Abstract: Frequency modulated empirical mode decomposition (FM-EMD) method is proposed. The mode mixing problem associated with the original EMD method when processing nonlinear signals with closely spaced frequencies is solved. The physical meaning of the identified intrinsic mode functions (IMFs) is improved. Assisted by the Hilbert-Huang transform, the proposed method can identify the instantaneous parameters of the weak nonlinear system with closely spaced frequencies. The effectiveness of the proposed method is verified by numerical simulations. With the proposed method, nonlinearity is identified in the aeroelastic vibration of the two DOF bridge deck sectional model of Humber Bridge.