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Detection method of ship-radiated noise based on fractional-order dual coupling oscillator

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Abstract

The popularly known integer-order chaotic oscillators are widely used to detect ship-radiated noise (S-RN). However, the current integer-order oscillators exhibit low accuracy in detecting complex S-RN. In this study, a method is proposed to detect ship-radiated noise based on double complexity and fractional-order dual coupling Duffing system to address the challenge. Firstly, embedding the integer derivative, we put forward a fractional-order dual coupling Duffing oscillator, a novel chaotic oscillator that considers the derivative changes. Secondly, determining the critical threshold of the system is to combine a double complexity algorithm with phase trajectory observation. The double complexity algorithm is utilized to determine the critical threshold and reduce the error in phase trajectory observation. Then, studying the dynamic behavior of the fractional-order dual coupling Duffing system, we demonstrate that the critical threshold of the fractional-order system is lower than the integer-order system and changes more drastically near the critical threshold. Finally, measured and analog signals are used to verify the performance of the proposed detection method. We empirically show that the method has a fine detection performance. Analyzing the system performance under the same detection signal and noise distribution, the signal-to-noise ratio threshold of the proposed detection method is −43.01 dB. This research generalizes the Duffing oscillator, aiming to explore the practical application of the fractional chaotic system.

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Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

References

  1. Yang, H., Shi, W.S., Li, G.H.: Underwater acoustic signal denoising model based on secondary variational mode decomposition. Def Technol 28, 87–110 (2023). https://doi.org/10.1016/j.dt.2022.10.011

    Article  Google Scholar 

  2. Yang, H., Yang, X.D., Li, G.H.: Dual feature extraction system for ship-radiated noise and its application extension. Ocean Eng. 285, 115352 (2023). https://doi.org/10.1016/j.oceaneng.2023.115352

    Article  Google Scholar 

  3. Li, J.H., Zakharov, Y.V., Henson, B.: Multibranch autocorrelation method for Doppler estimation in underwater acoustic channels. IEEE J. Oceanic Eng. 43(4), 1099–1113 (2018). https://doi.org/10.1109/JOE.2017.2761478

    Article  Google Scholar 

  4. Huang, S.H., Tsao, J., Yang, T.C., Cheng, S.W.: Model-based signal subspace channel tracking for correlated underwater acoustic communication channels. IEEE J. Oceanic Eng. 39(2), 343–356 (2014). https://doi.org/10.1109/JOE.2013.2251808

    Article  Google Scholar 

  5. Zhao, J.H., Yan, J., Zhang, H.M., Meng, J.X.: Two self-adaptive methods of improving multibeam backscatter image quality by removing angular response effect. J. Mar. Sci. Technol. 22(2), 288–200 (2017). https://doi.org/10.1007/s00773-016-0410-1

    Article  Google Scholar 

  6. Sun, J.P., Yang, J., Lin, J.H., Jiang, G.J., Yi, X.J., Jiang, P.F.: Theoretical model and simulation of ship underwater radiated noise. Acta Physica Sinica. 65(12), 124301 (2016). https://doi.org/10.7498/aps.65.124301

    Article  Google Scholar 

  7. Wu, G.L., Dong, H.F., Ke, G.P., Song, J.Q.: An adapted eigenvalue-based filter for ocean ambient noise processing. Geophysics 85(1), KS29–KS38 (2020). https://doi.org/10.1190/geo2018-0861.1

    Article  Google Scholar 

  8. MacGillivray, A., de Jong, C.: A reference spectrum model for estimating source levels of marine shipping based on automated identification system data. J. Mar. Sci. Eng. 9(4), 369 (2021). https://doi.org/10.3390/jmse9040369

    Article  Google Scholar 

  9. Yan, J.Q., Sun, H.X., Chen, H.L., Junejo, N.U.R., Cheng, E.: Resonance-based time-frequency manifold for feature extraction of ship-radiated noise. Sensors 18(4), 936 (2018). https://doi.org/10.3390/s18040936

    Article  Google Scholar 

  10. Yang, H., Li, L.L., Li, G.H.: A new denoising method for underwater acoustic signal. IEEE Access 8, 201874–201888 (2020). https://doi.org/10.1109/ACCESS.2020.3035403

    Article  Google Scholar 

  11. Li, G.H., Yang, Z.C., Yang, H.: A denoising method of ship radiated noise signal based on modified CEEMDAN, dispersion entropy, and interval thresholding. Electronics 8(6), 597 (2019). https://doi.org/10.3390/electronics8060597

    Article  MathSciNet  Google Scholar 

  12. Li, G.H., Bu, W.J., Yang, H.: Research on noise reduction method for ship radiate noise based on secondary decomposition. Ocean Eng. 268, 113412 (2023). https://doi.org/10.1016/j.oceaneng.2022.113412

    Article  Google Scholar 

  13. Kim, Y., Park, S.G.: On the second order effect of the springing response of large blunt ship. Int. J. Naval Archit. Ocean Eng. 7(5), 873–887 (2015). https://doi.org/10.1515/ijnaoe-2015-0061

