Time-varying system identification using variational mode decomposition

A new time-varying system identification approach is proposed in this paper by using variational mode decomposition. The newly developed variational mode decomposition technique can decompose the measured responses into a limited number of intrinsic mode functions, and the instantaneous frequencies of time-varying systems are identified by the Hilbert transform of each intrinsic mode function. Numerical and experimental verifications are conducted to demonstrate the effectiveness and accuracy of using the proposed approach for time-varying system identification, that is, to obtain the instantaneous frequency. Numerical studies on a structural system with time-varying stiffness are conducted. Experimental validations on analyzing the measured vibration data in the laboratory from a steel frame structure and a time-varying bridge–vehicle system are also conducted. The results from the presented technique are compared with those from empirical mode decomposition-based methods, which verify that the developed approach can identify the instantaneous frequencies with a better accuracy.