Experimental modeling of equilibrium surface for chip flow angle catastrophe based on transfer learning and catastrophe theory

It is difficult to accurately predict the critical depth of cut and the chip flow angle (CFA) using a single method provided by catastrophe theory. To solve this problem, an experimental modeling method for catastrophe phenomena combining transfer learning and catastrophe theory is proposed. This method is successfully used for the modeling of the equilibrium surface of the CFA catastrophe. First, the canonical equilibrium surface of cusp catastrophe provided by catastrophe theory is discretized in two paths (differentiated by $d$), and a series of canonical equilibrium point coordinates ($u,v,x$) are obtained. Then, a neural network model simulating the canonical equilibrium surface with three input nodes ($u,v,d$) and one output node ($x$) is constructed and trained. Next, the transfer learning method is applied to freeze the model and add fully connected layers before and after it to realize the required diffeomorphism from the actual parameters to the canonical parameters. The front layers have 3 nodes ($f,a_p,d\prime$) and the rear layers have 1 node ($\phi$). Finally, the model with the additional layers is fine-tuned using experimental data to obtain the actual equilibrium surface simulation model for the CFA catastrophe. The test results show that the prediction accuracies of the constructed model regarding the CFA and the critical depth of cut are better than those of the models established by other methods.