Publication: Semiphysical modelling of the nonlinear dynamics of a surface craft with LS-SVM
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Hindawi Publishing Corporation
One of the most important problems in many research fields is the development of reliable mathematical models with good predictive ability to simulate experimental systems accurately. Moreover, in some of these fields, as marine systems, these models play a key role due to the changing environmental conditions and the complexity and high cost of the infrastructure needed to carry out experimental tests. In this paper, a semiphysical modelling technique based on least-squares support vector machines (LS-SVM) is proposed to determine a nonlinear mathematical model of a surface craft. The speed and steering equations of the nonlinear model of Blanke are determined analysing the rudder angle, surge and sway speeds, and yaw rate from real experimental data measured from a zig-zag manoeuvre made by a scale ship. The predictive ability of the model is tested with different manoeuvring experimental tests to show the good performance and prediction ability of the model computed.
© 2013 David Moreno-Salinas et al. The authors wish to thank the Spanish Ministry of Science and Innovation (MICINN) for support under Projects DPI2009-14552-C02-01 and DPI2009-14552-C02-02. The authors wish to thank also the National University Distance Education (UNED) for support under Project 2012V/PUNED/0003.
1. L. Ljung, System Identification: Theory for the User, Prentice-Hall, Upper Saddle River, NJ, USA, 1999. 2. L. Ljung, “Identification of Nonlinear Systems,” in Proceedings of the International Conference on Control, Automation, Robotics and Vision, 2006. 3. D. E. Rivera, “Teaching semiphysical modeling to ChE students using a brine-water mixing tank experiment,” Chemical Engineering Education, vol. 39, no. 4, pp. 308–315, 2005. 4. P. Lindskog and L. Ljung, “Tools for semiphysical modelling,” International Journal of Adaptive Control and Signal Processing, vol. 9, no. 6, pp. 509–523, 1995. View at Publisher. 5. J. A. K. Suykens, T. van Geste, J. de Brabanter, B. de Moor, and J. Vandewalle, Least Squares Support Vector Machines. :, World Scientific, Singapore, 2002. 6. K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990. 7. V. Vapnik and Z. Chervonenkis, “On the uniform convergence of relative frequencies of events to their probabilities,” Doklady Akademii Nauk USS, vol. 4, no. 181, 1968. 8. M. Aizerman, E. Braverman, and L. Rozonoer, “Theoretical foundations of the potential function method in pattern recognition learning,” Automation and Remote Control, vol. 25, pp. 821–837, 1964. 9. B. Schölkopf and A. J. Smola, Learning With Kernels, MIT press, Cambridge, Mass, USA, 2002. 10. V. Vapnik, Statistical Learning Theory, John Wiley & Sons, New York, NY, USA, 1998. 11. A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Statistics and Computing, vol. 14, no. 3, pp. 199–222, 2004. 12. P. M. L. Drezet and R. F. Harrison, “Support vector machines for system identification,” in Proceedings of the International Conference on Control, pp. 688–692, September 1998. 13. S. Adachi and T. Ogawa, “A new system identification method based on support vector machines,” in Proceedings of the IFAC Workshop Adaptation and Learning in Control and Signal Processing, L'Aquila, Italy, 2001. 14. G. T. Jemwa and C. Aldrich, “Non-linear system identification of an autocatalytic reactor using least squares support vector machines,” Journal of The South African Institute of Mining and Metallurgy, vol. 103, no. 2, pp. 119–125, 2003. 15. W. Zhong, D. Pi, and Y. Sun, “SVM based nonparametric model identification and dynamic model control,” in Proceedings of the First International Conference on Natural Computation (ICNC '05), pp. 706–709, August 2005. 16. V. Verdult, J. A. K. Suykens, J. Boets, I. Goethals, and B. de Moor, “Least squares support vector machines for kernel cca in non-linear state-space identification,” in Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS '04), Leuven, Belgium, July 2004. 17. W. Zhong, H. Ge, and F. Qian, “Model identification and control for nonlinear discrete-time systems with time delay: a support vector machine approach,” in Proceedings of International Conference on Intelligent Systems and Knowledge Engineering (ISKE '07), Chengdu, China, October 2007. 18. S. Tötterman and H. T. Toivonen, “Support vector method for identification of Wiener models,” Journal of Process Control, vol. 19, no. 7, pp. 1174–1181, 2009. 19. X.-D. Wang and M.-Y. Ye, “Nonlinear dynamic system identification using least squares support vector machine regression,” in Proceedings of International Conference on Machine Learning and Cybernetics, pp. 941–945, Shanghai, China, August 2004. 