Rapid prediction of cavity expansion ratio field in the upsetting process based on proper orthogonal decomposition and machine learning

In the upsetting process, the cavity expansion ratio is commonly used to evaluate the cracking risk caused by improper process parameter settings. Although high accuracy can be achieved by first obtaining the stress and strain fields through finite element simulations and then calculating the cavity expansion ratio, repeated modeling and solving are still required when the process parameters change, resulting in high computational cost and making rapid evaluation difficult. In addition, changes in process conditions lead to the evolution of the workpiece geometric boundary, which causes inconsistency in the dimensions of physical-field data under different conditions and makes the conventional POD method difficult to apply directly. To address these issues, this paper proposes a rapid prediction method for the cavity expansion ratio under shape-varying conditions. First, the cross-sectional region of the workpiece is extracted from finite element results, and masks are used to characterize the geometric shape features under different conditions. Then, physical fields with different shapes are uniformly represented as rectangular regions of fixed size through interpolation-based extension, and a unified snapshot matrix satisfying the requirements of POD decomposition is constructed to extract the dominant modal features. On this basis, nonlinear mapping models between process parameters and workpiece shape, as well as between process parameters and POD modal coefficients, are established to achieve rapid prediction of the cavity expansion ratio field under target conditions. Finally, the true geometric region of the workpiece is restored using the predicted mask, yielding the cavity expansion ratio distribution under the target condition. The results show that the proposed method can effectively predict the cavity expansion ratio field under different conditions. The predicted results are in good agreement with the finite element results, and the errors are mainly concentrated in local boundary regions. Compared with conventional finite element simulations, the proposed method significantly improves computational efficiency and provides an efficient prediction tool for cracking-risk evaluation and process optimization in the upsetting process.