Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm

For thermal error compensation technology of CNC machine tools, the collinearity between temperature sensitive points is the main factor for determining the predicted robustness of thermal error model. The temperature sensitive points are input variables of the thermal error model. This paper studie...

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Vydané v:	International journal of machine tools & manufacture Ročník 113; s. 35 - 48
Hlavní autori:	Liu, Hui, Miao, En Ming, Wei, Xin Yuan, Zhuang, Xin Dong
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elmsford Elsevier Ltd 01.02.2017 Elsevier BV
Predmet:	Algorithms CNC machine tools Collinearity Correlation analysis Correlation coefficients Error analysis Error compensation Error detection Machine tools Mathematical models Modelling Numerical controls Predicted accuracy and robustness Regression Regression analysis Ridge regression Robustness (mathematics) Seasons Temperature Thermal error Three dimensional models Ridge regression Thermal error Collinearity Predicted accuracy and robustness CNC machine tools
ISSN:	0890-6955, 1879-2170
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Abstract	For thermal error compensation technology of CNC machine tools, the collinearity between temperature sensitive points is the main factor for determining the predicted robustness of thermal error model. The temperature sensitive points are input variables of the thermal error model. This paper studies the thermal error of Leaderway V-450 type CNC machine tools during different seasons. It is found that although the commonly used temperature sensitive point selection methods can significantly reduce the collinearity between temperature sensitive points, the correlation between some of the selected temperature-sensitive points and thermal error is weak. This causes the temperature-sensitive points to be variable and the predicted accuracy and robustness of thermal error to be reduced. Therefore, in this paper, the temperature sensitive points are selected directly by their correlation with thermal error to eliminate variability. However, the experimental results also show that the collinearity between temperature sensitive points is very large. Hence, the ridge regression algorithm is used to establish a thermal error model to inhibit the bad influence of collinearity on the thermal error predicted robustness. Thus, the “robustness ridge regression machine tool thermal error modeling method” is proposed, the “RRR method” for short. In addition, in the “RRR method”, the correlation coefficient is used to measure the correlation between temperature sensitive points and thermal error instead of the commonly used gray correlation; because this paper finds that the gray correlation algorithm is essentially inapplicable for measuring a negative correlation. Based on the thermal error experiment data for the whole year, the “RRR method” is compared with two currently used methods, and the results show that the “RRR method” can significantly enhance the long-term predicted accuracy and robustness of thermal error. Finally, the application effect of practical compensation shows that the “RRR method” is usable and effective. •The long-term prediction performance of commonly used traditional machine tool thermal error modeling methods is deeply studied.•Although the traditional methods can significantly reduce the collinearity between temperature sensitive points (Input variables of thermal error model), the correlation between some points and thermal error is weak.•The temperature sensitive points which have strong correlation with thermal error also have high collinearity between them.•The ridge regression algorithm is used to inhibit the bad influence of collinearity on the thermal error predicted robustness.•The thermal error predicted effect of proposed method is verified by 18 thermal error experiments done in different seasons.
AbstractList	For thermal error compensation technology of CNC machine tools, the collinearity between temperature sensitive points is the main factor for determining the predicted robustness of thermal error model. The temperature sensitive points are input variables of the thermal error model. This paper studies the thermal error of Leaderway V-450 type CNC machine tools during different seasons. It is found that although the commonly used temperature sensitive point selection methods can significantly reduce the collinearity between temperature sensitive points, the correlation between some of the selected temperature-sensitive points and thermal error is weak. This causes the temperature-sensitive points to be variable and the predicted accuracy and robustness of thermal error to be reduced. Therefore, in this paper, the temperature sensitive points are selected directly by their correlation with thermal error to eliminate variability. However, the experimental results also show that the collinearity between temperature sensitive points is very large. Hence, the ridge regression algorithm is used to establish a thermal error model to inhibit the bad influence of collinearity on the thermal error predicted robustness. Thus, the “robustness ridge regression machine tool thermal error modeling method” is proposed, the “RRR method” for short. In addition, in the “RRR method”, the correlation coefficient is used to measure the correlation between temperature sensitive points and thermal error instead of the commonly used gray correlation; because this paper finds that the gray correlation algorithm is essentially inapplicable for measuring a negative correlation. Based on the thermal error experiment data for the whole year, the “RRR method” is compared with two currently used methods, and the results show that the “RRR method” can significantly enhance the long-term predicted accuracy and robustness of thermal error. Finally, the application effect of practical compensation shows that the “RRR method” is usable and effective. •The long-term prediction performance of commonly used traditional machine tool thermal error modeling methods is deeply studied.•Although the traditional methods can significantly reduce the collinearity between temperature sensitive points (Input variables of thermal error model), the correlation between some points and thermal error is weak.•The temperature sensitive points which have strong correlation with thermal error also have high collinearity between them.•The ridge regression algorithm is used to inhibit the bad influence of collinearity on the thermal error predicted robustness.•The thermal error predicted effect of proposed method is verified by 18 thermal error experiments done in different seasons. For thermal error compensation technology of CNC machine tools, the collinearity between temperature sensitive points is the main factor for determining the predicted robustness of thermal error model. The temperature sensitive points are input variables of the thermal error model. This paper studies the thermal error of Leaderway V-450 type CNC machine tools during different seasons. It is found that although the commonly used temperature sensitive point selection methods can significantly reduce the collinearity between temperature sensitive points, the correlation between some of the selected temperature-sensitive points and thermal error is weak. This causes the temperature-sensitive points to be variable and the predicted accuracy and robustness of thermal error to be reduced. Therefore, in this paper, the temperature sensitive points are selected directly by their correlation with thermal error to eliminate variability. However, the experimental results also show that the collinearity between temperature sensitive points is very large. Hence, the ridge regression algorithm is used to establish a thermal error model to inhibit the bad influence of collinearity on the thermal error predicted robustness. Thus, the "robustness ridge regression machine tool thermal error modeling method" is proposed, the "RRR method" for short. In addition, in the "RRR method", the correlation coefficient is used to measure the correlation between temperature sensitive points and thermal error instead of the commonly used gray correlation; because this paper finds that the gray correlation algorithm is essentially inapplicable for measuring a negative correlation. Based on the thermal error experiment data for the whole year, the "RRR method" is compared with two currently used methods, and the results show that the "RRR method" can significantly enhance the long-term predicted accuracy and robustness of thermal error. Finally, the application effect of practical compensation shows that the "RRR method" is usable and effective.
Author	Liu, Hui Wei, Xin Yuan Zhuang, Xin Dong Miao, En Ming
Author_xml	– sequence: 1 givenname: Hui surname: Liu fullname: Liu, Hui – sequence: 2 givenname: En Ming surname: Miao fullname: Miao, En Ming email: miaoem@163.com – sequence: 3 givenname: Xin Yuan surname: Wei fullname: Wei, Xin Yuan – sequence: 4 givenname: Xin Dong surname: Zhuang fullname: Zhuang, Xin Dong
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SubjectTerms	Algorithms CNC machine tools Collinearity Correlation analysis Correlation coefficients Error analysis Error compensation Error detection Machine tools Mathematical models Modelling Numerical controls Predicted accuracy and robustness Regression Regression analysis Ridge regression Robustness (mathematics) Seasons Temperature Thermal error Three dimensional models
Title	Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm
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