基于粒子群算法的抛物线形渠道断面优化方法

针对试算法工作量大、计算误差大和精度低等问题,建立了以计算流量和设计流量之差最小为目标函数的抛物线形渠道断面优化数学模型,将粒子群优化算法引入到抛物线形渠道断面优化计算中,采用粒子群算法在全局空间下搜索渠道断面优化问题的全局最优解。并以陕西省石头河灌区五丈源支渠抛物线形混凝土渠道为例,对其二次抛物线形渠道断面的方程形状参数a和设计水深h进行了优化设计。结果表明,得到满足约束条件的最优方程形状参数a为5.06,最优设计水深h为0.398 2 m。与原设计相比模型计算所得渠道过水断面面积减少了0.102 1%,渠道土方量减少了6.225 4 m~3,混凝土衬砌量减少了4.764 1 m~3,工程占地面积也随之减少。粒子群优化算法能有效地解决抛物线形渠道断面设计中的优化问题,且具有收敛速度快、计算精度高和全局寻优能力强等优点。

Optimizing Channels with Parabolic Cross-Section Using the Particle Swarm Method

A mathematical model for optimizing channels with parabolic cross section was developed in this paperin attempts to resolving the problems such as high computation demanding,low accuracy associated with the trial-error method used in the conventional method.The objective in the optimization was to minimize the difference between the calculated flow rate and designed flow rate,and the optimal solutions were solved by particle swarm algorithm assuming that the cross section of the channel is Parabolic.We took the concrete channel in Wuzhangyuan branch in the Stone River Irrigation District of Shaanxi province as an example,and the equation shape parameter (a) and the design depth (h) of the second parabolic channel section were designed optimally.The results showed that a,which met the constraints,was 5.06 and h was 0.398 2 m.Compared to the original design,the cross section,the volume of the channel and the concrete lining quantity reduced by 0.102 1％,6.225 4 m3 and 4.764 1 m3,respectively.Therefore,the particle swarm optimization algorithm can effectively solve the optimization of parabolic channel and has the advantages of fast convergence,high accuracy and more efficient in searching the global optimization solution.