optimization model input. The first option is to Edit Pipe Links. If data already exists in the ArcView project for the pipe network, the Pipe Editor dialog is produced along with a table of attributes, one record for each pipe. The user can choose a pipe from the drop down list to begin editing it, or choose it directly from the table. The Select button permits the user to directly select a pipe from the map for editing. Attributes include the Hazen-Williams coefficient, and the diameter and length of the pipe. Note that the user is permitted to add a second diameter and length if the pipe is to be split to reduce overall system costs. The optimizer automatically splits pipes in two to use two different diameters to increase system cost-effectiveness when possible unless the user chooses to not exercise this option. From the Pipe Editor menu, the user can also choose the Add Pipe tool to add new pipes to the system. Nodes are automatically generated at the ends of each pipe added. If the end of a new pipe is drawn within a user-defined tolerance of an existing node, the existing node serves as the end node for that pipe.

Edit Nodes

The next data development option is to add pipe nodes and attributes including elevation and up to four demand scenarios. Using multiple demand scenarios insures that the resulting optimized system is robust. It ensures that a pipe is not eliminated as unnecessary or undersized. As with pipes, nodes can be selected directly from the map for editing as well as added or deleted from the Node Edit dialog. Two different kind of nodes can be added, supply or demand nodes. As opposed to demand nodes, supply nodes are added to represent a water supply tank or a reservoir.

Although not entirely functional yet, a script is being developed to allow all node elevations to be estimated from a map of ground elevation contours or a digital elevation model (DEM) grid minus a constant depth-to-pipe factor. Although this is a rough method, it makes data editing easier if values close to what they should be are already in the elevation field of the table. It also allows a rough optimization run to be executed to determine general areas of concern in pipe network design and expansion.

Edit Pipe Diameters and Costs

The third data development option is to set up a table of commercially available pipe diameters and costs.
By requiring the optimization model to only choose from available diameters, the feasibility and optimality of the solution is more certain. Updating pipe costs to current market prices will ensure that the optimal wds design results reflect reality. The Edit Pipe Cost Factors option allows design costs to be further adjusted for soil type, landuse and street width to improve realism, too.

Edit Pump Data for each Loading Scenario

WADSOP incorporates and effective way to optimize pump design as well as pipe design requiring minimal input. Only the amount of time each pump is set to run for each loading scenario and its load efficiency are required in the Edit Load and Pump Data dialog. Pumping head is automatically adjusted in the optimization model so that all minimum pressure requirements are satisfied. The Edit Energy and Cost Data dialog allows parameters to be set to determine when the cost of additional pumping is less than the cost of increasing pipe sizes, to compute an overall least cost solution for the wds.

Edit Pipe Cost Factors

In addition to the cost of a pipe itself, installation costs can be significantly affected by a number of site conditions, three of which include landuse (developed land being more expensive to excavate), road width (narrow roads causing more disturbance when under construction), and soil type (loose soils requiring shoring and firm soils more time and energy to excavate than typical). The Edit Pipe Cost Factors dialog allows these factors to considered by applying a factor to the cost of pipe based on site conditions. Road buffer, soils and landuse maps are prepared and spatial joins of their linked attributes used to develop an overall factor to apply to each pipe. The user can adjust the cost factors in the dialog and recalculate pipe costs before proceeding to optimization at any time. Adjusting costs and reruning the optimizer is a good way to determine how sensitive results are to changing conditions.

Help

Currently, every dialog includes a help button to obtain text-based information to assist the user in proceeding through the options as well as more general help accessed from the menu-system with details about the WADSOP application. A future goal is to replace this help system with a standard Windows-based one that includes hyperlinks, graphics, and a find function.

Optimization

After completing each dialog in the Data Development module the user is ready to use the WADSOP optimizer. Currently only the optimizer is available, but the simulator to analyze existing systems will soon follow. The Data Verification Check dialog allows the users to review information about the system and return to the editing mode if necessary before proceeding. When the user chooses Optimize from this dialog, all the tables developed during the input phase are converted to comma deliminated text and sent to the WADSOP executable. Results are written to the pipe and node tables, and map displayed colored coding changes to the original network and displaying pipes with a graduated symbol related to pipe diameter. Split pipes are also noted in the results with text labels.
The Crystal Reports extension can be used to generate typical wds reports of interest, as well as customized reports if desired.

