Penalty Parameter Selection Method for Variational Mode Decomposition and Time-Varying System Identification

As the penalty parameter in the variational mode decomposition (VMD) affects the decomposition performance, a penalty parameter selection method is proposed on the basis of data driven. The method firstly determines the penalty parameter at the main peak by using the Fourier transform. Then the mode parameters are adjusted to obtain the finite number of intrinsic mode function components. The pseudo component is eliminated by comparing the natural frequencies and damping ratios of the components under different mode parameters. Finally, the true intrinsic mode function components are processed with Hilbert transform to identify the instantaneous frequency of a time-varying system. In order to prove the validity and accuracy of the proposed method for time-varying system identification, the time-varying work processes of a structural system with time-varying stiffness and a diesel engine are studied respectively. The results of the proposed method are compared with those of the empirical mode decomposition method. The results show that when the penalty parameter is 1.5 to 16.0 times the maximum signal amplitude, the optimal decomposition results will be obtained. The proposed method can more accurately identify the instantaneous frequency, and be used for instantaneous frequency identification in engineering applications.