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Case Study: Interpretability of Fuzzy Systems Applied to Nonlinear Modelling and Control

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Design of Interpretable Fuzzy Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 684))

Abstract

Fuzzy systems have their limitations which result from a number of factors including a limited ability to assure their interpretability in various practical problems. If interpretability is not of paramount importance, then we can consider using methods from the “black box” group (e.g. artificial neural networks with a teacher) . However, if interpretability is of a great importance, then some dedicated approaches and algorithms should be developed.

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References

  1. Adjrad, M., Belouchrani, A.: Estimation of multicomponent polynomial-phase signals impinging on a multisensor array using state-space modeling. IEEE Trans. Signal Process. 55, 32–45 (2007)

    Article  MathSciNet  Google Scholar 

  2. Banerjee, A., Arkun, Y., Ogunnaike, B., Pearson, R.: Estimation of nonlinear systems using linear multiple models. AIChE J. 43, 1204–1226 (1997)

    Article  Google Scholar 

  3. Bartczuk, Ł., Przybył, A., Cpałka, K.: A new approach to nonlinear modelling of dynamic objects based on fuzzy rules. Int. J. Appl. Math. Comput. Sci. 26, 603–621 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boukezzoula, R., Galichet, S., Foulloy, L.: Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure. Int. J. Appl. Math. Comput. Sci. 2, 233–248 (2007)

    MathSciNet  MATH  Google Scholar 

  5. Caughey, T.K.: Equivalent linearization techniques. J. Acoust. Soc. Am. 11, 1706–1711 (1963)

    Article  MathSciNet  Google Scholar 

  6. Dieulot, J.Y., Thimoumi, I., Colas, F., Béarée, R.: Numerical aspects and performances of trajectory planning methods of flexible axes. Int. J. Comput. Commun. Control 4, 35–44 (2006)

    Article  Google Scholar 

  7. Erkorkmaz, K., Altintas, Y.: High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int. J. Mach. Tools Manuf. 41, 1323–1345 (2001)

    Article  Google Scholar 

  8. Grabowski, P., Callier, F.M.: Circle criterion and boundary control systems in factor form Input-output approach. Appl. Math. Comput. Sci. 11, 1387–1403 (2001)

    MathSciNet  MATH  Google Scholar 

  9. Háber, R., Keviczky, L.: Nonlinear System Identification – Input-Output Modeling Approach. Volume 1: Nonlinear System Parameter Identification. Mathematical Modelling Theory and Applications. Kluwer, The Netherlands (1999)

    Book  MATH  Google Scholar 

  10. Horzyk, A., Tadeusiewicz R.: Self-optimizing neural networks, advances in neural networks. In: Proceedings of the International Symposium on Neural Networks, pp. 150–155 (2004)

    Google Scholar 

  11. Huijberts, H., Nijmeijer, H., Willems, R.: System identification in communication with chaotic systems. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47, 800–808 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ikonen, E., Najim, K.: Advanced Process Identification and Control, vol. 9. CRC Press, New York (2001)

    MATH  Google Scholar 

  13. Jang, I.S.R., Sun, C.T.: Neuro-fuzzy modeling and control. In: Proceedings of the IEEE, pp. 378–406 (1995)

    Google Scholar 

  14. Jordan, A.: Linearization of non-linear state equation. Bull. Polish Acad. Sci. Tech. Sci. 1, 63–73 (2006)

    MATH  Google Scholar 

  15. Ki, N.Y.: A new velocity profile generation for high efficiency CNC machining application. City University of Hong Kong (Master Thesis), pp. 1–83 (2008)

    Google Scholar 

  16. Kluska, J.: Analytical Methods in Fuzzy Modeling and Control. Springer, Heidelberg (2009)

    Book  MATH  Google Scholar 

  17. Kluska, J.: Selected Applications of P1-TS Fuzzy Rule-Based Systems. Lecture Notes in Computer Science, pp. 195–206. Springer, Heidelberg (2015)

