Nonlinear Structure Identification Based On Kalman Filter With Nonparametric Model

Structural damage identification is one of the critical problems in structural health monitoring(SHM)and condition evaluation.Structural damage initiation and development lead to nonlinear behavior of engineering structures under strong dynamic loadings.The development of nonlinear behavior identification approaches plays key roles in structural damage identification and the description of the failure patterns under dynamic excitations.Civil engineering structures are the mode of different construction materials and structural types and it is hard to model their nonlinear behavior with a general parametric mathematic model.Moreover,the dynamic response measurement for identification is usually partially available with unknown external excitation information.It is critical to develop general structural nonlinear behavior identification approach using incomplete dynamic response measurement and unknown input information without using parametric mathematical model.Based on Kalman filter algorithm and various polynomials as nonparametric models,in this paper,several structural response reconstruction,structural parameter,non-linear restoring force(NRF)and external excitation identification approaches are proposed.The feasibility and applicability of the proposed algorithms are studied numerically and experimentally.The main research contents are listed as follows:(1)Aiming at structural response reconstruction,a modal Kalman filter based on multi-scale response with unknown input(MS-MKF-UI)is proposed to reconstruct unknown structural responses,including displacement,velocity and strain responses using limited structural acceleration observation with data fusion technology.(2)Aiming at the NRF identification without a parametric model,various polynomials are employed to describe the NRF in a nonparametric way and the NRF is identified with the least squares estimation.Moreover,the proposed approach is numerically illustrated with multi-degree-of-freedom structures equipped with two typical velocity and displacement damper models and experimentally illustrated by compared the identified NRF with the test measurements.(3)A two-stage identification algorithm based on Kalman filter and Chebyshev polynomial is proposed for the identification of non-linear structures.The identification of the nonlinearity location is carried out at first,and structural acceleration,velocity,displacement responses,structural mass,stiffness,damping parameters and NRF are identified.The applicability of this method is also verified by experimental data.(4)Aiming at model-free identification for non-linear structures under unknown excitation,an algorithm combining unknown input extended Kalman filter(EKF-UI)algorithm with Chebyshev polynomial is proposed to identify NRF without using any parametric models and known external excitation but using limited acceleration and displacement measurements.The data fusion technology employed is efficient in solving the drift problem in traditional extended Kalman filter with unknown input.Moreover,the applicability of this method is verified with experimental data.