Frequency and Amplitude Identification of Weak Signal Based on the Limit System of Smooth and Discontinuous Oscillator
Tóm tắt
In this paper, a new method is proposed to identify the frequency and amplitude of weak signals by using a non-smooth system. The variable scale limit system of smooth and discontinuous (SD) oscillator without considering the phase is adopted as the identification system. By using the non-smooth stochastic subharmonic-like Melnikov method, an analytical expression of chaotic threshold under Gaussian white noise is given. Based on the phase diagram and Poincaré section diagram, the influence of noise intensity on the recognition system is studied. According to the non-smooth variable scale-convex-peak frequency identification method, the frequency of the signal to be detected can be accurately identified. Using the numerical simulation, the amplitude of the signal to be measured is identified according to the amplitude bifurcation diagram of the reference signal. The optimal value range of the parameters of the identification system is determined. Through an example of early fault of wheelset bearing of high-speed train, the frequency and amplitude of the early weak fault signal can be identified and the fault location can be determined, which verifies the effectiveness of the above method. The results show that the non-smooth system can identify the frequency and amplitude of the weak signal submerged in strong noise, and it has a wider application and higher accuracy than the continuous system.
Tài liệu tham khảo
Zhai, D.Q., Liu, C.X., Liu, Y., Xu, Z.: Determination of the parameters of unknown signals based on intermittent chaos. Acta Phys. Sin. 59(2), 816–825 (2010)
Niu, D.Z., Chen, C.X., Ban, F., Xu, H.X., et al.: Blind angle elimination method in weak signal detection with Duffing oscillator and construction of detection statistics. Acta Phys. Sin. 64(6), 060503 (2015)
Cong, C., Li, X.K., Song, Y.: A method of detecting line spectrum of ship-radiated noise using a new intermittent chaotic oscillator. Acta Phys. Sin. 63(6), 168–179 (2014)
Lai, Z.H., Leng, Y.G., Sun, J.Q., Fan, S.B.: Weak characteristic signal detection based on scale transformation of Duffing oscillator. Acta Phys. Sin. 59(2), 816–825 (2010)
Tian, R.L., Zhao, Z.J., Xu, Y.: Variable scale-convex-peak method for weak signal detection. Sci. China Technol. Sci. 64(2), 331–340 (2020)
Zhao, Z.H., Yang, S.P.: Application of Van der pol-Duffing oscillator in weak signal detection. Comput. Electr. Eng. 41, 1–8 (2015)
Wang, H.W., Cong, C.: A new signal detection and estimation method by using Duffing system. Acta Electron. Sin. 44(6), 1450–1457 (2016)
Li, Y., Yang, B.J.: Chaotic system for the detection of periodic signals under the background of strong noise. Chin Sci. Bull. 48, 508–510 (2003)
Liu, H.B., Wu, D.W., Dai, C.J., Mao, H.: A new weak sinusoidal signal detection method based on Duffing oscillators. Acta Phys. Sin. 41(1), 8–12 (2013)
Liu, H.B., Wu, D.W., Jin, W., Wang, Y.Q.: Study on weak signal detection method with Duffing oscillators. Acta Phys. Sin. 62(05), 34–39 (2013)
Wang, Q.B., Yang, Y.J., Zhang, X.: Weak signal detection based on Mathieu-Duffing oscillator with time-delay feedback and multiplicative noise. Chaos Soliton Fract 137, 109832 (2020)
Gokyildirim, A., Uyaroglu, Y., Pehlivan, I.: A week signal detection application based on hyperchaotic Lorenz system. Teh Vjesn 25(3), 701–708 (2018)
Kunze, M.: Non-smooth Dynamical Systems. Springer, Berlin (2000)
Du, Z.D., Zhang, W.N.: Melnikov method for homoclinic bifurcation in nonlinear impact oscillators. Comput. Math. Appl. 50(3–4), 445–458 (2005)
Battelli, F., Fečkan, M.: Homoclinic trajectories in discontinuous systems. J. Dyn. Differ. Equ. 20(2), 337–376 (2008)
Granados, A., Hogan, S.J., Seara, T.M.: The Melnikov method and subharmonic orbits in a piecewise smooth system. Siam. J. Appl. Dyn. Syst. 11(3), 801–830 (2012)
Granados, A., Hogan, S.J., Seara, T.M.: The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks. Phys. D. 269(7), 1–20 (2014)
Tian, R.L., Zhou, Y.F., Zhang, B.L.: Chaotic threshold for a class of impulsive differential system. Nonlinear Dyn. 83(4), 2229–2240 (2016)
Li, S.B., Gong, X.J., Zhang, W., Hao, Y.X.: The Melnikov Method for detecting chaotic dynamics in a planar hybrid piecewise-smoothsSystem with a switching manifold. Nonlinear Dyn. 89, 939–953 (2017)
Cao, Q.J., Wiercigroch, M., Pavlovskaia, E.E., Thompson, J.M.T., Grebogi, C.: Archetypal oscillator for smooth and discontinuous dynamics. Phys. Rev. E. 74(4), 046218 (2006)
Cao, Q.J., Wiercigroch, M., Pavlovskaia, E.E., Thompson, J.M.T., Grebogi, C.: SD oscillator, the attractor and their applications. J. Vib. Eng. Technol. 20(5), 454–458 (2007)
Cao, Q.J., Wiercigroch, M., Pavlovskaia, E.E., Thompson, J.M.T., Grebogi, C.: Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics. Philos. Trans. R. Soc A. 366(1865), 635–652 (2008)
Cao, Q.J., Wiercigroch, M., Pavlovskaia, E.E., Thompson, J.M.T.: The limit case response of the archetypal oscillator for smooth and discontinuous dynamics. Int. J. Nonlinear Mech. 43, 462–473 (2008)
Shen, J., Li, Y.R., Du, Z.D.: Subharmonic and grazing bifurcations for a simple bilinear oscillator. Int. J. Nonlinear Mech. 60, 70–82 (2014)
Yi, T.T., Du, Z.D.: Degenerate grazing bifurcations in a simple bilinear oscillator. Int. J. Bifurcat. Chaos 24(11), 1450141 (2014)