A Multirate Extended Kalman Filter for the Joint Identification of Structural State‐Damage‐Unknown Inputs

Structural system identification provides a fundamental basis for the damage assessment of civil infrastructure. However, its practical implementation is challenged by inconsistent sensor sampling rates, unknown external excitations, and sparsely distributed structural damage. To this end, a multirate extended Kalman filter with unknown input (MREKF‐UI) is proposed for the joint identification of structural states, sparse damage, and external loads. The proposed MREKF‐UI constructs a dynamic observation model by fusing multirate acceleration and strain response data acquired synchronously or asynchronously. An l 1 ‐norm regularization term is incorporated as a sparsity constraint on damage and embedded into the MREKF‐UI filter update step via a pseudomeasurement strategy. The proposed framework formulates full‐field response, sparse damage identification, and unknown load estimation within a unified filtering scheme. Numerical simulations on an overhanging beam and a truss structure are conducted to validate the proposed method under synchronous and asynchronous multirate sampling conditions. The results demonstrate accurate damage localization and quantification, reliable identification of unmeasured displacement and velocity responses, and effective estimation of unknown external excitations. Therefore, the proposed MREKF‐UI provides a feasible framework for intelligent structural diagnosis using multisource heterogeneous sensor data under unmeasured excitation conditions.