Application of constrained unscented Kalman filter (CUKF) for system identification of coupled hysteresis under bidirectional excitation

System identification is primarily studied for unidirectional excitation using the Bouc–Wen model, neglecting the torsional coupling, even though real structure experiences multidirectional seismic excitation. Moreover, the high damping rubber bearings exhibit bidirectional effects, thereby requiring coupled biaxial Bouc–Wen (BBW) model and demand the estimation of model parameters for structural health monitoring. The current work presents three numerical case studies followed by experimental validation to demonstrate the applicability and efficacy of Bayesian filters named constraint unscented Kalman filter (CUKF) in identifying model parameters for the nondeteriorating system as well as deteriorating systems. With limited measurements and increased states, a two‐stage framework of the CUKF is used to enhance the performance in identifying the hysteresis parameters and system dynamics of the nondeteriorating systems. For the deteriorating system, the Paris–Erdogan law is coupled with the stiffness in the BBW model to introduce degradation as per the acceleration fatigue crack growth. The degradation parameters and deteriorating stiffness is captured through CUKF accurately. The application of CUKF to the experimental responses proves the robustness of the algorithm for coupled biaxial hysteresis system. Additionally, a unified structural health monitoring (SHM) framework is proposed for condition monitoring during extreme events and long‐term periodic maintenance through ambient vibrations. Overall, the result concludes that CUKF is a reliable Bayesian estimator for coupled biaxial hysteresis systems and demonstrates promising potential in identifying fatigue‐induced deterioration.