Nonlinear time-varying vibration system identification using parametric time-frequency transform with spline kernel

摘要

In real-life applications, mechanical vibration systems are not linear time invariant. Time-varying pattern arise, for instance, during deployment, aging, deformation, load variation, etc. In the absence of a complete physics-based description of a system, system identification (SI) is able to obtain the missed information of nonstationary pattern for the unknown system. The SI will face difficulty when the time-varying system involves the nonlinearity, which makes the system solution have both the nonlinear and nonstationary time-frequency patterns. This paper aimed to identify the system with linear and nonlinear time-varying characteristics using parametric time-frequency transform with spline kernel, which is known for offering great energy concentration in time-frequency domain and allows the accurate extraction of model feature. The efficacy of the proposed method is demonstrated on SDOF systems comprised of three types of nonlinear time-varying stiffness, including time-varying periodic modulation of stiffness, time-varying piecewise modulation of nonlinear stiffness and time-varying periodic modulation of nonlinear stiffness. Comparisons with the conventional time-frequency methods and the Hilbert transform-based SI validated that the proposed method is more robust in characterizing the nonlinear time-varying stiffness of the system with the presence of noise.