Optimal temperature variable selection by grouping approach for thermal error modeling and compensation

One of the difficult issues in a thermal error compensation scheme is to select appropriate temperature variables as well as to obtain accurate thermal error component models. In this research, an optimization method is presented to overcome this difficulty. The optimization objective function is formulated by a modified model adequacy criterion based on the Mallows' C_p statistic. A new search method is developed for discrete search domains with non-directional or unknown-order variables. The search process includes correlation grouping, representative searching, group searching and variable searching. It not only ensures optimal results but also reduces computational time greatly. One modeling example is presented. The optimal model is found with a 0.982 R²-value using four temperature variables selected from 46 candidates of temperature variables. The largest error residual is reduced down to 2.2 microns from 20.0 microns. The comparison of modeling results from the proposed approach and three other modeling methods is addressed as well.