正弦余弦算法求解含有异常值的非线性数据拟合  

Nonlinear data fitting with outliers based on sine cosine algorithm

作　　者：雍龙泉[1,2] 贾伟 黎延海 YONG Longquan;JIA Wei;LI Yanhai(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723001,China;Shaanxi Key Laboratory of Industrial Automation,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001 [2]陕西省工业自动化重点实验室,陕西汉中723001

出　　处：《安徽大学学报（自然科学版）》2023年第3期1-5,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(1401357);陕西省教育厅重点科学研究计划项目(20JS021)。

摘　　要：针对非线性数据拟合问题,建立以残差的平方和与绝对值和为目标的最小二乘与最小一乘模型,采用正弦余弦算法计算模型参数.计算结果表明:如果数据的分布是对称且无异常值,则最小二乘得到的结果与最小一乘得到的结果基本一致;如果数据存在异常值,则异常值对最小二乘有着较大的影响,而对最小一乘的影响较小.Aiming at the nonlinear data fitting problem,least squares regression and least absolute deviation models are established respectively aiming at the sum of squares and sum of absolute values of residuals,and the parameters of models are calculated by using sine cosine algorithm.Numerical computing shows that curvefitting results of least squares regression and least absolute deviation are very similar under the condition that the distribution of the data is symmetric and without outliers.When some outliers exist,curvefitting results show that the outliers have great influence on the least squares regression,but little influence on the least absolute deviation.

关 键 词：非线性数据拟合 最小二乘 最小一乘 正弦余弦算法 异常值 

分 类 号：O212[理学—概率论与数理统计] TP18[理学—数学]