Dynamic filling and prediction of environmental compensation parameters for positioning error interferometry of CNC machine tools based on a dual hybrid neural network

Laser interferometry is widely used to measure positioning errors in CNC machine tools. The Edlén formula utilizes environmental parameters to determine the air refractive index, enabling accurate correction of laser interferometric measurements. Nevertheless, current environmental sensing systems exhibit long data update intervals. During these intervals, conventional methods rely on the environmental parameters uploaded at the preceding moment for compensation, which leads to outdated compensation parameters and limited dynamic responsiveness to environmental variations, thus failing to meet the requirements for high temporal resolution measurement compensation. To overcome this, we propose what we believe to be a novel method based on a dual hybrid neural network. The method first employs a strategy that combines generative adversarial network (GAN) residual training with linear interpolation to perform mini-batch training, enabling the rapid generation of high temporal resolution datasets from limited data collected within short time windows (1-2 minutes), shortening training time while improving prediction accuracy. Subsequently, a hybrid model integrating long short-term memory (LSTM), linear regression, and support vector regression (SVR) is constructed and trained to achieve precise prediction of environmental parameters, filling the gap in the data update interval for environmental parameters. Under normal experimental conditions, for temperature, experiments show that the root mean square error (RMSE) of the filled values is as low as 0.011 °C. Compared to traditional methods, when the true displacement value is 1 m, compensation using predicted values can enhance the compensation accuracy by up to 128 nm.