Improvement of the regression model for spindle thermal elongation by a Boosting-based outliers detection approach
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Data-driven regression methods are adept at modeling the spindle thermal elongation for error reduction purposes, but are limited in their generalization ability for the established model to take effect under different work conditions, where one prime cause is that the measurement errors and environmental disturbances would inevitably lead to successive outliers in the experimental training data, and the regression algorithms tend to over-fit to such outliers in the thermal datasets which are usually small. Here, an approach is proposed for the first time to detect and remove the suspected outliers in the spindle thermal data while preserve most of the informative data at the same time, so that the disturbances from the outliers can be minimized. The proposed approach for outliers detection is a combination of Boosting and SVR (BSOD), where the support vector machine for regression (SVR) is used as the weak learner in Boosting. Furthermore, the SVR, which is now widely considered as the most suitable regression tool for mapping the temperature-thermal elongation relationship for a spindle, is adopted to regression model the spindle thermal elongation, where the genetic algorithm (GA) is employed to determine the optimal parameter setting for the modeling. Effectiveness of the BSOD approach was verified using four experimental datasets from two different spindles of precision boring machines under different work conditions. The results showed that the BSOD approach reduced the mean squared error MSE of the genetic algorithm optimized support vector machine estimation for unseen thermal elongation datasets in two cases by 66.09% and 49.13%, respectively. This research provides a feasible way to enhance the modeling quality for the thermal elongation of spindles during working process.
KeywordsSpindle Thermal elongation Boosting SVR Outlier detection
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This work is supported by the National Natural Science Foundation of China (No. 51605375), Research Project of State Key Laboratory of Mechanical System and Vibration MSV201701, State Key Laboratory for Manufacturing Systems Engineering sklms2017007, the China Postdoctoral Science Foundation (No. 2015M582645, 2017T100741), Natural Science Foundation of Shaanxi (No. 2017JM5081), and The Central Universities fundamental research funds (No. xjj2017164).
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