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Smart Structures and Systems
  Volume 24, Number 2, August 2019, pages 209-221

An improved Kalman filter for joint estimation of structural states and unknown loadings
Jia He, Xiaoxiong Zhang and Naxin Dai

    The classical Kalman filter (KF) provides a practical and efficient way for state estimation. It is, however, not applicable when the external excitations applied to the structures are unknown. Moreover, it is known the classical KF is only suitable for linear systems and can\'t handle the nonlinear cases. The aim of this paper is to extend the classical KF approach to circumvent the aforementioned limitations for the joint estimation of structural states and the unknown inputs. On the basis of the scheme of the classical KF, analytical recursive solution of an improved KF approach is derived and presented. A revised form of observation equation is obtained basing on a projection matrix. The structural states and the unknown inputs are then simultaneously estimated with limited measurements in linear or nonlinear systems. The efficiency and accuracy of the proposed approach is verified via a five-story shear building, a simply supported beam, and three sorts of nonlinear hysteretic structures. The shaking table tests of a five-story building structure are also employed for the validation of the robustness of the proposed approach. Numerical and experimental results show that the proposed approach can not only satisfactorily estimate structural states, but also identify unknown loadings with acceptable accuracy for both linear and nonlinear systems.
Key Words
    Kalman filter; state estimation; load identification; limited measurements; nonlinear hysteretic structures
Jia He, Xiaoxiong Zhang: College of Civil Engineering, Hunan University, Changsha, China;
Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan University, Changsha, China
Naxin Dai: The School of Civil Engineering, The University of South China, Hengyang, China

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