Skip to main content
SpringerLink
Log in

Black-box modeling of ship manoeuvring motion based on feed-forward neural network with Chebyshev orthogonal basis function

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

Based on polynomial interpolation and approximation theory, a novel feed-forward neural network, the feed-forward neural network with Chebyshev orthogonal basis function, is proposed for black-box modeling of ship manoeuvring motion. The neural model adopts a three-layer structure, in which the hidden layer neurons are activated by a group of Chebyshev orthogonal polynomial activation functions and the other two layers’ neurons use identity mapping as activation functions. Weight update formulas are derived by employing the standard back-propagation (BP) training method. With the simulated 15º/15º zigzag test data as input and calculated values of the hydrodynamic forces and moment as output, the feed-forward neural network with Chebyshev orthogonal basis function and the BP neural network are applied to identify the nonlinear functions in the nonlinear hydrodynamic model of ship manoeuvring motion. With the simulated 20º/20º zigzag test data and 35º turning test data as input, the hydrodynamic forces and moment are predicted by using the identified nonlinear functions. Comparison between the calculated and predicted hydrodynamic forces and moment shows that the feed-forward neural network with Chebyshev orthogonal basis function is superior to the BP neural network in identifying the nonlinear functions of the nonlinear hydrodynamic model of ship manoeuvring motion and is an effective method to conduct the black-box modeling of ship manoeuvring motion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Hess D, Faller W (2000) Simulation of ship manoeuvres using recursive neural networks. In: 23rd Symposium on Naval Hydrodynamics. Val de Reuil, France, September 2000

  2. Hess D, Faller W (2002) Using recursive neural networks for blind predictions of submarine manoeuvres, In: 24th Symposium on Naval Hydrodynamics. Fukuoka, Japan, July 2002

  3. Hess D, Faller W, Lee J et al (2006) Ship maneuvering simulation in wind and waves: a nonlinear time-domain approach using recursive neural networks. In: 26th Symposium on Naval Hydrodynamics. Rome, Italy, September 2006

  4. Hess D, Faller W, Lee J (2008) Real-time nonlinear simulation of maneuvers for US navy combatant DTMB 5415. In: Workshop on verification and validation of ship manoeuvring simulation methods, SIMMAN 2008, vol 1, E15-E21, Copenhagen, Denmark, April 2008

  5. Hess D, Faller W, Minnick L et al (2007) Maneuvering simulation of Sea Fighter using a fast nonlinear time domain technique. In: Ninth international conference on numerical ship hydrodynamics,Ann Arbor, Michigan, USA, August 2007

  6. Ebada A, Abdel-Maksoud M (2005) Applying artificial intelligence (A.I.) to predict the limits of ship turning manoeuvres, Jahrbuch der Schiffbautechnischen Gesellschaft, 99 Band:132–139

    Google Scholar 

  7. Fan SM, Zhu WM, Li ZC (1999) Prediction method for ship maneuverability based on artificial neural networks (in Chinese). Shipbuild China 4:7–12

    Google Scholar 

  8. Rumelhart DE, McClelland JL, PDP Research Group (1986) Parallel Distributed Processing, vol 1, Foundations[M]. MIT Press, Cambridge

  9. Chislett MS, Strǿm-Tejsen J (1965) Planar motion mechanism tests and full-scale steering and maneuvering predictions for a Mariner Class Vessel, Technical Report Hy-6. Hydro- and Aerodynamics Laboratory, Lyngby

    Google Scholar 

  10. Mathews JH, Fink KD (2004) Numerical methods using MATLAB. Pearson Education Inc., Beijing

    Google Scholar 

  11. Abkowitz MA (1964) Lectures on ship hydrodynamics - steering and manoeuvrability, Hydro- and Aerodynamics Laboratory, Report No. Hy-5, Lyngby, Denmark

  12. Ogawa A, Kasai H (1978) On the mathematical model of manoeuvring motion of ship. Int Shipbuild Prog 25(292):306–319

    Google Scholar 

  13. Nomoto K, Taguchi T, Honda K, Hirano S (1957) On the steering qualities of ships. Int Shipbuild Prog 4(35):354–370

    Google Scholar 

  14. Fossen TI (1994) Guidance and Control of Ocean Vehicles. John Wiley, Chichester

    Google Scholar 

  15. Cong S (1998) Neural Network Theory and Applications with MATLAB Tool boxes (in Chinese). Press of University of Science and Technology of China, Hefei

    Google Scholar 

Download references

Acknowledgments

Supported by the National Natural Science Foundation of China (Grant Nos. 50979060, 51079031) and the Foundation of National Science and Technology Key Laboratory of Hydrodynamics (Grant No. 9140C2201091001).

Author information

Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Xin-Guang Zhang & Zao-Jian Zou

  2. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zao-Jian Zou

Authors
  1. Xin-Guang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zao-Jian Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zao-Jian Zou.

About this article

Cite this article

Zhang, XG., Zou, ZJ. Black-box modeling of ship manoeuvring motion based on feed-forward neural network with Chebyshev orthogonal basis function. J Mar Sci Technol 18, 42–49 (2013). https://doi.org/10.1007/s00773-012-0190-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-012-0190-1

Keywords

Search

Navigation