Here, a multiple-input–multiple-output (MIMO) Phantom Omni robot made by SensAble Technologies Inc. is identified by using a least-square support vector regression (LS-SVR). To this end, a two-stage hybrid optimisation strategy combining coupled simulated annealing as a priori optimisation strategy and a derivative-free Simplex method as a complementary stage is proposed to solve the LS-SVR model selection problem. This extra step is a fine-tuning procedure to enhance the optimal tuning parameters and hence lead LS-SVR to a better performance. Generalised v-fold cross-validation is considered as the criterion of LS-SVR model selection problem. The Phantom robot model is implemented via OPAL-RT to assess the performance of the proposed algorithm compared with firefly algorithm and adaptive particle swarm optimisation in solving LS-SVR model selection in practical application of the Phantom robot modelling. Finally, the proposed approach is validated and implemented in the hardware-in-the-loop based on OPAL-RT to integrate the fidelity of physical simulation as well as the flexibility of numerical simulations.

References

1. 1)
  - 14. Sun, J., Zheng, C., Li, X., et al: ‘Analysis of the distance between two classes for tuning SVM hyperparameters’, IEEE Trans. Neural Netw., 2010, 21, (2), pp. 305–318.
2. 2)
  - 30. Bordes, A., Ertekin, S., Weston, J., et al: ‘Fast kernel classifiers with online and active learning’, J. Mach. Learn. Res., 2005, 6, pp. 1579–1619.
3. 3)
  - 33. Zhang, H., Zhang, Y., Yin, C.: ‘Hardware-in-the-loop simulation of robust mode transition control for a series-parallel hybrid electric vehicle’, IEEE Trans. Veh. Technol., 2016, 65, (3), pp. 1059–1069.
4. 4)
  - 5. Aguirre, L.A., Coelho, M.C.S., Correa, M.V.: ‘On the interpretation and practice of dynamical differences between Hammerstein and Wiener models’, IEEE Proc., Part D: Contr. Theory Appl., 2004, 152, (4), pp. 349–356.
5. 5)
  - 8. Khooban, M.H., Almasi, O.N., Niknam, T., et al: ‘Intelligent robust PI adaptive control strategy for speed control of EV (s)’, IET Sci. Meas. Technol., 2016, 10, (5), pp. 433–441.
6. 6)
  - 10. Almasi, B.N., Almasi, O.N., Kavousi, M., et al: ‘Computer-aided diagnosis of diabetes using least square support vector machine’, J. Adv. Comput. Sci. Technol., 2013, 2, (2), pp. 68–76.
7. 7)
  - 27. Nelder, J.A., Mead, R.: ‘A Simplex method for function minimization’, Comput. J., 1965, 7, (4), pp. 308–313.
8. 8)
  - 31. Suykens, J.A.K., Yalcin, M.E., Vandewalle, J.: ‘Coupled chaotic simulated annealing processes’. IEEE Int. Symp. on Circuits and Systems (ISCAS), Thailand, 2003, pp. 582–585.
9. 9)
  - 12. Chapelle, O., Vapnik, V.N., Bousquet, O., et al: ‘Choosing multiple parameters for support vector machines’, Mach. Learn., 2002, 46, (1), pp. 131–159.
10. 10)
  - 2. Almasi, O.N., Mollaei, N., Behzad, H., et al: ‘Neuro-fuzzy based approach for identification of a phantom robot’, Int. J. Control Sci. Eng., 2014, 4, (2), pp. 36–48.
11. 11)
  - 18. Lin, S.W., Ying, K.C., Chen, S.C., et al: ‘Particle swarm optimization for parameter determination and feature selection of support vector machines’, Expert Syst. Appl., 2008, 35, (4), pp. 1817–1824.
12. 12)
  - 4. Coelho, L.D.S., Pessôa, M.W.: ‘Nonlinear model identification of an experimental ball-and-tube system using a genetic programming approach’, Mech. Syst. Signal Process., 2009, 23, (5), pp. 1434–1446.
13. 13)
  - 28. Taati, B., Tahmasebi, A.M., Hashtrudi-Zaad, K.: ‘Experimental identification and analysis of the dynamics of a phantom premium 1.5 a haptic device’, Teleoperators Virtual Environ., 2008, 17, (4), pp. 327–343.
14. 14)