20. I. Goethals, K. Pelckmans, J. A. K. Suykens, and B. de Moor, “Identification of MIMO Hammerstein models using least squares support vector machines,” Automatica, vol. 41, no. 7, pp. 1263–1272, 2005. 21. Z. Yu and Y. Cai, “Least squares wavelet support vector machines for nonlinear system identification,” in Proceedings of the Second International Symposium on Neural Networks: Advances in Neural Networks (ISNN '05), pp. 436–441, June 2005. 22. L. Wang, H. Lai, and T. Zhang, “An improved algorithm on least squares support vector machines,” Information Technology Journal, vol. 7, no. 2, pp. 370–373, 2008. 23. J. van Amerongen and A. J. Udink Ten Cate, “Model reference adaptive autopilots for ships,” Original Research Article Automatica, vol. 11, no. 5, pp. 441–449, 1975. 24. K. J. Åström and C. G. Källström, “Identification of ship steering dynamics,” Automatica, vol. 12, no. 1, pp. 9–22, 1976. 25. C. G. Källström and K. J. Åström, “Experiences of system identification applied to ship steering,” Automatica, vol. 17, no. 1, pp. 187–198, 1981. 26. M. A. Abkowitz, “Measurement of hydrodynamic characteristics from ship maneuvering trials by system identification,” Transactions of Society of Naval Architects and Marine Engineers, vol. 88, pp. 283–318, 1981. 27. T. I. Fossen, S. I. Sagatun, and A. J. Sørensen, “Identification of dynamically positioned ships,” Modeling, Identification and Control, vol. 17, no. 2, pp. 153–165, 1996. 28. T. Perez, A. J. Sørensen, and M. Blanke, “Marine vessel models in changing operational conditions—a tutorial,” in Proceedings of the 14th IFAC Symposium on System Identification, Newcastle, Australia, 2006. 29. M. Caccia, G. Bruzzone, and R. Bono, “A practical approach to modeling and identification of small autonomous surface craft,” IEEE Journal of Oceanic Engineering, vol. 33, no. 2, pp. 133–145, 2008. 30. T. I. Fossen, Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics, Trondheim, Norway, 2002. 31. J. M. de La Cruz, J. Aranda, and J. M. Giron, “Automática Marina: una revision desde el punto de vista de control,” Revista Iberoamericana de Automatica e Informatica Industrial, vol. 9, pp. 205–218, 2012. 32. F. J. Velasco, E. Revestido, L. Eopez , and E. Moyano, “Identification for a heading autopilot of an autonomous in-scale fast ferry,” IEEE Journal of Oceanic Engineering, vol. 38, no. 2, pp. 263–274, 2013. 33. R. Skjetne, Ø. N. Smogeli, and T. I. Fossen, “A nonlinear ship manoeuvering model: identification and adaptive control with experiments for a model ship,” Modeling, Identification and Control, vol. 25, no. 1, pp. 3–27, 2004. 34. M. Blanke, Ship propulsion losses related to automated steering and prime mover control [Ph.D. thesis], The Technical University of Denmark, Lyngby, Denmark, 1981. 35. M. A. Abkowitz, “Lectures on ship hydrodynamics steering and manoeuvrability,” Tech. Rep. Hy-5, Hydro and Aerodynamics Laboratory, Denmark, 1964. 36. M. R. Haddara and Y. Wang, “Parametric identification of manoeuvring models for ships,” International Shipbuilding Progress, vol. 46, no. 445, pp. 5–27, 1999. 37. M. R. Haddara and J. Xu, “On the identification of ship coupled heave-pitch motions using neural networks,” Ocean Engineering, vol. 26, no. 5, pp. 381–400, 1998. 38. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989. 39. A. B. Mahfouz, “Identification of the nonlinear ship rolling motion equation using the measured response at sea,” Ocean Engineering, vol. 31, no. 17-18, pp. 2139–2156, 2004. 40. W. L. Luo and Z. J. Zou, “Parametric identification of ship maneuvering models by using support vector machines,” Journal of Ship Research, vol. 53, no. 1, pp. 19–30, 2009. 41. X.-G. Zhang and Z.-J. Zou, “Identification of Abkowitz model for ship manoeuvring motion using ϵ-support vector regression,” Journal of Hydrodynamics, vol. 23, no. 3, pp. 353–360, 2011. 42. D. Moreno-Salinas, D. Chaos, J. M. de la Cruz, and J. Aranda, “Identification of a surface marine vessel using LS-SVM,” Journal of Applied Mathematics, vol. 2013, Article ID 803548, 11 pages, 2013. 43. F. Xu, Z.-J. Zou, J.-C. Yin, and J. Cao, “Identification modeling of underwater vehicles’nonlinear dynamics based on support vector machines,” Ocean Engineering, vol. 67, Article ID 002980, pp. 68–76, 2013. 44. J. Mercer, “Functions of positive and negative type and their connection with the theory of integral equations,” Philosophical Transactions of the Royal Society A, vol. 209, pp. 415–446, 1909. 45. K. Nomoto, T. Taguchi, K. Honda, and S. Hirano, “On the steering qualities of ships,” Tech. Rep., International Shipbuilding Progress, 1957. 46. G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: a new learning scheme of feedforward neural networks,” in Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 985–990, July 2004. 47. R. Rajesh and J. Siva Prakash, “Extreme learning machines—a review and state-of-the-art,” International Journal of Wisdom Based Computing, vol. 1, no. 1, 2011.