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The stochastic resonance (SR) in a bistable system
driven by nonlinear frequency modulation (NLFM)
signal and strong noise is studied. Combined
with empirical mode decomposition (EMD) and
piecewise idea, an adaptive piecewise re-scaled
SR method based on the optimal intrinsic mode
function (IMF), is proposed to enhance the weak
NLFM signal. At first, considering the advantages
of EMD for dealing with non-stationary signals,
the segmented NLFM signal is processed by EMD.
Meanwhile, the cross-correlation coefficient is used
as the measure to select the optimal IMF that
contains the NLFM signal feature. Then, the spectral
amplification gain indicator is proposed to realize the
adaptive SR of the optimal IMF of each sub-segment
signal and reconstruct the enhanced NLFM signal.
Finally, the effectiveness of the proposed method
is highlighted with the analysis of the short-time
Fourier transform spectrum of the simulation results.
As an application example, the proposed method
is verified adaptability in bearing fault diagnosis
under the speed-varying condition that represents a
typical and complicated NLFM signal in mechanical
engineering. The research provides a new way for
the enhancement of weak non-stationary signals.