河道断面分形维数对面积测算误差的影响研究  

River section topography simulation and section area error analysis

作　　者：元媛[1] 卢金友[1] 齐孟骥 张小峰[2] YUAN Yuan LU Jin-you QI Meng-ji ZHANG Xiao-feng(Changfiang River Scientific Research Institute of Changjiang Water Resources Commission, Wuhan 430010, China State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China)

机构地区：[1]长江水利委员会长江科学院,湖北武汉430010 [2]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072

出　　处：《泥沙研究》2017年第5期13-18,共6页Journal of Sediment Research

基　　金：国家科技支撑计划项目(2013BAB12B02;2013BAB12B01;2013BAB12B04);国家重点研发计划课题(2016YFC0402309);中央级公益性科研院所基本科研业务费项目(CKSF201710/HL)

摘　　要：采用分形布朗运动模型和数学函数模拟了不同形态的断面。参考长江河道地形测量方式,按一定间距在断面上提取测点数据并计算断面面积,引入分形维数描述断面不规则程度。通过断面面积的相对误差与分形维数之间的相关性分析,揭示了横断面面积计算误差的根源是河道地形起伏,误差随着断面分形维数的增大而呈幂函数递增。The fractional Brown motion and mathematical function was applied to simulate river cross section with different morphology.Measuring points were extracted according to certain distance based on the topographic survey of the Yangtze River.Sectional areas were computed by the triangle method and trapezoidal method by sampling data,in addition to the relative errors of the section areas.Fractal dimension was introduced to depict the complexity of cross-section.Through correlation analysis between relative error and the fractal dimension,this study shows that the causes of the calculation error is river topographic relief,and the relative error has a correlation of power function with the fractal dimension of the cross-section.

关 键 词：河床演变 河道断面 断面面积 分形理论 误差 

分 类 号：TV147[水利工程—水力学及河流动力学]