Research on precision prediction of heavy-duty lathes based on hybrid PINNS neural network

A positioning error prediction method based on hybrid physical information neural networks ( Hybrid-PINNs) was proposed to solve the problem of heavy CNC lathe positioning accuracy which is difficult to reliably predict in few-shot and complex working conditions.By combining the easily obtained spatial position sensor data with the engineering approximate physical constraints (position continuity and smoothness), the data item and physical residual item were introduced into the neural network training objective at the same time, so as to improve the extrapolation and robustness of the model. Based on the actual measured data of Z-axis of a certain type of heavy lathe (Section A for augmented training, Section B/C for extrapolation test).The results show that the hybrid model demonstrates a significant improvement compared with the single model in test of Section B, Section C and the merged B C.In section B, relative to BP, PINNs reduced error by 60.4%, and Hybrid-PINNs further reduced it to 82.8%; relative to RBF, Hybrid-PINNs achieved a 70.1% reduction. In section C, relative to BP, PINNs reduced error by 82.0%, and Hybrid-PINNs further reduced it to 86.8%; relative to PINNs, Hybrid-PINNs still achieved a 76.9%reduction. In Section B and C, relative to BP, Hybrid-PINNs reduced overall error by 85.3%; relative to RBF, the reduction reached 79.0%. To ensure the engineering applicability, the article also detailed the preprocessing approach using sixth-order polynomial fitting and equidistant sampling, along with the model architecture, loss weighting, training procedure, and linear calibration workflow. The study provides a feasible technical path with both physical consistency and data-driven capability for online state monitoring and accuracy compensation of heavy machine tools.