关键词: 随机共振/
信号检测/
频域信息交换/
尺度变换
English Abstract
Stochastic resonance based on frequency information exchange
Liu Jin-Jun1,Leng Yong-Gang1,
Lai Zhi-Hui2,
Tan Dan1
1.School of Mechanical Engineering, Tianjin University, Tianjin 300350, China;
2.School of Mechatronics Engineering, Nanchang University, Nanchang 330031, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 51275336), and Tianjin Research Program of Application Foundation and Advanced Technology, China (Grant No. 15JCZDJC32200).Received Date:27 June 2016
Accepted Date:22 August 2016
Published Online:05 November 2016
Abstract: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.
Keywords: stochastic resonance/
signal detection/
frequency-information exchange/
re-scaling frequency
