Solution of Large Scale Pipe Networks by Improved Mathematical Approaches

摘要

Approximate solutions to the classical pipe network analysis problem are traditionally obtained by direct solution of the nonlinear network equations arising from mass conservation and pressure continuity conditions. Iterative methods are commonly used to solve these network equations. It is shown that these conditions are stationary point conditions. As a consequence, a revolutionary approach involving optimization techniques for solving this important engineering problem is proposed and evaluated. Kuhn-Tucker theory is used to show that there exists two mathematical programming models, a Content Model and a Co-Content Model, whose solution is precisely the solution to the pipe network analysis problem. The Content Model has a special structure well suited to nonlinear optimization techniques. Three optimization algorithms are coded and used to solve four pipe network analysis problems. A state of the art Newton-Raphson code is also used to provide a comparison of the computational behavior between these three optimization techniques and traditional solution methods.