基于改进粒子群算法求解马蹄形断面正常水深

Applying Particle Swarm Optimization algorithmon normal depth calculation of horse-shoe section tunnel

为了解决马蹄形断面正常水深无显函数计算方法的现状,通过对明渠恒定均匀流方程进行数学变换,得到了标准Ⅰ,Ⅱ型马蹄形过水断面正常水深求解的分段非线性约束优化问题.将粒子群算法中的权重函数随着迭代次数和不同粒子与最优粒子之间的距离大小进行调整,用以加速算法的收敛速度和提高粒子的搜索能力,并将调整惯性权重模型的粒子群优化算法运用到马蹄形断面正常水深的求解中.通过实例计算及误差分析表明:分段优化模型在水深特征点连续,且该法能100%收敛到全局最优解,故该方法求解马蹄形断面正常水深适用性强、计算精度高、算法实现简单,为马蹄形过水断面水力计算提供了一条新途径.

Owing to the fact that the calculation lormulas of normal depth for free flow in horseshoe section of tunnel and drainage culvert are not expressed bv 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 tbr ealculation 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.