Date of Award
Doctor of Philosophy (PhD)
Professor Alan A. Smith
The objective is the development of two reIated mathematical models to provide minimum cost designs of water distribution and waste-water collection networks.
This wealth of literature is classified in terms of problems formation and method of solution. This places individual contributions in perspective and serves to identify the major shortcomings of existing techniques. These are:-
1- Inability to handle large network systems efficiently. 2- lnadequate treatment of the hydraulics of the system. 3- Absence of a satisfactory discrete solution.
The results presented are considered to be more comprehensive than any other technique reported in the literature to the author's knowledge. The major contributions presented are:-
(i) Both problems are formulated in the form of a nonlinear programming problem and in terms of practical engineering variables and solved by application of the MINOS package.
(ii) A standard data format is suggested which allows user input to be defined in a very compact and logical form.
(iii) Pre-and Post-processors are developed which free the user from the complicated and extremely error-prone tasks of creating the necessary input data and interpreting the resultant output files of the MINOS package.
(iv) For distribution networks, a comparison is presented between the explicit use of a network analyser (coupled with an efficient optimization package) and the implicit incorporation of the analysis stage within the linear and nonlinear constraints of a comprehensive nonlinear model. The latter method is shown to have significant advantages.
(v) For collection networks, a model formulation is presented which properly represents the hydraulics of part full flow in circular sewers. The problem size is reduced by the introduction of an equality constraint which correlates velocity and discharge under these conditions. The accuracy of the method is checked by comparison with a more rigorous but significantly more expensive problem formulation.
(vi) Methods are suggested whereby pumps, reservoirs, pressure reducing valves and minor loss devices can be easily and correctly incorporated in a distribution network design.
(vii) Techniques involving variable transformation and the partitioning of basic, nonbasic and superbasic variables are developed which greatly increase the efficiency of solution.
(viii) For both types of network, the models are augmented to allow a very good discrete solution to be obtained in terms of pipe diameter. A heuristic argument is presented which suggests that the solution for distribution networks must be very close to optimal although optimality cannot be rigorously proven. For collection networks it is shown that discretization may frequently be infeasible unless at least one of the constraints is relaxed in the form of a 'soft' constraint.
(ix) Both types of network design are demonstrated using problems of substantial size. For distribution networks a method is demonstrated whereby the analysis or design problem can be solved as special cases of the more general optimization problem.
El-Bahrawy, Aly N., "Optimal Design of Water and Wastewater Networks" (1985). Open Access Dissertations and Theses. Paper 1204.