Sparsity‐Constrained Online Identification of Parameter Degradation in Multidamper Systems

The long‐term degradation of damper performance under adverse conditions compromises energy dissipation, posing a potential risk to structural safety. Online degradation identification approaches provide benefits, including in situ evaluation, real‐time processing, and high computational efficiency, among which Kalman filter–based methods offer unbiased minimum variance estimates from partial measurements. However, parameter identification in multidamper systems remains challenging, primarily due to the ill‐posed nature of estimating numerous unknowns from limited measurements. To overcome this limitation, this paper proposes a novel sparse extended Kalman filter under unknown input (SEKF‐UI) algorithm. In this method, damper damage factors are incorporated into an extended state vector while explicitly leveraging their sparsity as prior information. The sparsity constraint is seamlessly embedded within the recursive steps via the pseudomeasurement (PM) technique, thereby avoiding additional offline optimization and preserving the real‐time advantage. Thus, the proposed approach effectively addresses the ill‐posed inverse problem, enabling the simultaneous identification of multidamper damage factors and unknown inputs. Moreover, it preserves the recursive framework of the classical Kalman filter while significantly enhancing its robustness and accuracy. Numerical validation employs an 8‐story shear frame, a single‐span truss, and a 3‐story benchmark model, each equipped with a different damper mechanical model. Results confirm that the proposed algorithm outperforms conventional methods in identifying parameter degradation across multidamper systems.