    Google Scholar 

  18. Lei, W.T., Sung, M.P., Lin, L.Y., Huang, J.J.: Fast real-time NURBS path interpolation for CNC machine tools. Int. J. Mach. Tools Manuf. 47, 1530–1541 (2007)

    Article  Google Scholar 

  19. Lin, M.T., Tsai, M.S., Yau, H.T.: Development of an dynamics-based NURBS interpolator with real-time look-ahead algorithm. Int. J. Mach. Tools Manuf. 47, 2246–2262 (2007)

    Article  Google Scholar 

  20. Ljung, L.: Approaches to identification of nonlinear systems. In: Proceedings of the 29th Chinese Control Conference, pp. 1–5 (2010)

    Google Scholar 

  21. Lo Bianco, C.G., Zanasi, R.: Smooth profile generation for a tile printing machine. IEEE Trans. Ind. Electron. 50, 471–477 (2003)

    Article  Google Scholar 

  22. Macfarlane, S.: On-Line smooth trajectory planning for manipulators. The University of British Columbia (Master Thesis), pp. 1–146 (2001)

    Google Scholar 

  23. Mohan, S., Kweon, S.H., Lee, D.M., Yang, S.H.: Parametric NURBS curve interpolators: a review. Int. J. Precis. Eng. Manuf. 9, 84–92 (2008)

    Google Scholar 

  24. Mrugalski, M.: Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis. Studies in Computational Intelligence. Springer, Heidelberg (2014)

    Book  MATH  Google Scholar 

  25. Murray-Smith, R., Johansen, T.: Multiple Model Approaches to Nonlinear Modelling and Control. CRC Press, Boca Raton (1997)

    Google Scholar 

  26. Nelles, O.: Nonlinear System Identification From Classical Approaches to Neural Networks and Fuzzy Models. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  27. Ogata, K.: System Dynamics. Pearson/Prentice Hall, Upper Saddle River (2004)

    MATH  Google Scholar 

  28. Osario-Rios, R.A., Romero-Trosncoso, R.D.J., Herera-Ruiz, G., Casteneda-Miranda, R.: FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors. Robot. Comput. Integr. Manuf. 25, 379–392 (2009)

    Article  Google Scholar 

  29. Pedro, J., Dahunsi, O.: Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system. Int. J. Appl. Math. Comput. Sci. 21, 137–147 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Pessen, D.W.: Industrial Automation. Circuit Design and Components. Willey, New York (1989)

    Google Scholar 

  31. Przybył, A., Cpałka, K.: A New Method to Construct of Interpretable Models of Dynamic Systems. Lecture Notes in Computer Science, pp. 697–705. Springer, Heidelberg (2012)

    Google Scholar 

  32. Przybył, A., Jelonkiewicz, J.: Genetic algorithm for observer parameters tuning in sensorless induction motor drive, neural networks and soft computing. In: Proceedings of the Sixth International Conference on Neural Networks and Soft Computing. Springer, pp. 376–381 (2003)

    Google Scholar 

  33. Puig, V., Witczak, M., Nejjari, F., Quevedo, J., Korbicz, J.: A gmdh neural network-based approach to passive robust fault detection using a constraint satisfaction backward test. Eng. Appl. Artif. Intell. 20, 886–897 (2007)

    Article  Google Scholar 

  34. Roffel, B., Betlem, B.H.: Advanced Practical Process Control. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  35. Rutkowski, L.: Computational Intelligence. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  36. Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online Speed Profile Generation for Industrial Machine Tool Based on Neuro Fuzzy Approach. Lecture Notes in Computer Science, vol. 6114, pp. 645–650. Springer, Heidelberg (2010)

    Google Scholar 

  37. Rutkowski, L., Przybył, A., Cpałka, K.: Novel on-line speed profile generation for industrial machine tool based on flexible neuro-fuzzy approximation. IEEE Trans. Ind. Electron. 59, 1238–1247 (2012)

