Enhancement detection of characteristic signal using stochastic resonance by adding a harmonic excitation

For a bistable nonlinear system, deterministic and stochastic excitations play equivalent roles in promotion of chaos according to qualitative results of Melnikov theory. When a bistable system maintains the state of stochastic resonance (SR), the output of system is chaotic, and the most effective spectral shape is obtained when the output power is distributed closet to the frequency of the Melnikov scale's peak. In classical SR, improvement of the signal-to-noise ratio (SNR) is achieved by increasing the noise intensity, but this approach may be unwieldy. Instead of it in this paper, the more effective SNR enhancement is achieved by adding a harmonic excitation with frequency based on the system's Melnikov scale factor to the system while the noise is left unchanged. The effectiveness of this method is confirmed and replicated by numerical simulations. Combined with the strategy of scale transform, the method cab be used to detect weak periodic signal with arbitrary frequency buried in the heavy noise. At last, the method for enhancement detection of machinery fault characteristic signal is discussed via a case data.