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T–S Fuzzy Model Identification with Sparse Bayesian Techniques

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Abstract

This paper introduces a novel method for fuzzy modeling based on sparse Bayesian techniques. The sparse representation problems in the Takagi–Sugeno (T–S) fuzzy system identification are studied, which is to establish a T–S fuzzy system with a adaptive number of fuzzy rules and simultaneously have a minimal number of nonzero consequent parameters. The proposed method is called sparse Bayesian fuzzy inference systems (B-sparseFIS). There are two main procedures in the paper. Firstly, initial fuzzy rule of antecedent part is extracted automatically by an AP clustering method. By using the algorithm of adaptive block orthogonal matching pursuit, the number of rules is computed statistically then the main important fuzzy rules can be selected. In the algorithm, the redundant rules are eliminated for better model accuracy and generalization performance; secondly, an adaptive B-sparseFIS is exploited. The consequence of fuzzy system is identified and simplified with sparse Bayesian techniques such that many consequent parameters will approximate to zero. Four examples are provided to illustrate the effectiveness of the proposed algorithm. Furthermore, the performances of the algorithm are validated through the results of statistical analyses including parameter estimate error, MSE, NRMSE, etc.

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References

  1. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  2. Ge C, Wang H, Liu Y et al (2018) Stabilization of chaotic systems under variable sampling and state quantized controller. Fuzzy Sets Syst 344:129–144

    Article  MathSciNet  MATH  Google Scholar 

  3. Veloz A, Salas R, Allende-Cid H (2016) Identification of lags in nonlinear autoregressive time series using a flexible fuzzy model. Neural Process Lett 43(3):641–666

    Article  Google Scholar 

  4. Shen H, Li F, Yan H et al (2018) Finite-time event-triggered \(\cal{H} _\infty \) control for TS fuzzy Markov jump systems. IEEE Trans Fuzzy Syst 26(5):3122–3135

    Article  Google Scholar 

  5. Cheng J, Park JH, Karimi HR et al (2018) A flexible terminal approach to sampled-data exponentially synchronization of Markovian neural networks with time-varying delayed signals. IEEE Trans Cybern 48(8):2232–2244

    Article  Google Scholar 

  6. Qi W, Zong G, Karim HR (2018) Observer-based adaptive SMC for nonlinear uncertain singular semi-Markov jump systems with applications to DC motor. IEEE Trans Circuits Syst I Regul Pap 65(9):2951–2960

    Article  MathSciNet  Google Scholar 

  7. Wang LX, Mendel JM (1992) Back-propagation fuzzy systems as nonlinear dynamic system identifiers. In: Proceedings of IEEE 5th international fuzzy systems, San Diego, pp 1409–1418

  8. Kim E, Lee H, Park M, Park M (1998) A simply identified Sugeno-type fuzzy model via double clustering. Inf Sci 110(1–2):25–39

    Article  Google Scholar 

  9. Kim E, Park M, Ji S et al (1997) A new approach to fuzzy modeling. IEEE Trans Fuzzy Syst 5(3):328–337

    Article  Google Scholar 

  10. Setnes M (2000) Supervised fuzzy clustering for rule extraction. IEEE Trans Fuzzy Syst 8(4):416–424

    Article  Google Scholar 

  11. Wang LX, Mendel JM (1992) Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans Neural Netw 3(5):807–814

    Article  Google Scholar 

  12. Gomez-Skarmeta AF, Delgado M, Vila MA (1999) About the use of fuzzy clustering techniques for fuzzy model identification. Fuzzy Sets Syst 106:179–188

    Article  Google Scholar 

  13. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Kluwer/Plenum, Boston

    Book  MATH  Google Scholar 

  14. Tsekouras GE (2005) On the use of the weighted fuzzy c-means in fuzzy modeling. Adv Eng Softw 36(5):287–300

    Article  MATH  Google Scholar 

  15. Lughofer E (2008) Extensions of vector quantization for incremental clustering. Pattern Recogn 41(3):995–1011

    Article  MATH  Google Scholar 

  16. Wang LX, Mendel JM (1992) Generating fuzzy rules by learning from examples. IEEE Trans Syst Man Cybern 22(6):1414–1427

    Article  MathSciNet  Google Scholar 

  17. Kroll A (1996) Identification of functional fuzzy models using multidimensional reference fuzzy sets. Fuzzy Sets Syst 80(2):149–158

    Article  MathSciNet  Google Scholar 

  18. Chen JQ, Xi YG, Zhang ZJ (1998) A clustering algorithm for fuzzy model identification. Fuzzy Sets Syst 98(3):319–329

    Article  MathSciNet  Google Scholar 

  19. de Souza FJ, Vellasco MMR, Pacheco MAC (2002) Hierarchical neuro-fuzzy quadtree models. Fuzzy Sets Syst 130(2):189–205

