TY - JOUR
T1 - Robust moving total least squares
T2 - A technique for the reconstruction of measurement data in the presence of multiple outliers
AU - Gu, Tianqi
AU - Lin, Hongxin
AU - Tang, Dawei
AU - Lin, Shuwen
AU - Luo, Tianzhi
N1 - Funding Information:
This work was supported by the National Natural Science Foundation of China (Grant No. 51605094 and 11572316 ), the Science Project of Anhui Province in China (Grant No. 201903a07020019), and the Fundamental Research Funds for the Central Universities (Grant No. WK2480000006 ).
Publisher Copyright:
© 2021 Elsevier Ltd
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2022/3/15
Y1 - 2022/3/15
N2 - This article is concerned with the reconstruction of contaminated measurement data based on the moving total least squares (MTLS) method, which is extensively applied to many engineering and scientific fields. Traditional MTLS method is lack of robustness and sensitive to the outliers in measurement data. Based on the framework of MTLS method, we proposed a robust MTLS method called RMTLS method by introducing a two-step pre-process to detect and remove the anomalous nodes in the support domain. The first step is an iterative regression procedure that combines with k-medoids clustering to automatically reduce the weight of anomalous node for a regression-based reference (curve or surface). Based on the distances between reference and discrete points, the second step adopts a density function defined by a sorted distance sequence to select the normal points without setting a threshold artificially. After the two-step pre-process, weighted total least square is performed on the selected point set to obtain the estimation value. By disposing of the anomalous nodes in each independent support domain, multiple outliers can be suppressed within the whole domain. Furthermore, the suppression of multiple continual outliers is possible by adopting asymmetric support domain and introducing previous estimation points. The proposed method shows great robustness and accuracy in reconstructing the simulation and experiment data.
AB - This article is concerned with the reconstruction of contaminated measurement data based on the moving total least squares (MTLS) method, which is extensively applied to many engineering and scientific fields. Traditional MTLS method is lack of robustness and sensitive to the outliers in measurement data. Based on the framework of MTLS method, we proposed a robust MTLS method called RMTLS method by introducing a two-step pre-process to detect and remove the anomalous nodes in the support domain. The first step is an iterative regression procedure that combines with k-medoids clustering to automatically reduce the weight of anomalous node for a regression-based reference (curve or surface). Based on the distances between reference and discrete points, the second step adopts a density function defined by a sorted distance sequence to select the normal points without setting a threshold artificially. After the two-step pre-process, weighted total least square is performed on the selected point set to obtain the estimation value. By disposing of the anomalous nodes in each independent support domain, multiple outliers can be suppressed within the whole domain. Furthermore, the suppression of multiple continual outliers is possible by adopting asymmetric support domain and introducing previous estimation points. The proposed method shows great robustness and accuracy in reconstructing the simulation and experiment data.
KW - Measurement data
KW - Moving least squares
KW - K-medoids clustering
KW - Outlier
UR - http://www.scopus.com/inward/record.url?scp=85118500006&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2021.108542
DO - 10.1016/j.ymssp.2021.108542
M3 - Article
VL - 167
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 108542
ER -