  - 1. Spong, M.W., Vidyasagar, M.: ‘Robot modeling and control’ (Wiley, New York, 2006).
15. 15)
  - 19. Almasi, O.N., Naghedi, A.A., Tadayoni, E., et al: ‘Optimal design of TS fuzzy controller for a nonlinear system using a new adaptive particle swarm optimization algorithm’, J. Adv. Comput. Sci. Technol., 2014, 3, (1), pp. 37–47.
16. 16)
  - 23. Almasi, O.N., Akhtarshenas, E., Rouhani, M.: ‘An efficient model selection for SVM in real-world datasets using BGA and RGA’, Neural Netw. World, 2014, 24, (5), pp. 501–520.
17. 17)
  - 15. Stone, M.: ‘Cross-validatory choice and assessment of statistical predictions’, J. R. Stat. Soc., Ser. B (Methodol.), 1974, 36, (2), pp. 11–147.
18. 18)
  - 24. Suykens, J.A. K., Vandewalle, J., De Moor, B.: ‘Intelligence and cooperative search by coupled local minimizers’, Int. J. Bifurcation Chaos, 2001, 11, (8), pp. 2133–2144.
19. 19)
  - 7. Almasi, O.N., Khooban, M.H.: ‘PI adaptive LS-SVR control scheme with disturbance rejection for a class of uncertain nonlinear systems’, Eng. Appl. Artif. Intell., 2016, 52, pp. 135–144.
20. 20)
  - 26. Xavier-de-Souza, S., Suykens, J.A.K., Vandewalle, J., et al: ‘Coupled simulated annealing’, IEEE Trans. Syst., Man, Cybern., B: Cybern., 2010, 40, (2), pp. 320–335.
21. 21)
  - 13. Keerthi, S.S.: ‘Efficient tuning of SVM hyperparameters using radius/margin bound and iterative algorithms’, IEEE Trans. Neural Netw., 2002, 13, (5), pp. 1225–1229.
22. 22)
  - 20. Almasi, O.N., Khooban, M.H.: ‘A parsimonious SVM model selection criterion for classification of real-world data sets via an adaptive population-based algorithm’, Neural Comput. Appl., 2017, 28, pp. 1–9.
23. 23)
  - 29. Sciavicco, L., Siciliano, B.: ‘A survey on robot control technology’. Proc. of the 4th Jordanian Int. Electrical and Electronics Engineering Conf., Jordan, 2001, pp. 395–400.
24. 24)
  - 3. Ljung, L.: ‘System identification – theory for the user’ (PTR Prentice-Hall, Upper Saddle River, USA, 1999).
25. 25)
  - 17. Li, K.-C.: ‘Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation: discrete index set’, Ann. Stat., 1987, 15, (3), pp. 958–975.
26. 26)
  - 21. Almasi, O.N., Rouhani, M.: ‘A new fuzzy membership assignment and model selection approach based on dynamic class centers for fuzzy SVM family using the firefly algorithm’, Turk. J. Electr. Eng. Comput. Sci., 2016, 24, (3), pp. 1797–1814.
27. 27)
  - 25. Yao, X.: ‘A new simulated annealing algorithm’, Int. J. Comput. Math., 1995, 56, (3–4), pp. 161–168.
28. 28)
  - 9. Suykens, J.A.K., Gestel, T.V., De Brabanter, J., et al: ‘Least squares support vector machines’ (World Scientific Publishing, Singapore, 2002).
29. 29)
  - 32. Cao, Y., Golubev, Y.: ‘On oracle inequalities related to smoothing splines’, Math. Methods Stat., 2006, 15, (4), pp. 398–414.
30. 30)
  - 22. Zhang, W., Niu, P.: ‘LS-SVM based on chaotic particle swarm optimization with simulated annealing and application’. IEEE Conf. on Intelligent Control and Information Processing, China, 2011, pp. 931–935.
31. 31)
  - 6. Chen, S., Billings, S.A.: ‘Representations of nonlinear systems: the NARMAX model’, Int. J. Control, 1989, 49, (3), pp. 1013–1032.
32. 32)
  - 11. Almasi, O.N., Rouhani, M.: ‘Fast and de-noise support vector machine training method based on fuzzy clustering method for large real world datasets’, Turk. J. Electr. Eng. Comput. Sci., 2016, 24, (1), pp. 219–233.
33. 33)
  - 16. Craven, P., Wahba, G.: ‘Smoothing noisy data with spline functions’, Numer. Math., 1979, 31, (4), pp. 377–403.

Non-linear MIMO identification of a Phantom Omni using LS-SVR with a hybrid model selection

References

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