Quartic double-well system modulation for under-damped stochastic resonance tuning

In this paper a novel methodology for stochastic resonance (SR) tuning, based on the classical quartic double-well (QDW) system modulation is proposed. The QDW modulation is accomplished by finding the optimal stable focus separation, well depth and damping parameters of the Duffing system, enhancing a weak signal buried in additive white Gaussian (AWG) noise. Hence, direct parameter tuning SR through geometric QDW system modulation is developed unlike classical SR, where linear and non-linear stiffness parameters, indirectly, modulates the QDW system. To evaluate the harmonic content of the SR response, signal-to-noise and distortion ratio (SINAD) was used thus, optimal SR response was chosen under maximum SINAD criteria. Signal-to-noise ratio (SNR) was also used to compare our methodology with state-of-the-art weak signal detection (WSD) methods of autocorrelation and discrete wavelet transform (DWT). After applying the proposed methodology on three noisy signals with different input SNR, results showed an important signal enhancement of 50dB in SNR gain, for all cases, far above the results obtained with other methods compared. Moreover, signal enhancement with the lowest harmonic distortion was achieved with SR, compared with autocorrelation and DWT, demonstrating the feasibility of SR for WSD in highly noisy environments.