    Article  Google Scholar 

  38. Salapa, K., Trawińska, A., Roterman, I., Tadeusiewicz, R.: Speaker identification based on artificial neural networks. Case study the polish vowel (pilot study). Bio-Algorithms Med-Syst. 10, 91–99 (2014)

    Google Scholar 

  39. Schröder, D. (ed.): Intelligent Observer and Control Design for Nonlinear Systems. Springer, Heidelberg (2000)

    Google Scholar 

  40. Sun, Y., Wang, J., Guo, D.: Guide curve based interpolation scheme of parametric curves for precision CNC machining, parametric NURBS curve interpolators: a review. Int. J. Mach. Tools Manuf. 46, 235–242 (2006)

    Article  Google Scholar 

  41. Sun, F., Li, L., Li, H.X., Liu, H.: Neuro-fuzzy dynamic-inversion-based adaptive control for robotic manipulators-discrete time case. IEEE Trans. Ind. Electron. 54, 342–1351 (2007)

    Article  Google Scholar 

  42. Tadeusiewicz, R.: Using neural networks for simplified discovery of some psychological phenomena. Artif. Intell. Soft Comput. 6114, 104–123 (2010)

    Google Scholar 

  43. Tadeusiewicz, R., Figura, I.: Phenomenon of tolerance to damage in artificial neural networks. Comput. Methods Mater. Sci. 11, 501–513 (2011)

    Google Scholar 

  44. Tadeusiewicz, R., Chaki, R., Chaki, N.: Exploring Neural Networks with C#. CRC Press, Boca Raton (2014)

    Google Scholar 

  45. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    Article  MATH  Google Scholar 

  46. Tan, Z.: Time-varying time-delay estimation for nonlinear systems using neural networks. Int. J. Appl. Math. Comput. Sci. 1, 63–68 (2004)

    MathSciNet  Google Scholar 

  47. Tsai, M.S., Nien, H.W., Yau, H.T.: Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery. Comput. Aided Des. 40, 554–566 (2008)

    Article  Google Scholar 

  48. Tseng, S.J., Lin, K.Y., Lai, J.Y., Ueng, W.D.: A NURBS curve interpolator with jerk-limited trajectory planning. J. Chin. Inst. Eng. 32, 215–228 (2009)

    Article  Google Scholar 

  49. Witkowska, A., Śmierzchalski, R.: Designing a ship course controller by applying the adaptive backstepping method. Int. J. Appl. Math. Comput. Sci. 4, 985–997 (2012)

    MathSciNet  MATH  Google Scholar 

  50. Xie, Y., Guo, B., Xu, L., Li, J., Stoica, P.: Multistatic adaptive microwave imaging for early breast cancer detection. IEEE Trans. Biomed. Eng. BME 53, 1647–1657 (2006)

    Article  Google Scholar 

  51. Yau, H.T., Wang, J.B.: Fast Bezier interpolator with real-time lookahead function for high-accuracy machining. Int. J. Mach. Tools Manuf. 47, 1518–1529 (2007)

    Article  Google Scholar 

  52. Yau, H.T., Wang, J.B., Hsu, C.Y., Yeh, C.H.: PC-based controller with real-time look-ahead NURBS interpolator. Comput. Aided Des. Appl. 4, 331–340 (2007)

    Google Scholar 

  53. Zheng, C., Su, Y., Müller, P.C.: Simple on-line smooth trajectory generation for industrial systems. Mechatronics 19, 571–576 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Intelligence, Częstochowa University of Technology, Częstochowa, Poland

    Krzysztof Cpałka

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  1. Krzysztof Cpałka
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Correspondence to Krzysztof Cpałka .

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Cpałka, K. (2017). Case Study: Interpretability of Fuzzy Systems Applied to Nonlinear Modelling and Control. In: Design of Interpretable Fuzzy Systems. Studies in Computational Intelligence, vol 684. Springer, Cham. https://doi.org/10.1007/978-3-319-52881-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-52881-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52880-9

  • Online ISBN: 978-3-319-52881-6

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