Finite element model updating based on response reconstruction using a modified Kalman filter

To overcome the incomplete measurement and ill-posed problem in model updating, the response reconstruction technique is introduced into finite element model updating (FEMU). The unmeasured responses can be reconstructed by a few responses at measured positions applying the modified Kalman filter (MKF) algorithm. In the reconstruction process, the LWOA-ELM model, an extreme learning machine (ELM) model optimized by Levy whale optimization algorithm (LWOA), is adopted to predict mode shapes. The objective function's goal is to reduce the disparity between the analytical responses and the reconstructed responses. And LWOA is additionally utilized to get the updating results. Numerical simulations of a three-dimensional truss structure, a seven-story steel frame model, and a test study of a cantilever beam are employed to validate the methodology, respectively. The results indicate that MKF can effectively estimate the unknown external excitation and state vectors. The proposed strategy for FEMU based on response reconstruction is feasible and applicable to achieve a better solution.