Stochastic resonance in a delay-controlled dissipative bistable potential for weak signal enhancement

Abstract

This paper attempts to investigate the stochastic resonance (SR) phenomenon in a delay-controlled dissipative bistable potential with time-delayed feedback under the action of harmonic excitation and additive noise by using small delay approximation theory and signal-to-noise ratio (SNR) theory. The time delay and feedback strength are able to adjust the potential shapes precisely by fusing potential parameters. Moreover, the steady-state probability distribution (SPD) and output SNR are derived to demonstrate that time-delayed feedback is able to control and improve the SR for enhancing the useful signal embedded in a noisy signal, where moderate time delay and feedback strength can maximize the output SNR. Therefore, a controlled SR method via time-delayed feedback is proposed to enhance useful signals embedded in mechanical signals for mechanical fault diagnosis, where the widely used frequency-shifted and rescaling transform is used to preprocess large-parameter vibration signals of double row cylindrical bearings. The experimental results indicate that the controlled SR method via time-delayed feedback can enhance the useful signal embedded in the vibration signal from double row cylindrical bearings where its amplitude is amplified up to tenfold than that in the envelope spectrum of raw signal.