Neural Network Modeling of Air Spring Dynamic Stiffness Based on Its Pneumatic Physics

To meet the real-time computational requirements of active suspension control systems, this study shifts from complex microscopic physical equations to a direct nonlinear functional mapping between the relative motion states (displacement and velocity) and the output force of air springs. This approach aims to preserve critical nonlinear hysteresis characteristics while significantly reducing the computational overhead. A progressive modeling strategy is implemented to characterize these complex behaviors. Initially, polynomial fitting is employed to identify key input features; however, its limited capacity to capture intricate nonlinearities necessitates more advanced methods. Subsequently, standard Feedforward Neural Networks (FNN) are explored for their nonlinear mapping capabilities, yet their inherent “black-box” nature often leads to convergence difficulties and restricted generalization. To address these issues, a Physics-Informed Neural Network (PINN) architecture is introduced, embedding physical governing equations as regularization constraints within the loss function to integrate data-driven flexibility with mathematical rigor. Recognizing that conventional PINNs often encounter convergence challenges due to conflicts between PDE constraints and data-driven loss terms, this research develops a Physics-Embedded Hierarchical Network (PEHN). By deriving specialized PDE constraints tailored to air spring dynamics and designing a hierarchical architecture aligned with these physical requirements, the PEHN effectively balances physical priors with experimental data. Experimental results demonstrate that the proposed PEHN ensures robust convergence and superior accuracy in capturing complex nonlinearities, hysteresis effects, and dynamic stiffness variations compared to baseline models.