Physics-informed neural identification of unmeasurable contact damping in helical hydraulic actuators via spectral-aware hard-gating mechanism

The helical oscillating cylinder (HOC) is a compact, high-torque-density actuator whose internal contact damping is difficult to measure directly, limiting dynamic-model calibration. We present a model-based identification framework that integrates architectural and training strategies to address high-frequency transient responses, pre-impact causality, and coupled damping-parameter optimization. A four-degree-of-freedom lumped-parameter model describes startup impacts using a modified Hertzian viscoelastic contact law. On this basis, a hard-gating physics-informed neural network (HG-PINN) combines spectral-aware Fourier features, causal hard gating, and freeze–thaw two-phase training. Ablation studies examine how these components and the training strategy contribute to transient-response reconstruction and stable damping-parameter identification. In tests using synthetic acceleration responses with additive Gaussian noise, both damping-parameter errors remained below 1% at 30% noise and below 3% at 50% noise. Against a deterministic Levenberg– Marquardt baseline under identical forward-model settings, HG-PINN retained substantially lower errors as noise increased. It required no external forward-model evaluations during parameter updates. These modelto- model tests support the robustness of HG-PINN under the tested noise conditions and motivate future experimental validation for digital-twin calibration of hydraulic actuators.