钟亮, 许光祥. 床面粗糙形态的二元分形插值模拟[J]. 水科学进展, 2011, 22(5): 662-667.
引用本文: 钟亮, 许光祥. 床面粗糙形态的二元分形插值模拟[J]. 水科学进展, 2011, 22(5): 662-667.
ZHONG Liang, XU Guang-xiang. Bivariate fractal interpolation for estimating rough channel bedform[J]. Advances in Water Science, 2011, 22(5): 662-667.
Citation: ZHONG Liang, XU Guang-xiang. Bivariate fractal interpolation for estimating rough channel bedform[J]. Advances in Water Science, 2011, 22(5): 662-667.

床面粗糙形态的二元分形插值模拟

Bivariate fractal interpolation for estimating rough channel bedform

  • 摘要: 针对床面粗糙形态具有自相似性的特点,应用二元分形插值迭代函数系统,对床面粗糙形态进行了分形插值模拟,模拟中分形插值邻域Ak根据Kriging空间插值方法的变异函数球状模型确定,垂直比例因子sm,n通过基于插值点数据的多元统计分析确定。结果表明:分形插值重构的床面粗糙形态与原床面形态的相似程度将随着插值点信息量ic的增加而提高,且ic仅需达到某一较小值(如ic≥0.0625),得到的床面粗糙形态即可具有较高的逼真度,其分维数也与理论值接近。因此,在测量数据不足的情况下,采用二元分形插值模拟方法可获得逼真度较高的精细床面粗糙形态。

     

    Abstract: The rough bedform is estimated using the self-similar characteristics of bedforms together with the bivariate fractal interpolation method that is based upon the iterative function system. The interpolation fields Ak are determined using the Kriging interpolation method with a spherical variogram for Kriging. The vertical scaling factors sm,n are obtained through the use of the multi-variate statistical analysis of interpolated data. The results show that the similarity between the estimated bedforms and the initial bedforms can be improved with increasing the number of data items interpolation ic. In particular, when ic approaches to a very low value of the threshold (0.0625), a high level similarity in bedforms is reached. The estimated fractal dimension will be also close to its theoretical value. The bivariate fractal interpolation method can be used as an effective means of estimating irregular bedforms in rough channels with a high level similarity, where observed data are insufficient.

     

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