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In the past few decades, stochastic resonance (SR) has attracted considerable attention of researchers due to a curious phenomenon appearing in a nonlinear system:an input weak periodic signal can be amplified and optimized by the assistance of noise. It has been proved that the classical stochastic resonance (CSR) has the adiabatic limit, so the performance of CSR in high-frequency signal detection is restricted in practical engineering. To break the restriction, a number of methods have been suggested, such as re-scaling frequency stochastic resonance (RFSR), parameters normalized stochastic resonance, modulated stochastic resonance, etc. Although the high-frequency signal can be detected by the above methods in specific conditions, there are some problems that restrict their applications in different circumstances. In this paper, a new method, stochastic resonance based on frequency-information exchange (FIESR), is developed to deal with the adiabatic limit of CSR. The mechanism of FIESR is analyzed in detail by the theory of single-side band modulation (SSB) which is based on phase shift. The information in small-parameter frequency domain is swapped with the information of the high-frequency target signal. Then the amplitude and phase of the target signal are moved to the small-parameter frequency domain. Consequently the target signal can be enhanced and detected by CSR in small-parameter frequency domain. Besides, a necessary plan, narrow band spectrum exchange, is put forward to diminish the influence of the spectrum leakage of FIESR. It is well known that the RFSR is a method of detecting the practical signal with large-parameter frequency. Through rescaling the time interval of the signal and compressing its frequency according to the scale R, the large-parameter frequency is compressed into a small-parameter frequency. The RFSR has a good performance in mechanical incipient fault diagnosis. However, it has a high sampling ratio limitation. The ratio of sampling frequency to target signal frequency is more than 50. To overcome this weakness of RFSR, frequency-information exchange (FIE) is introduced into RFSR. A new signal detection method based on FIE and RFSR, named F-RFSR, is put forward simultaneously. The flow of F-RFSR consists of three steps. Firstly, the frequency of the original input signal is compressed linearly according to the estimated scale. Then, the frequency information is exchanged between the compressed target signal and the small-parameter signal in the frequency domain. Finally, the CSR is used to amplify and detect the weak target signal processed by re-scaling frequency and FIE. Performance analysis of signal detection and numerical simulation are carried out to demonstrate that F-RFSR has more efficient sampling ratio than RFSR for practical application.
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Keywords:
- stochastic resonance /
- signal detection /
- frequency-information exchange /
- re-scaling frequency
[1] Beniz R, Sutera A, Vulpiani A 1981J. Phys. A:Math. Gen. 14 L453
[2] McNamara B, Wiesenfeld K 1989Phys. Rev. A 39 4854
[3] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998Rev. Mod. Phys. 70 223
[4] Hu G 1994Stochastic Forces and Nonlinear System (Shanghai:Shanghai Science & Technology Education Press) pp219-254(in Chinese)[胡岗1994随机力与非线性系统(上海:上海科技教育出版社)第219–254页]
[5] Bates R, Blyuss O, Zaikin A 2014Phys. Rev. E 89 032716
[6] Yang Y B, Jiang Z P, Xu B H 2009J. Phys. A:Math. Theor. 42 145207
[7] Dylov D V, Fleischer J W 2010Nat. Photon. 4 323
[8] Jha R K, Biswas P K, Chatterji B N 2012IET Image Process. 6 230
[9] Duan F B, Xu B H 2003Int. J. Bifurcat. Chaos 13 411
