基于移动最小二乘法的稳健重构方法

doi:10.13229/j.cnki.jdxbgxb20191050

Abstract

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

CLC Number:

TP391.9

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.

Figures/Tables 9

Fig.1

Fig.2

Table 1

Result of two methods for example 1"

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

Table 1

Fig.3

Table 2

Result of two methods for example 2"

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

Table 2

Fig.4

Fig.5

Table 3

Fig.6

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