    Article  MathSciNet  MATH  Google Scholar 

  20. Kukolj D (2002) Design of adaptive Takagi–Sugeno–Kang fuzzy models. Appl Soft Comput 2(2):89–103

    Article  Google Scholar 

  21. Tsekouras G, Sarimveis H, Kavakli E (2005) A hierarchical fuzzy-clustering approach to fuzzy modeling. Fuzzy Sets Syst 150(2):245–266

    Article  MathSciNet  MATH  Google Scholar 

  22. Zou W, Li C, Zhang N (2017) A T-S fuzzy model identification approach based on a modified inter type-2 FRCM algorithm. IEEE Trans Fuzzy Syst 26(3):1104–1113

    Article  Google Scholar 

  23. Cordon O, Herrera F (1999) A two-stage evolutionary process for designing TSK fuzzy rule-based systems. IEEE Trans Syst Man Cybern Part B (Cybernetics) 29(6):703–715

    Article  Google Scholar 

  24. Green P, Cross E, Worden K (2015) Bayesian system identification of dynamical systems using highly informative training data. Mech Syst Signal Process 56:109–122

    Article  Google Scholar 

  25. Green PL (2015) Bayesian system identification of a nonlinear dynamical system using a novel variant of simulated annealing. Mech Syst Signal Process 52:133–146

    Article  Google Scholar 

  26. Au SK, Zhang FL (2016) Fundamental two-stage formulation for Bayesian system identification. Part I General Theory Mech Syst Signal Process 66:31–42

    Article  Google Scholar 

  27. Yv Beck JL, Li H (2017) Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment. Comput Methods Appl Mech Eng 318:382–411

    Article  MathSciNet  Google Scholar 

  28. Lozano AC, Swirszcz G, Abe N (2009) Grouped orthogonal matching pursuit for variable selection and prediction, Adv Neural Inf Process Syst 1150–1158

  29. Bai T, Li Y, Tang Y (2011) Structured sparse representation appearance model for robust visual tracking. In: 2011 IEEE international conference on robotics and automation (ICRA). IEEE, pp 4399–4404

  30. Zhang T (2009) On the consistency of feature selection using greedy least squares regression. J Mach Learn Res 10:555–568

    MathSciNet  MATH  Google Scholar 

  31. Luo MN, Sun FC, Liu HP (2014) A novel T–S fuzzy systems identification with block structured sparse representation. J Franklin Inst 351(7):3508–3523

    Article  MathSciNet  MATH  Google Scholar 

  32. Frey B, Dueck D (2007) Clustering by passing messages between data points. Science 315(5814):972–976

    Article  MathSciNet  MATH  Google Scholar 

  33. Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1:211–244

    MathSciNet  MATH  Google Scholar 

  34. Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197(4300):287–289

    Article  MATH  Google Scholar 

  35. Box GEP, Jenkins GM (1970) Time series analysis, forecasting and control, 2nd edn. Holden Day, San Francisco

    MATH  Google Scholar 

  36. Lin Y, Cunningham GA (1995) A new approach to fuzzy-neural system modeling. IEEE Trans Fuzzy Syst 3(2):190–198

    Article  Google Scholar 

  37. Chiu S (1996) Selecting input variables for fuzzy models. J Intell Fuzzy Syst 4(4):243–256

    Article  Google Scholar 

  38. Oh SK, Pedrycz W (2000) Identification of fuzzy systems by means of an auto-tuning algorithm and its application to nonlinear systems. Fuzzy Sets Syst 115(2):205–230

    Article  MathSciNet  MATH  Google Scholar 

  39. Li CS, Zhou JZ, Fu B et al (2012) T–S fuzzy model identification with a gravitational search-based hyperplane clustering algorithm. IEEE Trans Fuzzy Syst 20(2):305–317

    Article  Google Scholar 

  40. Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection//Ijcai. 14(2):1137–1145

  41. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74(366a):427–431

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation (NNSF) of China under Grant (61703149); Natural Science Foundation of Hebei Province of China (F2019111009); Foundation of Hebei Educational Committee (BJ2017106); Cooperative Education Project of the Chinese Education Commission (201802151038); Open projects in Hebei (HBSJQ0705).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Hengshui University, Hengshui City, 053000, China

    Limin Zhang

  2. College of Intelligence and Computing, Tianjin University, Tianjin City, 300072, China

    Limin Zhang

  3. Institute of Electrical Engineering, Yanshan University, Qinhuangdao City, 066004, China

    Junpeng Li

  4. School of Electrical and Information Engineering, Tianjin University, Tianjin City, 300072, China

    Hongjiu Yang

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  1. Limin Zhang
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  2. Junpeng Li
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  3. Hongjiu Yang
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Correspondence to Limin Zhang.

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Zhang, L., Li, J. & Yang, H. T–S Fuzzy Model Identification with Sparse Bayesian Techniques. Neural Process Lett 50, 2945–2962 (2019). https://doi.org/10.1007/s11063-019-10071-3

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