基于π定理及多元线性回归的河道稳定水力几何形态公式研究

Study on Formula for Stable Hydraulic Geometry of Channel Based onπTheorem and Multiple Linear Regression

基于量纲分析—π定理找出了河道稳定水力几何形态的影响参数Π1和Π2,将303组原型观测和水槽实验资料作为样本数据进行多元线性回归分析,提出了一套稳定河宽B R和稳定水深h R的计算公式。选取Yalin和da Silva方法作为标准方法对该公式进行检验比较,结果表明:两者计算散点图中计算河宽和计算水深值均与实测值接近;总体而言,公式各误差指标略优于Yalin和da Silva方法,但从各误差指标的数值上看两者差别不大。故可认为2种方法计算精度相当,可将公式应用于工程实践。

The influence parameters(Π1 andΠ2)of the stable hydraulic geometry of the channel were found based on the dimensional analysis,namelyπtheorem.In addition,a set of calculation formulas for stable channel width B R and stable channel depth h R were proposed,with multiple linear regression conducted on 303 sets of sample data from prototype measurements and flume experiments.Yalin and da Silva methods were selected as standard methods to test and compare the formula in this paper,and the results show that the channel width and the channel depth calculated in the scatter plots with both methods are all close to the measured values.In general,the error indexes of the formula in this paper are slightly better than those of the Yalin and da Silva methods,while the difference between them is not significant in terms of the values of the error indexes.Therefore,it can be considered that the calculation accuracy of the two methods is equivalent,and the formula in this paper can be applied to engineering practice.