We propose the piecewise re-scaled vibrational resonance (VR) method and the piecewise twice sampling VR method to amplify the weak linear frequency-modulated (LFM) signal. The system used to amplify the weak LFM signal is a typical bistable system with fractional-order deflection nonlinearity. The concrete procedures of both the piecewise re-scaled VR method and the piecewise twice sampling VR method are explained in detail. Through studying the effect of the factional-order exponent on VR, we find that the traditional bistable system is not the optimal model to improve the weak LFM signal. By investigating different parameters on the VR phenomenon, we verify the effectiveness of the two proposed methods.
ChizhevskyVNGiacomelliG (2008) Vibrational resonance and the detection of aperiodic binary signals. Physical Review E77(5): 051126.
2.
Dixon RC (1994) Spread spectrum systems: with commercial applications. New York: Wiley.
3.
ElgamelSASoraghanJJ (2011) Using EMD-FrFT filtering to mitigate very high power interference in chirp tracking radars. IEEE Signal Processing Letters18(4): 263–266.
4.
GammaitoniLHänggiPJungPet al.(1996) Stochastic resonance. Reviews of Modern Physics70(1): 223–287.
5.
Han X, Hu P, Du H, et al. (2006) High frame rate ultrasonic imaging system based-on linear frequency-modulated signal. Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the IEEE 2(6): 1712–1715.
6.
Huang D, Yang J, Zhang J, et al. (2017) An improved adaptive stochastic resonance method for improving the efficiency of bearing faults diagnosis. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science doi:10.1177/0954406217719924.
7.
KannoAHondaSYamanakaRet al.(2010) Ultrafast and broadband frequency chirp signal generation using a high-extinction-ratio optical modulator. Optics Letters35(24): 4160–4162.
8.
KronaugeMRohlingH (2014) New chirp sequence radar waveform. IEEE Transactions on Aerospace and Electronic Systems50(4): 2870–2877.
9.
KwuimyCKLitakGNatarajC (2015) Nonlinear analysis of energy harvesting systems with fractional order physical properties. Nonlinear Dynamics80(1–2): 491–501.
10.
KwuimyCKNbendjoBN (2011) Active control of horseshoes chaos in a driven Rayleigh oscillator with fractional order deflection. Physics Letters A375(39): 3442–3449.
11.
LandaPSMcClintockPVE (2000) Vibrational resonance. Journal of Physics A Mathematical and General33(45): L433–L438.
12.
LengYGWangTYGuoYet al.(2007) Engineering signal processing based on bistable stochastic resonance. Mechanical Systems and Signal Processing21(1): 138–150.
13.
LiHLiaoXUllahSet al.(2012) Analytical proof on the existence of chaos in a generalized Duffing-type oscillator with fractional-order deflection. Nonlinear Analysis: Real World Applications13(6): 2724–2733.
14.
LiQWangTYLengYGet al.(2007) Engineering signal processing based on adaptive step-changed stochastic resonance. Mechanical Systems and Signal Processing21(5): 2267–2279.
15.
LinLWangHLvW (2017a) Stochastic resonance system with linear random frequency fluctuation for aperiodic LFM signal. Nonlinear Dynamics2(88): 1361–1371.
16.
LinLWangHLvWet al.(2016) A novel parameter-induced stochastic resonance phenomena in fractional Fourier domain. Mechanical Systems and Signal Processing76: 771–779.
17.
LinLFYuLWangHet al.(2017b) Parameter-adjusted stochastic resonance system for the aperiodic echo chirp signal in optimal FrFT domain. Communications in Nonlinear Science and Numerical Simulation43: 171–181.
18.
LiuHGLiuXLYangJHet al.(2017) Detecting the weak high-frequency character signal by vibrational resonance in the Duffing oscillator. Nonlinear Dynamics89: 2621–2628.
19.
LiuXLiuHYangJet al.(2017) Improving the bearing fault diagnosis efficiency by the adaptive stochastic resonance in a new nonlinear system. Mechanical Systems and Signal Processing96: 58–76.
20.
LuSHeQZhangHet al.(2017) Rotating machine fault diagnosis through enhanced stochastic resonance by full-wave signal construction. Mechanical Systems and Signal Processing85: 82–97.
21.
MichaelsJELeeSJCroxfordAJet al.(2013) Chirp excitation of ultrasonic guided waves. Ultrasonics53(1): 265–270.
22.
QiaoZLeiYLinJet al.(2017) An adaptive unsaturated bistable stochastic resonance method and its application in mechanical fault diagnosis. Mechanical Systems and Signal Processing84: 731–746.
YangJHSanjuánMAFLiuHG (2017) Enhancing the weak signal with arbitrary high-frequency by vibrational resonance in fractional-order duffing oscillators. Journal of Computational and Nonlinear Dynamics12(5): 051011.
25.
ZhuFZhangQLeiQet al.(2011) Reconstruction of moving target’s HRRP using sparse frequency-stepped chirp signal. IEEE Sensors Journal11(10): 2327–2334.
