Modal parameter identification of time-varying structures via moving least square method

For modal parameter identification of time-varying structures, an improved identification approach is presented, which uses the moving least square method based on a functional series vector time-dependent AR model (FS-VTAR). The method stems from the local approximation using shape function in the mesh free method. The basis function of moving least square method (MLS) is improved by weighted orthogonal basis function, which makes numerical conditions problem of gaining the shape function matrix solve in the estimation time domain. The modal parameter identification precision is improved. 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 method, the time-varying coefficients are known. 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 improved MLS method avoids the form choice and high order of basis functions as well as high efficiency. Moreover, compared with MLS method, the improved MLS method solves efficiently the numerical conditions problem, and has higher modal parameter identification precision.