梯度下降法在沉积物粒度分布拟合中的应用

被引：13

作者：

陈海波 ^{[1
]}

吕咸青 ^{[1
]}

乔彦松 ^{[2
]}

机构：

[1] 中国海洋大学物理海洋实验室

[2] 中国地质科学院地质力学研究所

来源：

数学的实践与认识 | 2011年 / 41卷 / 13期

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;

D O I：

暂无

中图分类号：

O241.5 [数值逼近]; P512.2 [剥蚀作用、搬运作用、沉积作用];

学科分类号：

070102 [计算数学]; 070908 [沉积学（含古地理学）];

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.

引用

页码：78 / 87

页数：10

共 14 条

[1]

Grain-size and accumulation rate records from Late Cenozoic aeolian sequences in northern China: Implications for variations in the East Asian winter monsoon and westerly atmospheric circulation.[J].Donghuai Sun;Ruixia Su;Jan Bloemendal;Huayu Lu.Palaeogeography; Palaeoclimatology; Palaeoecology.2008, 1

[2]

Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start.[J]..Journal of Computational and Applied Mathematics.2008, 1

[3]

On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution [J].

Jukic, Dragan ;

Bensic, Mirta ;

Scitovski, Rudolf .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2008, 52 (09) :4502-4511

[4]

Monsoon and westerly circulation changes recorded in the late Cenozoic aeolian sequences of Northern China [J].

Donghuai, S .

GLOBAL AND PLANETARY CHANGE, 2004, 41 (01) :63-80

[5]

A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances [J].

Atieg, A ;

Watson, GA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (02) :277-296

[6]

A review of the parameter estimation problem of fitting positive exponential sums to empirical data [J].

Holmström, K ;

Petersson, J .

APPLIED MATHEMATICS AND COMPUTATION, 2002, 126 (01) :31-61

[7]

Grain-size distribution function of polymodal sediments in hydraulic and aeolian environments; and numerical partitioning of the sedimentary components.[J].Donghuai Sun;J Bloemendal;D.K Rea;J Vandenberghe;Fuchu Jiang;Zhisheng An;Ruixia Su.Sedimentary Geology.2002, 3

[8]

Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola [J].