Optimal linear combination of neural networks to model thermally induced error of machine tools

In recent years, neural network (NN) modelling methods with different architectures and training strategies have been widely used in machine tool thermal error compensation field. Most of them are typically trial-and-error procedures in choosing the 'best network', while discarding all the rest. This paper introduces a new modelling method combining all of the trained NNs. This method is called optimal linear combination of neural networks (OLCNN), which can integrate the useful knowledge of the component NNs and thus improve model accuracy and generalisation ability (i.e., model robustness). Algorithms for selecting the component networks are presented after some associated critical issues are discussed. Real cutting experiments are conducted on a CNC turning machine to validate the effectiveness of the method. Analysis of different modelling conditions indicates that the best situation for using OLCNN is when the component networks are merely moderately trained. The modelling results show that significant improvement in the model accuracy and robustness is achieved comparing with single best NN and simple average of trained NNs. It is also applicable to hybrid different modelling methods other than NN.