Abstract
A two-dimensional Duffing oscillator which can produce stochastic resonance (SR) is studied in this paper. We introduce its SR mechanism and present a generalized parameter-adjusted SR (GPASR) model of this oscillator for the necessity of parameter adjustments. The Kramers rate is chosen as the theoretical basis to establish a judgmental function for judging the occurrence of SR in this model; and to analyze and summarize the parameter-adjusted rules under unmatched signal amplitude, frequency, and/or noise-intensity. Furthermore, we propose the weak-signal detection approach based on this GPASR model. Finally, we employ two practical examples to demonstrate the feasibility of the proposed approach in practical engineering application.
Highlights
The term Stochastic Resonance (SR) was first coined by Benzi et al, and used to explain the switching of the Earth’s climate between ice ages and periods of relative warmth over a roughly100,000-year cycle [1,2,3]
We present the generalized parameter-adjusted model of a Duffing oscillator and classify parameters in Section 3; we analyze the parameters of a Duffing system based on Kramers rate, and comprehensively study the mechanism of generalized parameter-adjusted SR (GPASR) in a Duffing oscillator when the signal amplitude, frequency and/or noise-intensity are unmatched
The biggest difficulty of the application of a Duffing oscillator as a weak-signal detector is that the signal amplitude, frequency and/or noise-intensity of the test signal do not always optimally match with the nonlinear system
Summary
The term Stochastic Resonance (SR) was first coined by Benzi et al, and used to explain the switching of the Earth’s climate between ice ages and periods of relative warmth over a roughly. The adjusted rules summarized in [31] were not complete because we did not fully discuss the situations that the input signal amplitude does not match with other parameters, and we need to propose a GPASR-based weak-signal detection method and realize its application on engineering practice such as incipient fault diagnosis of mechanical equipment. We present the generalized parameter-adjusted model of a Duffing oscillator and classify parameters in Section 3; we analyze the parameters of a Duffing system based on Kramers rate, and comprehensively study the mechanism of GPASR in a Duffing oscillator when the signal amplitude, frequency and/or noise-intensity are unmatched .
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