[10] Hu N Q, Chen M, Wen X S 2003Mech. Syst. Signal Pr. 17 883
[11] Li J M, Chen X F, He Z J 2013Mech. Syst. Signal Pr. 36 240
[12] Wang J, He Q B, Kong F R 2014J. Sound Vib. 333 7401
[13] Shi P M, Ding X J, Han D Y 2014Measurement 47 540
[14] Han D Y, Li P, An S J, Shi P M 2016Mech. Syst. Signal Pr. 70 995
[15] Zhao W L, Wang J, Wang L Z 2013Chaos 23 033117
[16] Berdichevsky V, Gitterman M 1999Phys. Rev. E 60 1494
[17] Jia Y, Yu S N, Li J R 2000Phys. Rev. E 62 1869
[18] Jin Y F 2012Physica A 391 1928
[19] Leng Y G, Leng Y S, Wang T Y, Guo Y 2006J. Sound Vib. 292 788
[20] Leng Y G, Wang T Y, Guo Y, Xu Y G 2007Mech. Syst. Signal Pr. 21 138
[21] Chen M, Hu N Q, Qin G J, An M C 2009Chin. J. Mech. Eng. 45 131(in Chinese)[陈敏, 胡茑庆, 秦国军, 安茂春2009机械工程学报45 131]
[22] Yang D X, Hu Z, Yang Y M 2012Acta Phys. Sin. 61 080501(in Chinese)[杨定新, 胡政, 杨拥民2012 61 080501]
[23] Ye Q H, Huang H N, He X Y, Zhang C H 2003OCEANS 2003 Proceedings San Diego, CA, USA, September 22-26, 2003 p2410
[24] Lin M, Huang Y M 2006Acta Phys. Sin. 55 3277(in Chinese)[林敏, 黄咏梅2006 55 3277]
[25] Tan J Y, Chen X F, Wang J Y, Chen H X 2009Mech. Syst. Signal Pr. 23 811
[26] Yang D X, Hu N Q 2003J. Natl. Univ. Def. Technol. 25 91(in Chinese)[杨定新, 胡茑庆2003国防科技大学学报2591]
[27] Zhai R C, Xie W S 2000Numerical Analysis (Tianjin:Tianjin University Press) pp235-236(in Chinese)[翟瑞彩, 谢伟松2000数值分析(天津:天津大学出版社)第235–236页]
[28] Leng Y G 2011Acta Phys. Sin. 60 020503(in Chinese)[冷永刚2011 60 020503]
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[1] Beniz R, Sutera A, Vulpiani A 1981J. Phys. A:Math. Gen. 14 L453
[2] McNamara B, Wiesenfeld K 1989Phys. Rev. A 39 4854
[3] Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998Rev. Mod. Phys. 70 223
[4] Hu G 1994Stochastic Forces and Nonlinear System (Shanghai:Shanghai Science & Technology Education Press) pp219-254(in Chinese)[胡岗1994随机力与非线性系统(上海:上海科技教育出版社)第219–254页]
[5] Bates R, Blyuss O, Zaikin A 2014Phys. Rev. E 89 032716
[6] Yang Y B, Jiang Z P, Xu B H 2009J. Phys. A:Math. Theor. 42 145207
[7] Dylov D V, Fleischer J W 2010Nat. Photon. 4 323
[8] Jha R K, Biswas P K, Chatterji B N 2012IET Image Process. 6 230
[9] Duan F B, Xu B H 2003Int. J. Bifurcat. Chaos 13 411
[10] Hu N Q, Chen M, Wen X S 2003Mech. Syst. Signal Pr. 17 883
[11] Li J M, Chen X F, He Z J 2013Mech. Syst. Signal Pr. 36 240
[12] Wang J, He Q B, Kong F R 2014J. Sound Vib. 333 7401
[13] Shi P M, Ding X J, Han D Y 2014Measurement 47 540
[14] Han D Y, Li P, An S J, Shi P M 2016Mech. Syst. Signal Pr. 70 995
[15] Zhao W L, Wang J, Wang L Z 2013Chaos 23 033117
[16] Berdichevsky V, Gitterman M 1999Phys. Rev. E 60 1494
[17] Jia Y, Yu S N, Li J R 2000Phys. Rev. E 62 1869
[18] Jin Y F 2012Physica A 391 1928
[19] Leng Y G, Leng Y S, Wang T Y, Guo Y 2006J. Sound Vib. 292 788
[20] Leng Y G, Wang T Y, Guo Y, Xu Y G 2007Mech. Syst. Signal Pr. 21 138
[21] Chen M, Hu N Q, Qin G J, An M C 2009Chin. J. Mech. Eng. 45 131(in Chinese)[陈敏, 胡茑庆, 秦国军, 安茂春2009机械工程学报45 131]
[22] Yang D X, Hu Z, Yang Y M 2012Acta Phys. Sin. 61 080501(in Chinese)[杨定新, 胡政, 杨拥民2012 61 080501]
[23] Ye Q H, Huang H N, He X Y, Zhang C H 2003OCEANS 2003 Proceedings San Diego, CA, USA, September 22-26, 2003 p2410
[24] Lin M, Huang Y M 2006Acta Phys. Sin. 55 3277(in Chinese)[林敏, 黄咏梅2006 55 3277]
[25] Tan J Y, Chen X F, Wang J Y, Chen H X 2009Mech. Syst. Signal Pr. 23 811
[26] Yang D X, Hu N Q 2003J. Natl. Univ. Def. Technol. 25 91(in Chinese)[杨定新, 胡茑庆2003国防科技大学学报2591]
[27] Zhai R C, Xie W S 2000Numerical Analysis (Tianjin:Tianjin University Press) pp235-236(in Chinese)[翟瑞彩, 谢伟松2000数值分析(天津:天津大学出版社)第235–236页]
[28] Leng Y G 2011Acta Phys. Sin. 60 020503(in Chinese)[冷永刚2011 60 020503]
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