Application of GNNMCI(1, N) to environmental thermal error modelling of CNC machine tools

Thermal errors are often quoted as being the largest contributor to inaccuracy of CNC machine tools, but they can be effectively reduced using error compensation. Success in obtaining a reliable and robust model depends heavily on the choice of system variables involved as well as the available input-output data pairs and the domain used for training purposes. In this paper, a new prediction model “Grey Neural Network model with Convolution Integral (GNNMCI(1, N))” is proposed, which makes full use of the similarities and complementarity between Grey system models and Artificial Neural Networks (ANNs) to overcome the disadvantage of applying a Grey model and an artificial neural network individually. A Particle Swarm Optimization (PSO) algorithm is also employed to optimize the Grey neural network. The proposed model is able to extract realistic governing laws of the system using only limited data pairs, in order to design the thermal compensation model, thereby reducing the complexity and duration of the testing regime. This makes the proposed method more practical, cost-effective and so more attractive to CNC machine tool manufacturers and especially end-users.