    Article  Google Scholar 

  14. Xiao, Q., Zhao, W.J., Zhu, R.C.: Effects of wave-field nonlinearity on motions of ship advancing in irregular waves using HOS method. Ocean Eng. 199, 106947 (2020). https://doi.org/10.1016/j.oceaneng.2020.106947

    Article  Google Scholar 

  15. Zhang, J.W., Hou, G., Wang, H., Zhao, Y., Huang, J.L.: Operation feature extraction of flood discharge structure based on improved variational mode decomposition and variance dedication rate. J. Vib. Control 26(3–4), 229–240 (2019). https://doi.org/10.1177/1077546319878542

    Article  MathSciNet  Google Scholar 

  16. Dong, H.T., Wang, H.Y., Shen, X.H., Jiang, Z.: Effects of second-order matched stochastic resonance for weak signal detection. IEEE Access. 6, 46505–46515 (2018). https://doi.org/10.1109/ACCESS.2018.2866170

    Article  Google Scholar 

  17. Dong, H.T., Wang, H.Y., Shen, X.H., He, K.: Parameter matched stochastic resonance with damping for passive sonar detection. J. Sound Vib. 458, 479–496 (2019). https://doi.org/10.1016/j.jsv.2019.06.021

    Article  Google Scholar 

  18. Li, Z., Lian, X.Y.: The application of chaos theory in the ship radiated noise feature extraction. Ship Sci. Technol. 39(20), 28–30 (2017)

    Google Scholar 

  19. Huang, S.H., Hou, X.G., Liu, W.W., Liu, G.J., Dai, Y.W., Tian, W.: Mimicking ship-radiated noise with chaos signal for covert underwater acoustic communication. IEEE Access 8, 180341–180351 (2020). https://doi.org/10.1109/ACCESS.2020.3027022

    Article  Google Scholar 

  20. Yang, H., Li, L.L., Li, G.H., Guan, Q.R.: A novel feature extraction method for ship-radiated noise. Def. Technol. 18(4), 604–617 (2022). https://doi.org/10.1016/j.dt.2021.03.012

    Article  Google Scholar 

  21. Liu, F., Li, G.H., Yang, H.: A new feature extraction method of ship radiated noise based on variational mode decomposition, weighted fluctuation-based dispersion entropy and relevance vector machine. Ocean Eng. 266(5), 113143 (2022). https://doi.org/10.1016/j.oceaneng.2022.113143

    Article  Google Scholar 

  22. Zhang, Y.H., Mao, H.L., Mao, H.Y., Huang, Z.F.: Detection the nonlinear ultrasonic signals based on modified Duffing equations. Res. Phys. 7, 3243–3250 (2017). https://doi.org/10.1016/j.rinp.2017.08.054

    Article  Google Scholar 

  23. Jiao, S.B., Jiang, W., Lei, S., Huang, W.C., Zhang, Q.: Research on detection method of multi-frequency weak signal based on stochastic resonance and chaos characteristics of Duffing system. Chin. J. Phys. 64, 333–347 (2020). https://doi.org/10.1016/j.cjph.2019.12.001

    Article  MathSciNet  Google Scholar 

  24. Wang, Q., Yang, Y., Zhang, X.: Weak signal detection based on Mathieu–Duffing oscillator with time-delay feedback and multiplicative noise. Chaos, Solitons Fract. 137, 109832 (2020). https://doi.org/10.1016/j.chaos.2020.109832

    Article  MathSciNet  Google Scholar 

  25. Li, G.H., Cui, J.Y., Yang, H.: A new detecting method for underwater acoustic weak signal based on differential double coupling oscillator. IEEE Access 9, 18842–18854 (2021). https://doi.org/10.1109/ACCESS.2021.3052057

    Article  Google Scholar 

  26. Li, G.H., Hou, Y.M., Yang, H.: A novel method for frequency feature extraction of ship radiated noise based on variational mode decomposition, double coupled Duffing chaotic oscillator and multivariate multiscale dispersion entropy. Alex. Eng. J. 61(8), 6329–6347 (2022). https://doi.org/10.1016/j.aej.2021.11.059

    Article  Google Scholar 

  27. Ortiz, A., Yang, J.H., Coccolo, M., Seoane, J.M., Sanjun, M.A.F.: Fractional damping enhances chaos in the nonlinear Helmholtz oscillator. Nonlinear Dyn. 102(4), 2323–2337 (2020). https://doi.org/10.1007/s11071-020-06070-y

    Article  Google Scholar 

  28. Cui, Y., He, H.J., Sun, G., Lu, C.H.: Analysis and control of fractional order generalized Lorenz chaotic system by using finite time synchronization. Adv. Math. Phys. 2019, 3713789 (2019). https://doi.org/10.1155/2019/3713789

    Article  MathSciNet  Google Scholar 

  29. Cermák, J., Nechvátal, L.: Local bifurcations and chaos in the fractional Rössler system. Int. J. Bifurc. Chaos. 28(8), 1850098 (2018). https://doi.org/10.1142/S0218127418500980

