| 梯度下降法在沉积物粒度分布拟合中的应用 |
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| 引用本文： | 陈海波,吕咸青,乔彦松.梯度下降法在沉积物粒度分布拟合中的应用[J].数学的实践与认识,2011,41(13). |
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| 作者姓名： | 陈海波 吕咸青 乔彦松 |
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| 作者单位： | 1. 中国海洋大学物理海洋实验室,山东青岛,266100
2. 中国地质科学院地质力学研究所,北京,100081 |
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| 基金项目： | 国家863计划(2007AA09Z118,2008AA09A402); 国家自然科学基金(41076006,40472088) |
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| 摘 要： | 结合实测数据,以三个对数正态分布函数的和函数为拟合函数,以梯度下降法为主要方法,对沉积物粒度分布进行了数据拟合,通过数值实验我们发现:利用梯度下降法可以有效地优化分布函数的各参数,实现拟合残差的稳步持续减小,具有良好的可操作性,拟合效果是令人满意的,它为我们进行数据拟合提供了一条新的思路,同时此方法也可以推广到解决其他极值问题.
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| 关 键 词： | 非线性数据拟合 最小二乘 梯度 3个对数正态分布的叠加 激光粒度 |
Application of Gradient Descent Method to the Sedimentary Grain-Size Distribution Fitting |
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| CHEN Hai-bo,LV Xian-qing,QIAO Yan-song.Application of Gradient Descent Method to the Sedimentary Grain-Size Distribution Fitting[J].Mathematics in Practice and Theory,2011,41(13). |
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| Authors: | CHEN Hai-bo LV Xian-qing QIAO Yan-song |
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| Institution: | CHEN Hai-bo~1,LV Xian-qing~1,QIAO Yan-song~2 (1.Laboratory of Physical Oceanography,Ocean University of China,Qingdao 266100,China) (2.Institute of Geomechanics,Chinese Academy of Geological Sciences,Beijing 100081,China) |
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| Abstract: | The gradient descent(GD)method is used to fit the measured data(i.e.the laser grain-size distribution of the sediments)with a sum of three weighted lognormal functions. The numerical results indicate that the GD method not only operates easily but also could effectively optimize the parameters of the fitting function with the error decreasing steadily. Meanwhile the overall fitting results are satisfactory.As a new way of data fitting,the GD method could also expand to be used to solve other optimization pr... |
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| Keywords: | nonlinear least squares data fitting gradient descent mixture distribution of three lognormal components laser grain-size |
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