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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。
A fractal Brownian motion model and mathematical function were used to simulate different cross sections. Reference to the Yangtze River terrain measurement method, according to a certain distance in the cross-section of the measured data points to extract and calculate the cross-sectional area, the introduction of fractal dimension describes the extent of irregular cross-section. The correlation analysis between the relative error of cross-sectional area and the fractal dimension revealed that the root cause of the cross-sectional area error was the undulation of the river channel, and the error increased exponentially with the increase of the fractal dimension of the cross-section.