A novel dynamic modeling method for magnetorheological damper based on physics-informed residual learning

Magnetorheological dampers (MRD) exhibit strongly nonlinear hysteretic behavior, which poses significant challenges for accurate dynamic modeling and limits the full exploitation of their controllable performance. To address this issue, a physics-informed residual learning framework is proposed for modeling the nonlinear dynamics of MRD. A Physics-Informed B-spline Curve Hysteresis (PIBSH) model is first developed to establish a morphology-based white-box parametric formulation, enabling a physically interpretable phenomenological representation of the damping force. The proposed model decomposes the damping force into linear components and a nonlinear hysteretic component described by B-spline functions. By leveraging B-spline basis functions and control points, the model effectively captures the mapping between motion states and local hysteretic characteristics. To further enhance predictive accuracy, a Kolmogorov–Arnold Transformer (KAT) is constructed, integrating nonlinear feature extraction capability of the Kolmogorov–Arnold Network (KAN) with the attention-based temporal modeling advantage of the Transformer. Based on this structure, a hybrid model termed PIKAT is established, where KAT learns and compensates for the residuals between the PIBSH predictions and experimental measurements. Comparative experiments demonstrate that the PIBSH model achieves superior accuracy in representing local hysteretic behavior, while the residual-enhanced PIKAT model further improves prediction precision and generalization performance, achieving a maximum accuracy of 0.9956 under multiple working conditions.