Applying Particle Swarm Optimization algorithm on normal depth calculation of horse-shoe section tunnel
Zhang Kuandi1, Wang guangqian2， Lü Hongxin1, Cheng Junying1, Hong Cheng3
(1.College of Water Resources and Architectural Engineering, Northwest A ＆ F University, Yangling, Shaanxi 712100, China; 2.State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; 3.Huaihe River Commission Ministry of Water Resource, Bengbu, Anhui 233000, China)
Abstract Owing to the fact that the calculation formulas of normal depth for free flow in horseshoe section of tunnel and drainage culvert are not expressed by explicit function in hydraulics. By mathematical transformation of normal depth equation of horse-shoe section tunnel, a model of nonlinear constrained optimization for calculating the normal depths of standard Ⅰ-type and Ⅱ-type horse-shoe section tunnel was established. In order to accelerate the convergence rate of the algorithm and improve the searching ability of particle, an improved Particle Swarm Optimization algorithm was presented. The dynamic inertia weight was changed in every loop according to the particle′s positions and the distance between the optimization particle. Error analysis and a computed illustration using the new method indicate that it is much more applicable, precise and simple than traditional methods for calculation of normal water depth. At the same time, the correctness and validity of the new method was demonstrated. So it provided a new tool for obtaining normal depth of open channel with horse-shoe section problem.
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