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 se lect appropriate temperature variables as well as to obtain accurate therma l error component models. In this research, an optimization method is prese nted to overcome this difficulty. The optimization objective function is fo rmulated by a modified model adequacy criterion based on the Mallows' C-p s tatistic. A new search method is developed for discrete search domains with non-directional or unknown-order variables. The search process includes co rrelation grouping, representative searching, group searching and variable searching. It not only ensures optimal results but also reduces computation al time greatly. One modeling example is presented. The optimal model is fo und with a 0.982 R-2-value using four temperature variables selected from 4 6 candidates of temperature variables. The largest error residual is reduce d 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 a s well. (C) 1999 Elsevier Science Ltd. All rights reserved.