Thermal Error Modeling Based on Genetic Algorithm and BP Neural Network of High-Speed Spindle System

Abstract

In order to improve the prediction accuracy of the thermal error models, grey cluster grouping and correlation analysis were proposed to optimize and select the heat-sensitive points to improve the performances of the thermal error model and minimize the independent variables to reduce modeling cost. Subsequently, the neural network with back propagation (BP) algorithm was proposed to construct the strongly nonlinear mapping relationship between spindle thermal errors and typical temperature variables. However, the shortcomings of the BP network restricted the accuracy, robustness and convergence of thermal error models. Then, a genetic algorithm (GA), which regarded the reciprocal of the absolute value sum of the differences between the predicted and desired outputs as the number of nodes in the hidden layer, was proposed to optimize the structure and initial values of the network. And the number of the nodes in the hidden layer can be determined by performing such operations of GAs. Moreover, the reciprocal of the sum square of the difference between the predicted and expected outputs of individuals is regarded as the fitness function and the weights and thresholds of the BP neural network are optimized by setting the control parameters of GAs. Then, the elongation and thermal tilt angle models of high-speed spindles were proposed based on BP and GA-BP networks and the fitting and prediction abilities were compared. The results showed that the grey cluster grouping and correlation analysis could depress the multicollinearity among temperature variables and improve the stability and accuracy of the thermal error models. Moreover, although the traditional BP network had better fitting ability, its convergence and generality were far worse than the GA-BP model and it is more suitable to use the GA-BP neural network as the thermal error modeling method in the compensation system.