Stochastic resonance: Linear response and giant nonlinearity

Dykman, M. I.; Luchinsky, D. G.; Mannella, R.; McClintock, Peter V. E.; Stein, N. D.; Stocks, Nigel G.

doi:10.1007/bf01053982

Cited by 41 publications

(10 citation statements)

References 22 publications

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“…From the contrast result between Figure 6(b) and Figure 6(d), we know that the weak periodic signal cannot be enhanced by using classical SR theory when the noise intensity D is greater than 1. More information on why SR can only handle small-parameter problems can be obtained from the works of adiabatic approximation theory [19,20] and linear response theory [21]. Another limitation of the classical SR theory is that the sampling frequency fs should be greater than 50 times of the periodic signal frequency f, i.e.,…”

Section: Of 15mentioning

confidence: 99%

A Novel Underwater Location Beacon Signal Detection Method Based on Mixing and Normalizing Stochastic Resonance

Liang

Wan

Wang

et al. 2020

Sensors

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A flight data recorder (FDR) is an electronic recording device placed in an aircraft for the purpose of facilitating the investigation of aviation accidents. If an aircraft crashes into water, an underwater locator beacon (ULB), which is installed on the FDR, is triggered by water immersion, and emits an ultrasonic 10 ms pulse signal once per second at 37.5 kHz. This pulse signal can be detected by sonar equipment. However, the ULB signal only can be detectable 1-2 kilometers from the surface in normal conditions. Stochastic resonance (SR) is a rising theory in the field of weak signal detection. The classical stochastic resonance limits state that the input must be small-parameter and the sampling frequency must be 50 times higher than the signal frequency. It cannot be applied to the ULB signal detection. To resolve this problem, this paper presents a novel approach named mixing and normalizing stochastic resonance (MNSR). By mixing the ULB signal and normalizing SR system parameters, MNSR provides a new way to detect weak ULB signal. Meanwhile, we propose the parameters adjustment method of MNSR. We prove the effectiveness through numerical simulation. An experiment in a tank is employed to verify the practicability of this method.Sensors 2020, 20, 1292 2 of 15 classical stochastic resonance cannot detect the large-parameter (large-amplitude or high-frequency) signal directly. To make SR more practical, researchers have proposed several large-parameter stochastic resonance (LPSR) methods, such as twice sampling stochastic resonance [11], re-scaling frequency stochastic resonance (RFSR) [13], system parameters normalization transform stochastic resonance, or parameters normalized stochastic resonance (PNSR) [14]. These methods transform the large-parameter signal into a small-parameter signal which satisfies the small-parameter conditions numerically. The disadvantage is the requirement of a high sampling frequency (at least 50 times to the signal frequency, and generally 200 times or more). It is hard to achieve in engineering application scenarios when the weak signal frequency is high. Another LPSR method, modulated stochastic resonance (MSR) [15], modulates the high-frequency weak signal immersed with noise to a low difference frequency signal to implement LPSR. MSR requires a long signal duration to ensure that the duration contains at least two complete periods of the low difference frequency signal. To realize the detection of ULB signal which is high frequency and short pulse by SR method, mixing and normalizing stochastic resonance (MNSR) is proposed in this paper. Through mixing the ULB signal with a carrier signal, the ULB signal detection can be replaced by the "low" frequency difference signal detection. Here, the "low" means the difference signal frequency is lower than the ULB signal frequency and the sampling frequency. Under the restriction that the sampling frequency must be 50 times higher than the signal frequency, MNSR allows the sampling frequency to be much lower than RFSR, which detects ...

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Section: Of 15mentioning

confidence: 99%

A Novel Underwater Location Beacon Signal Detection Method Based on Mixing and Normalizing Stochastic Resonance

Liang

Wan

Wang

et al. 2020

Sensors

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“…As stated in [8,9] , for a bistable system with noise and a periodic signal, the improvement of the signal-to-noise ratio (SNR) achieved by increasing the noise intensity is known as stochastic resonance (SR) [10,11] (i.e., classical SR in these papers). Here, The signal to noise ratio (SNR) is expressed in dB as SNR=10log10(S/N), where S and N are, respectively, the ordinate of the output power spectrum and the ordinate of the broadband output power spectrum at the signal frequency ω 0 .…”

Section: Principle Of Sr Explained By Chaotic Dynamic Approachmentioning

confidence: 99%

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

Zhang

et al. 2012

J. Phys.: Conf. Ser.

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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.

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“…It has been observed in a large variety of physical, chemical and biological systems. [6][7][8][9][10][11][12][13][14][15][16][17][18] Most of the previous studies focus on conventional overdamped bistable systems and there have been many theoretical developments of SR. [19][20][21][22][23][24] On the other hand, behavior similar to SR has also been found in linear systems. [25][26][27][28][29] Recently, stochastic resonance in underdamped bistable systems was investigated.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Resonance in a Bistable System Driven by Weak Periodic Signal With Multiple Delays

Zhang

Sun

et al. 2011

Int. J. Mod. Phys. B

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The phenomenon of stochastic resonance in a bistable system with multiple delays is investigated. The analytic expression of approximation stationary probability density is obtained by using small delay approximation based on probability density approach. Numerical simulation is performed and it is shown that the analytic results are in good agreement with Monte Carlo simulation. Then the expression of the signal-to-noise (SNR) is derived by using two-state theory. Finally, the effect of multiple delays on SNR is discussed. It is found that the stochastic resonance phenomenon can be suppressed or promoted when multiple delays are increased.

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Stochastic resonance: Linear response and giant nonlinearity

Cited by 41 publications

References 22 publications

A Novel Underwater Location Beacon Signal Detection Method Based on Mixing and Normalizing Stochastic Resonance

A Novel Underwater Location Beacon Signal Detection Method Based on Mixing and Normalizing Stochastic Resonance

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

Stochastic Resonance in a Bistable System Driven by Weak Periodic Signal With Multiple Delays

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