Abstract: The installation of dampers in structures is a widely adopted and effective technique in civil engineering for disaster prevention and mitigation. However, under long-term multi-factor influences such as loads and environmental conditions, dampers are prone to failure or damage during service. To address current limitations, which include the prevalent reliance on mechanical models for damper failure identification, the ill-posed nature of identifying multi-damper systems, and the lack of integrated identification of damper failure and structural damage, this paper proposes a novel sparse Extended Kalman filter under unknown inputs (SEKF-UI) method. This method treats the damper failure forces as unknown virtual forces, constructs the extended state vector incorporating structural damage factors, and considers the sparsity of failed dampers and damaged structural elements. By embedding sparsity constraints into the Kalman filtering process via pseudo-measurement techniques, the method effectively mitigates the inversion ill-posedness. It enables the nonparametric integrated online identification of damper failure and structural damage without requiring the damper failure model, making it suitable for multi-damper systems. To validate the effectiveness of the proposed method, simulations are conducted on a single-span truss, a multi-span continuous beam, and a planar frame equipped with different types of dampers under various failure and damage scenarios. The results demonstrate that the proposed method achieves more accurate identification compared to traditional approaches.