Physics-Informed Modeling of Electrohydraulic Semi-Active Dampers Using LSTM, Transformer and Extended Hyperbolic Tangent Model

This study investigates physics-informed and data-driven hybrid modeling strategies for an automotive-grade electrohydraulic (EH) semi-active damper system. Although deep sequence learning architectures such as Long Short-Term Memory (LSTM) networks and Transformers can provide high predictive accuracy, purely data-driven approaches may struggle to preserve physical consistency and maintain robustness under unseen operating conditions. These limitations become more pronounced for EH dampers, whose hysteretic characteristics exhibit highly nonlinear and non-proportional variations under different current and frequency excitations, unlike the more scalable behavior commonly observed in magnetorheological (MR) dampers. To address these challenges, two physics-informed integration strategies are investigated. The first strategy combines physical and data-driven models through parallel loss-function synthesis. The second strategy introduces a learnable physics layer (PINN-Hybrid), in which the coefficients of the extended hyperbolic tangent formulation are adaptively learned within the neural network architecture. In this framework, the physical model acts as a structural regularization mechanism that guides the learning process while preserving the flexibility of data-driven sequence modeling. The proposed models are evaluated under abrupt valve-control operating conditions. Comparative results indicate that the proposed physics-informed architectures improve hysteresis continuity, physical plausibility, and robustness compared with purely data-driven approaches, particularly in low-velocity and transition regions. The proposed framework therefore demonstrates the potential of physics-informed learning strategies for reliable real-time modeling of nonlinear automotive EH damper systems.