基于移动最小二乘法的稳健重构方法

doi:10.13229/j.cnki.jdxbgxb20191050

摘要/Abstract

摘要：

在实际工程问题中，由于人为或环境等外界因素的影响，通过仪器测量获得的数据，不可避免地会存在粗大误差，以某种方式偏离测量数据，导致数据重构的精度不稳定。针对包含粗大误差的测量数据，本文提出一种基于移动最小二乘法的稳健重构方法，该方法对支持域内节点采用最小二乘法进行拟合，将生成的拟合点根据引入的几何特征参数α，量化各节点的异常程度并剔除异常值。对支持域内的剩余节点采用加权最小二乘法确定局部拟合系数，移动支持域完成全域的曲线曲面重构。在每个支持域内仅剔除一个点，就能有效地处理多个粗大误差，且剔除过程无需主观地设定阈值或分配权重。数值模拟与测量实验结果表明：本文方法可有效剔除测量数据中的粗大误差，与传统移动最小二乘法相比，本文数值案例精度能提高60%以上，具有良好的重构稳健性。

关键词: 计算机应用, 移动最小二乘法, 曲线曲面重构, 粗大误差, 稳健性

Abstract:

In practical engineering problems， due to the influence of external factors such as artificial or environmental disturbance， there will inevitably be outliers in the measurement data obtained by instruments. The outliers will deviate from the measurement data in some way， resulting in the instability of the accuracy of data reconstruction. For the measurement data with outliers， a robust reconstruction method based on Moving Least Squares （MLS） is proposed. This method fits the nodes with the least square method in the influence domain. The abnormal degree of generated fitting point is quantified according to the geometric characteristic parameter α， and the outliers is eliminated. The local fitting coefficients are determined with the weight least square by using the remaining nodes in the influence domain， and the curve and surface reconstruction is completed by moving the influence domain. By trimming only one point in each influence domain， the multiple outliers of measurement data can be effectively handled， and it is unnecessary to set threshold values subjectively or assign weights， which avoids the negative influence of manual operations. The numerical simulation and experimental results show that the proposed method can effectively eliminate the outliers in the measurement data. Compared with the MLS method， the accuracy of the numerical case can be improved by more than 60%.

Key words: computer application, moving least squares, curve and surface reconstruction, outliers, robust

中图分类号:

TP391.9

顾天奇,胡晨捷,涂毅,林述温. 基于移动最小二乘法的稳健重构方法[J]. 吉林大学学报(工学版), 2021, 51(2): 685-691.

Tian-qi GU,Chen-jie HU,Yi TU,Shu-wen LIN. Robust reconstruction method based on moving least squares algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 685-691.

图/表 9

图1

图2

表1

案例一两种方法的重构结果"

重构方法	$s$	RMS
移动最小二乘法	0.392 431	0.004 299
稳健重构方法	0.058 993	0.000 375

表1

图3

表2

案例二两种方法的重构结果"

重构方法	$s$	RMS
移动最小二乘法	1.815 587	0.023 557
稳健重构方法	0.742 394	0.003 551

表2

图4

图5

表3

图6

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