Optimal Design of Urban Drainage Systems using Genetic Algorithms
Control of sewer overflows is vital to reducing risks to public health and protecting the environment from water pollution. Sewer overflows are a leading cause of water pollution in the nation’s lakes, streams and inland bays. The untreated sewage from these overflows contains microbial pathogens, suspended solids, toxics, nutrients, trash, and other pollutants that deplete dissolved oxygen and can contaminate our waters, causing serious water quality problems and threatening drinking water supplies, fish and shellfish. This sewage can also back up into basements, causing property damage and creating threats to public health for those who come in contact with the untreated sewage. There are about 19,500 sewer systems nationwide designed to handle an average daily flow of roughly 50 billion gallons of raw sewage (Nicklow et al., 2004, 2006).
Sanitary sewer overflows (SSOs) or combined sewer overflows (CSOs) may release partially treated or untreated sewage to surface waters. High wet weather flows from rainfall-derived inflow and infiltration (RDII) can exceed system capacity, resulting in an SSO. The measured volume for this type of SSO is typically much greater than other causes of SSO. SSOs are most frequently caused by grease and debris blockage. Other causes for SSOs include sediments buildup, pipe breaks, leaking manholes, offset joints, equipment failures, undersized sewer pipes, power outages, and other reasons. When an SSO occurs, sewage flows into streets, playgrounds and streams.
CSOs occur in older combined sewer systems that were designed to carry both sanitary sewage and storm water runoff to a wastewater treatment plant (WWTP). Under dry conditions, the WWTP treats the sewage and then discharges it to a water body. During periods of heavy rainfall or snowmelt, however, the wet weather volume in the combined sewer system exceeds the available hydraulic capacity of the sewer system or treatment plant. This leads to the discharge of excess wastewater directly to nearby streams, rivers, or other water bodies. Combined sewer systems in the United Sates serve roughly 746 communities containing about 40 million people. Although there are combined sewers in 32 states and the District of Columbia, they are mostly located in the Northeast and Great Lakes regions, and the Pacific Northwest (U.S. EPA, 2004).
With the growing expectations by the public for quality services, the U.S. Environmental Protection Agency (EPA) under the authority of the Clean Water Act adopted by Congress has implemented pollution control programs and set wastewater standards for the industry. In order to meet these requirements, comprehensive modeling and analysis of these sewer systems becomes necessary for developing sound cost-effective solutions for enhancing system integrity and performance to reliably convey sewer flows without surcharging, overflows, flooding, and backups.
Today, many wastewater utilities and engineering consulting companies utilize drainage network simulation models to plan improvements and design better systems. Technology to achieve these improvements includes: the addition of new sewer pipes or treatment capacity as well as increasing conduit capacity (bigger interceptors), more storage volume, and pumping capacity. Current practice involves a tedious trial-and-error evaluation procedure that seldom leads to the most effective or most economical solutions for upgrading collection systems. This requires using the drainage network simulation model to evaluate the hydraulic performance of the existing system with different design alternatives (modifications) under a range of loading conditions. The design that meets the target hydraulic criteria for the lowest cost is then selected from among the alternative designs. The complexity of this manual trial-and-error procedure increases exponentially with the number of proposed system modifications and corresponding operating conditions. It is important to point out, however, that even if the operating specifications are met, the trial-and-error procedure has no inherent feature that assures that the solutions reached are cost optimum or even cost effective. Therefore, good engineering procedure dictates that the iterations continue until a number of promising alternatives have been evaluated. The cost of each feasible alternative is then computed to arrive at a recommended solution. Time restraint or limited understanding of sewer network hydraulics generally prevents engineers from obtaining hydraulically reliable recommendations. Given the vast number of possible combinations of system enhancements, it is unlikely that even the most experienced modeler will be able to determine the least-cost improvement alternative. This process is also not able to ensure that the final design could perform adequately under all possible loading and operating conditions. The result of using the traditional trial-and-error evaluation approach is often inefficient performance at greater cost.
One way to circumvent the previous problems is to employ optimization theory. This chapter presents a rigorous optimal design methodology, which eliminates the need of the traditional manual design technique. The problem of choosing least-cost improvements for urban drainage systems is cast as a nonlinear optimization problem and solved using optimization theory. The optimization problem consists of determining the optimal design improvement solutions that produce the minimum overall cost while satisfying target system performance requirements. The decision variables can include any selected combination of pipe slope and upsizing, storage, pumping and new piping. Performance criteria include maximum allowable depth to diameter ratio, minimum and maximum pipe velocities, maximum head loss for force mains, and minimum and maximum pipe slopes. This gives practicing engineers complete control over the solution process.
The proposed approach links a comprehensive drainage network simulator with an efficient stochastic optimization model and iterates between the simulator and the optimization model until the best solution is found. It is structured in an object-oriented framework allowing very large and complex sewer collection systems to be solved in expeditious times. The optimization procedure employed is based on the fast messy genetic algorithm (fmGA), which delivers reliable solutions in sub-quadratic time. The urban drainage network simulation is performed using an extended version of the EPA storm water management model, SWMM 5 (Rossman, 2005). The optimization model generates improved sets of decision variables that seek to minimize rehabilitation costs. These decision variables are then passed directly to the appropriate objects in the simulation program for use in quantifying system hydraulics. The hydraulic simulation results are passed back to the optimization model for checking for any constraint violations. The iterations continue until the least cost solution is found. This allows rapid solutions to be obtained with a minimal computational overhead. The value and performance of the method are illustrated by application to an example stormwater collection system. The method should prove useful to any wastewater utility in planning and designing reliable systems and optimizing their capital improvement programs.
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