Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection
Abstract
:1. Introduction
2. Principle of SR in a Duffing Oscillator
3. GPASR in a Duffing Oscillator Based on Kramers Rate
3.1. GPASR of a Duffing Oscillator
3.2. Parameters Analysis of a Duffing System Based on Kramers Rate
- (i)
- the value of is independent of ;
- (ii)
- is a monotone increasing Function of , , , and ;
- (iii)
- is a monotone decreasing Function of , and ;
- (iv)
- is a monotone increasing Function of when , and is a monotone decreasing Function of when .
3.3. GPASR in a Duffing Oscillator under Unmatched Signal Amplitude
3.4. GPASR in a Duffing Oscillator under Unmatched Signal Frequency
3.5. GPASR in a Diffing Oscillator under Unmatched Noise-Intensity
3.5.1. Adjustment of Damping Ratio k
3.5.2. Adjustment of System Parameter a
3.5.3. Adjustment of System Parameter b
3.5.4. Adjustment of Amplitude-Transformation Coefficient ε
3.5.5. Adjustment of Scale-Transformation Coefficient R
3.6. Conclusion of the GPASR Rules of a Duffing Oscillator
k | a | b | ε | R | ||
---|---|---|---|---|---|---|
Large | Invalid | Invalid | Invalid | Decrease ε | Invalid | |
Small | Invalid | Invalid | Invalid | Increase ε | Invalid | |
f0 is a large-parameter | Invalid | Invalid | Invalid | Invalid | Adjust R to make satisfy the small-parameter limits | |
Large | Increase k | Adjust a far from when | Decrease b | Decrease ε appropriately | Decrease R appropriately | |
Small | Decrease k | Adjust a near when | Increase b | Increase ε appropriately | Increase R appropriately |
4. Engineering Applications
4.1. Weak-signal Detection Method Based on GPASR of a Duffing Oscillator
4.2. Practical Examples
4.2.1. Diagnosis of a Rotor Shaft-Bending Fault
4.2.2. Diagnosis of a Rolling Bearing Outer Ring Fault
4.3. Discussion
5. Conclusions and Summary
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Lai, Z.-H.; Leng, Y.-G. Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection. Sensors 2015, 15, 21327-21349. https://doi.org/10.3390/s150921327
Lai Z-H, Leng Y-G. Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection. Sensors. 2015; 15(9):21327-21349. https://doi.org/10.3390/s150921327
Chicago/Turabian StyleLai, Zhi-Hui, and Yong-Gang Leng. 2015. "Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection" Sensors 15, no. 9: 21327-21349. https://doi.org/10.3390/s150921327
APA StyleLai, Z.-H., & Leng, Y.-G. (2015). Generalized Parameter-Adjusted Stochastic Resonance of Duffing Oscillator and Its Application to Weak-Signal Detection. Sensors, 15(9), 21327-21349. https://doi.org/10.3390/s150921327