Development of a cascaded multitask physics-informed neural network (CM-PINN) to construct the muti-physical field model of rubber bushing press fitting

The real-time and accurate prediction of the stress–strain and deformations field of material is a vital function for the intelligent press fitting system of the rubber bushing. The physics-informed neural network (PINN) provide an efficient approach to constructing physical fields with high robustness and interpretability in real time. However, currently, PINN usually solves problems under known boundary conditions, which are not given explicitly in most realistic engineering problems. This study proposes a cascaded multitask PINN (CM-PINN) that divides the problem solving of rubber bushing interference fit into two phases: boundary computation and forward solving of the physical field. In CM-PINN, one sub-network is used for boundary computation, while two other sub-networks are used for computing the physical fields of hyperelastic material, rubber. In both stages, physical constraints are incorporated into the sub-networks. These subnetworks are trained hybridly through the cascaded framework using data obtained from the finite element model (FEM), which was verified by experimental results. In order to validate the CM-PINN model, FEM data are used as a reference solution for comparison with conventional PINN. To evaluate the advantages of CM-PINN, ablation tests are conducted by randomly selecting training samples with different sizes. It is found that CM-PINN has higher accuracy and convergence compared to hybrid output PINNs. CM-PINN shows remarkable improvement in its generalization ability in the case of small sample size, underscoring its robust applicability across different data scenarios.