Network Routing

Although the main purpose of WADSOP is network optimization, ArcView GIS can provide a great deal of additional functionality. Through the use of the Network Analyst extension, the least cost path can be determined for planning a new pipe along an existing road network. The user only has to indicate from where to where they wish to route, and if length or some other impedance factor will determine which way is the "longest".

Allocation

The final WADSOP module being developed to date aids in network allocation. Two common uses are for determining which water supply sources can supply which sectors of a municipality, or for defining pressure zones as the distance out from a pressure supply head (pump) that can be serviced before impedance along pipes causes the minimum pressure to be reached.

CONCLUSIONS

Although significant progress has been made on the WADSOP extension to ArcView GIS to date, it is not ready for commercial distribution at this time. However, the authors would look forward to entities that would like to test the beta and offer recommendations for improvements. Some of the most pressing work includes the following:

Improve interface to allow for more input options such as determining node elevations from contours.
Complete network allocation module to assign supply or pressure zones.
Allow more flexibility in input parameters to the optimization model.
Include a simulation model for comparison to optimization and for expanded functionality.

REFERENCES

Alperovits, E. and U. Shamir, Design of optimal water distribution systems, Water Resour. Res., 13 (6), 885-900, 1977.
Bao, Y. and L. Mays, Model for water distribution system reliability, J. Hydraul. Div. Am. Soc. Civ. Eng., 116 ( 9), 1119-1137, 1990.
Bhave, P., and V. Sonak, A critical study of the linear programming gradient method for optimal design of water supply networks, Water Resour. Res., 28 (6), 1577-1584, 1992.
Chiplunkar, A., S. Mehndiratta, and P. Khanna, Looped water distribution system optimization for single loading, J. Env. Eng. Div. Am. Soc. Civ. Eng., 112 (2), 264-279, 1986.
Cunha, M. and J. Sousa, Water distribution network design optimization: simulated annealing approach, J. Water Res. Plan. Manage. Div. Soc. Civ. Eng., 125 (4), 215-221, 1999.
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Gessler, J., Optimization of pipe networks, Proc. of the Ninth International. Symposium on Urban Hydrology, Hydraulics and Sediment Control, Univ. of Ky., Lexington, July 27-30, 1982.
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Lansey, K., N. Duan, L. Mays, and Y. Tung, Water distribution system design under uncertainties, J. Water Res. Plan. Manage. Am. Soc. Civ. Eng., 115 (5), 630-645, 1989.
Lansey, K. and L. Mays, Optimization model for water distribution system design, J. Hydraul. Div. Am. Soc. Civ. Eng., 115 (10), 1401-1418, 1989.
Morgan, D., and I. Goulter, Optimal urban water distribution design, Water Resour. Res., 21 (5), 642-652, 1985.
Savic, D. and G. Walters, Genetic algorithms for least-cost design of water distribution networks, J. Water Res. Plan. Manage. Div. Soc. Civ. Eng., 123 (2), 67-77, 1997.
Taher, S. and J. Labadie, Optimal design of water distribution networks with GIS, J. Water Res. Plan. Manage. Div. Soc. Civ. Eng., 122 (4), 301-311, 1996.

AUTHOR INFORMATION

John W. Labadie, P.E.
Professor, Dept. of Civil Engineering
Colorado State University
Fort Collins, Colorado 80523-1372
Tel: 970-491-6898
Fax: 970-491-7727
email: labadie@engr.colostate.edu

Margaret T. Herzog, P.E.
Civil Engineer / GIS Coordinator
Foothill Engineering Consultants, Inc.
350 Indiana Street, Suite 315
Golden, Colorado 80401
Tel: 303-278-0622
Fax: 303-278-0624
Home: 303-237-4158
email: mherzog@foothilltmc.com