    Article  Google Scholar 

  30. Cermák, J., Nechvátal, L.: Stability and chaos in the fractional Chen system. Chaos Solitons Fractals 125, 24–33 (2019). https://doi.org/10.1016/j.chaos.2019.05.007

    Article  MathSciNet  Google Scholar 

  31. Wang, X.Y., Wang, M.J.: Dynamic analysis of the fractional-order Liu system and its synchronization. Chaos 17(3), 033106 (2007). https://doi.org/10.1063/1.2755420

    Article  Google Scholar 

  32. Aledealat, K., Obeidat, A., Gharaibeh, M., Jaradat, A., Khasawinah, K., Hasan, M.K., Rousan, A.: Dynamics of Duffing–Holmes oscillator with fractional order nonlinearity. Eur. Phys. J. B. 92(10), 233 (2019). https://doi.org/10.1140/epjb/e2019-100299-8

    Article  Google Scholar 

  33. Coccolo, M., Seoane, J.M., Lenci, S., Sanjuán, M.A.: Fractional damping effects on the transient dynamics of the Duffing oscillator. Commun. Nonlinear Sci. Numer. Simul. 117, 106959 (2023). https://doi.org/10.1016/j.cnsns.2022.106959

    Article  MathSciNet  Google Scholar 

  34. Niu, J.C., Liu, R.Y., Shen, Y.J., Yang, S.P.: Chaos detection of Duffing system with fractional-order derivative by Melnikov method. Chaos 29(12), 123106 (2019). https://doi.org/10.1063/1.5124367

    Article  MathSciNet  Google Scholar 

  35. Huang, P., Chai, Y., Chen, X.: Multiple dynamics analysis of Lorenz-family systems and the application in signal detection. Chaos Solitons Fractals 156, 111797 (2022). https://doi.org/10.1016/j.chaos.2022.111797

    Article  Google Scholar 

  36. He, Y., Fu, Y., Qiao, Z., Kang, Y.: Chaotic resonance in a fractional-order oscillator system with application to mechanical fault diagnosis. Chaos, Solitons Fract. 142, 110536 (2021). https://doi.org/10.1016/j.chaos.2020.110536

    Article  MathSciNet  Google Scholar 

  37. Li, G.H., Hou, Y.M., Yang, H.: A new Duffing detection method for underwater weak target signal. Alex. Eng. J. 61(4), 2859–2876 (2022). https://doi.org/10.1016/j.aej.2021.08.016

    Article  Google Scholar 

  38. Li, G.H., Zhang, X.Y., Yang, H.: Complexity analysis of three-dimensional fractional-order chaotic system based on entropy theory. IEEE Access. 9, 73012–73028 (2021). https://doi.org/10.1109/ACCESS.2021.3081024

    Article  Google Scholar 

  39. Baskonus, H.M., Bulut, H.: On the numerical solutions of some fractional ordinary differential equations by fractional Adams–Bashforth–Moulton method. Open Math. 13, 547–556 (2015). https://doi.org/10.1515/math-2015-0052

    Article  MathSciNet  Google Scholar 

  40. Li, G.H., Zhang, X.Y., Yang, H.: Numerical analysis, circuit simulation, and control synchronization of fractional-order unified chaotic system. Mathematics. 7(11), 1077 (2019). https://doi.org/10.3390/math7111077

    Article  Google Scholar 

  41. Ouannas, A., Khennaoui, A.A., Momani, S., Pham, V.T.: The discrete fractional Duffing system: Chaos, 0–1 test, C-0 complexity, entropy, and control. Chaos 30(8), 083131 (2020). https://doi.org/10.1063/5.0005059

    Article  MathSciNet  Google Scholar 

  42. He, S.B., Sun, K.H., Wang, H.H.: Complexity analysis and DSP implementation of the fractional-order Lorenz hyperchaotic system. Entropy 17(12), 8299–8311 (2015). https://doi.org/10.3390/e17127882

    Article  Google Scholar 

  43. Santos-Dominguez, D., Torres-Guijarro, S., Cardenal-Lopez, A., Pena-Gimenez, A.: ShipsEar: An underwater vessel noise database. Appl. Acoust. 113, 64–69 (2016). https://doi.org/10.1016/j.apacoust.2016.06.008

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51709228).

Funding

National Natural Science Foundation of China, 51709228, Guohui Li

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Authors and Affiliations

  1. School of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, 710121, Shaanxi, China

    Guohui Li, Ruiting Xie & Hong Yang

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  1. Guohui Li
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Contributions

Guohui Li: Conceptualization, Methodology. Ruiting Xie: Data curation, Software, Writing- Original draft preparation. Hong Yang: Supervision, Investigation, Writing- Reviewing and Editing.

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Correspondence to Guohui Li.

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Li, G., Xie, R. & Yang, H. Detection method of ship-radiated noise based on fractional-order dual coupling oscillator. Nonlinear Dyn 112, 2091–2118 (2024). https://doi.org/10.1007/s11071-023-09150-x

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