Modal parameter identification of linear time-varying structures using Kriging shape function

Recently, it is essential and imperative to conduct the study of the time-varying dynamic characteristic of aerospace flight vehicle. Due to representation parsimony, high accuracy and improved tracking, the output-only parametric time-domain time-dependent time series models become the research hotspot. Above all, the function series vector time-dependent autoregressive (FS-VTAR) models are applied. Yet, the conventional FS-VTAR model needs to choose a suitable type and quite high order of basis function to certify its merit, which is complex and time-consuming. Stemmed from the moving least square (MLS) method via shape function in the mesh free method, a modal parameter identification method of time-varying structures via Kriging shape function is presented. Firstly, Kriging shape function adaptive to the signals is introduced to this method. Then, the time-varying coefficients are expanded into a linear combination of the shape functions. Once the unknown coefficients of shape functions are obtained via least square (LS) method, the time-varying coefficients are known. Finally, modal parameters are extracted from a generalized eigenvalue problem, which is transformed from an eigenvalue equation of the time-varying model. The identification approach is validated by non-stationary vibration signals of a system with time-varying stiffness. Compared with the traditional FS-VTAR model, the FS-VTAR method based on Kriging shape function avoids the form choice and high order of basis functions as well as high efficiency and has high precision. Moreover, compared with MLS method, this method solves efficiently the numerical conditions problem and has higher modal parameter identification precision.