Deep learning LSTM for predicting thermally induced geometric errors using rotary axes’ powers as input parameters

Abstract

Temperature changes within a machine tool, which are partly due to internal heat sources related to the power consumption at the machine drives, result in thermally induced geometric errors of the machine. Predicting the thermally affected machine geometry facilitates the prediction of volumetric errors throughout the 5-axis machine volume. Measuring power instead of temperature is easier to implement in practice but causes drift issues. Stacked Long Short Term Memory (LSTM) with two hidden LSTM layers is applied to determine the relationship between powers and the thermal variation of geometric error parameters by remembering previous states and learning complex non-linear relationships through optimized generalized parameters of the predicting model. Optimizers Adam, RMSprop, and SGD based on exponential moving average of first order and second order moments of gradients are combined with Stacked LSTM for faster learning convergence to an optimal solution. Validation trials with various B- and C-axis motion sequences demonstrate a capability of predicting multi time steps ahead over a 40 hours period without re-measuring the geometric error parameters of the model. Stacked LSTM with the Adam optimizer has the best capability by predicting up to 93% of the main geometric error compared to the other optimizers.