Identification of time-varying nonlinear structural physical parameters by integrated WMA and UKF/UKF-UI

The identification of time-varying physical parameters of nonlinear systems is still a challenging task. Limited studies based on the wavelet multiresolution analysis (WMA) have been attempted, which requires full measurements of structural displacement, velocity and acceleration responses of all degrees of freedom and exact information of external excitations. This limits the engineering application of these methods. This paper proposes approaches to identify the time-varying physical parameters of nonlinear structures in three cases using only partially measured structural responses. Firstly, the identification of time-varying nonlinear structures with a small number of elements under known excitations is discussed. The fading-factor unscented Kalman filter (FUKF) method is applied to locate the time-varying parameters, and the WMA integrated with UKF method is employed using partially measured acceleration responses. Secondly, it is further extended to the identification of time-varying nonlinear structures with a small number of elements but under unknown excitations. An improved fading-factor unscented Kalman filter under unknown input (FUKF-UI) method is proposed to locate the time-varying parameters, and WMA integrated with UKF-UI method is utilized with partially observed acceleration and displacement responses. Thirdly, for practical engineering applications, the identification of time-varying nonlinear structure with more elements under unknown excitations is conducted. The proposed FUKF-UI method is employed to locate the time-varying parameters of the whole structure. Then, the whole structure is divided into several substructures and the unknown interaction forces are regarded as the fictitious unknown inputs to the substructure. Thus, physical parameters of each substructure can be identified in parallel by the combination of WMA and UKF-UI. Three numerical studies corresponding to these three cases are conducted, respectively, to demonstrate the effectiveness and accuracy of the proposed methods.