Effects of underdamped step-varying second-order stochastic resonance for weak signal detection

Abstract Stochastic resonance (SR) has been proved to be an effective approach for weak signal detection. In this paper, an underdamped step-varying second-order SR (USSSR) method is proposed to further improve the output signal-to-noise ratio (SNR). In the method, by selecting a proper underdamped damping factor and a proper calculation step, the weak periodic signal, the noise and the potential can be matched with each other in the regime of second-order SR to generate an optimal dynamical system. The proposed method has three distinct merits as: 1) secondary filtering effect produces a low-noise output waveform; 2) good band-pass filtering effect attenuates the multiscale noise that locates in high- and (or) low-frequency domains; and 3) good anti-noise capability in detecting weak signal being submerged in heavy background noise. Numerical analysis and application verification are performed to confirm the effectiveness and efficiency of the proposed method in comparison with a traditional SR method.

[1]  L. Qiang,et al.  Engineering signal processing based on adaptive step-changed stochastic resonance , 2007 .

[2]  Hu,et al.  Periodically forced Fokker-Planck equation and stochastic resonance. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[3]  Eyal Buks,et al.  Signal amplification in a nanomechanical Duffing resonator via stochastic resonance , 2007 .

[4]  Zhengjia He,et al.  Adaptive stochastic resonance method for impact signal detection based on sliding window , 2013 .

[5]  Bulsara,et al.  Intrawell stochastic resonance versus interwell stochastic resonance in underdamped bistable systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

[7]  Bart Kosko,et al.  Adaptive stochastic resonance in noisy neurons based on mutual information , 2004, IEEE Transactions on Neural Networks.

[8]  Sinan Gezici,et al.  Noise enhanced hypothesis-testing according to restricted Neyman-Pearson criterion , 2014, Digit. Signal Process..

[9]  A. Kenfack,et al.  Stochastic resonance in coupled underdamped bistable systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Yanyang Zi,et al.  Study of frequency-shifted and re-scaling stochastic resonance and its application to fault diagnosis , 2009 .

[11]  Fanrang Kong,et al.  Multiscale noise tuning of stochastic resonance for enhanced fault diagnosis in rotating machines , 2012 .

[12]  W. L. Reenbohn,et al.  Periodically driven underdamped periodic and washboard potential systems: dynamical states and stochastic resonance. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Youguo Wang.  Nonlinear statistics to improve signal detection in generalized Gaussian noise , 2008, Digit. Signal Process..

[14]  Derek Abbott,et al.  Weak signal detection: Condition for noise induced enhancement , 2013, Digit. Signal Process..

[15]  Australia,et al.  EVALUATION OF BISTABLE SYSTEMS VERSUS MATCHED FILTERS IN DETECTING BIPOLAR PULSE SIGNALS , 2004, cond-mat/0410412.

[16]  B. Kosko,et al.  Adaptive stochastic resonance , 1998, Proc. IEEE.

[17]  Fanrang Kong,et al.  Wayside acoustic diagnosis of defective train bearings based on signal resampling and information enhancement , 2013 .

[18]  Zhengjia He,et al.  Multi-stable stochastic resonance and its application research on mechanical fault diagnosis , 2013 .

[19]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[20]  Robert B. Randall,et al.  Differential Diagnosis of Gear and Bearing Faults , 2002 .

[21]  Zhengjia He,et al.  A new noise-controlled second-order enhanced stochastic resonance method with its application in wind turbine drivetrain fault diagnosis , 2013 .

[22]  D. Mei,et al.  Stochastic resonance, reverse-resonance and stochastic multi-resonance in an underdamped quartic double-well potential with noise and delay , 2011 .

[23]  Qingbo He,et al.  Note: signal amplification and filtering with a tristable stochastic resonance cantilever. , 2013, The Review of scientific instruments.

[24]  François Chapeau-Blondeau.  Stochastic Resonance and Optimal Detection of Pulse Trains by Threshold Devices , 1999, Digit. Signal Process..

[25]  Yang Yu,et al.  The application of energy operator demodulation approach based on EMD in machinery fault diagnosis , 2007 .

[26]  Dong Han,et al.  Planetary gearbox fault diagnosis using an adaptive stochastic resonance method , 2013 .

[27]  Fanrang Kong,et al.  Sequential Multiscale Noise Tuning Stochastic Resonance for Train Bearing Fault Diagnosis in an Embedded System , 2014, IEEE Transactions on Instrumentation and Measurement.

[28]  Sinan Gezici,et al.  Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework , 2012, Digit. Signal Process..

[29]  Niaoqing Hu,et al.  Stochastic resonance in multi-scale bistable array , 2013 .

[30]  Xiaofei Zhang,et al.  Multi-scale bistable stochastic resonance array: A novel weak signal detection method and application in machine fault diagnosis , 2013 .

[31]  Lenan Wu,et al.  Nonlinear signal detection from an array of threshold devices for non-Gaussian noise , 2007, Digit. Signal Process..

[32]  Tai Yong Wang,et al.  Numerical analysis and engineering application of large parameter stochastic resonance , 2006 .

[33]  Rajarshi Ray,et al.  Stochastic Resonance in Underdamped, Bistable Systems , 2005, nlin/0506039.

[34]  Fanrang Kong,et al.  Stochastic resonance with Woods-Saxon potential for rolling element bearing fault diagnosis , 2014 .

[35]  Jian-Xue Xu,et al.  Observing stochastic resonance in an underdamped bistable Duffing oscillator by the method of moments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[37]  Jun Wang,et al.  Effects of multiscale noise tuning on stochastic resonance for weak signal detection , 2012, Digit. Signal Process..

[38]  Lu-Chun Du,et al.  Amplification of weak signals via the non-adiabatic regime of stochastic resonance in a bistable dynamical system with time delay , 2011 .

[39]  Fanrang Kong,et al.  Adaptive Multiscale Noise Tuning Stochastic Resonance for Health Diagnosis of Rolling Element Bearings , 2015, IEEE Transactions on Instrumentation and Measurement.

[40]  Robert X. Gao,et al.  Dual-scale cascaded adaptive stochastic resonance for rotary machine health monitoring , 2013 .