Fuzzy jump wavelet neural network based on rule induction for dynamic nonlinear system identification with real data applications

English version

Autoři: Mohsen Kharazihai Isfahani ^aff001; Maryam Zekri ^aff001; Hamid Reza Marateb ^aff002; Miguel Angel Mañanas ^aff003
Působiště autorů: Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran ^aff001; Biomedical Engineering Department, Engineering Faculty, University of Isfahan, Isfahan, Iran ^aff002; Biomedical Engineering Research Centre (CREB), Automatic Control Department (ESAII) Universitat Politècnica de Catalunya-Barcelona Tech (UPC), Barcelona, Spain ^aff003; Biomedical Research Networking Center in Bioengineering, Biomaterials, and Nanomedicine (CIBER-BBN), Spain ^aff004
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0224075

Souhrn

Aim

Fuzzy wavelet neural network (FWNN) has proven to be a promising strategy in the identification of nonlinear systems. The network considers both global and local properties, deals with imprecision present in sensory data, leading to desired precisions. In this paper, we proposed a new FWNN model nominated “Fuzzy Jump Wavelet Neural Network” (FJWNN) for identifying dynamic nonlinear-linear systems, especially in practical applications.

Methods

The proposed FJWNN is a fuzzy neural network model of the Takagi-Sugeno-Kang type whose consequent part of fuzzy rules is a linear combination of input regressors and dominant wavelet neurons as a sub-jump wavelet neural network. Each fuzzy rule can locally model both linear and nonlinear properties of a system. The linear relationship between the inputs and the output is learned by neurons with linear activation functions, whereas the nonlinear relationship is locally modeled by wavelet neurons. Orthogonal least square (OLS) method and genetic algorithm (GA) are respectively used to purify the wavelets for each sub-JWNN. In this paper, fuzzy rule induction improves the structure of the proposed model leading to less fuzzy rules, inputs of each fuzzy rule and model parameters. The real-world gas furnace and the real electromyographic (EMG) signal modeling problem are employed in our study. In the same vein, piecewise single variable function approximation, nonlinear dynamic system modeling, and Mackey–Glass time series prediction, ratify this method superiority. The proposed FJWNN model is compared with the state-of-the-art models based on some performance indices such as RMSE, RRSE, Rel ERR%, and VAF%.

Results

The proposed FJWNN model yielded the following results: RRSE (mean±std) of 10e-5±6e-5 for piecewise single-variable function approximation, RMSE (mean±std) of 2.6–4±2.6e-4 for the first nonlinear dynamic system modelling, RRSE (mean±std) of 1.59e-3±0.42e-3 for Mackey–Glass time series prediction, RMSE of 0.3421 for gas furnace modelling and VAF% (mean±std) of 98.24±0.71 for the EMG modelling of all trial signals, indicating a significant enhancement over previous methods.

Conclusions

The FJWNN demonstrated promising accuracy and generalization while moderating network complexity. This improvement is due to applying main useful wavelets in combination with linear regressors and using fuzzy rule induction. Compared to the state-of-the-art models, the proposed FJWNN yielded better performance and, therefore, can be considered a novel tool for nonlinear system identification.

Klíčová slova:

Approximation methods – Cell signaling structures – Electromyography – Neural networks – Neurons – Nonlinear dynamics – Nonlinear systems – Torque

Zdroje

1. Feng S, Chen CLP. Nonlinear system identification using a simplified Fuzzy Broad Learning System: Stability analysis and a comparative study. Neurocomputing. 2019;337:274–86. doi: 10.1016/j.neucom.2019.01.073

2. Labati RD, Genovese A, Muñoz E, Piuri V, Scotti F. Applications of computational intelligence in industrial and environmental scenarios. In: Sgurev V, Piuri V, Jotsov V, editors. Learning Systems: From Theory to Practice. 756: Springer; 2018. p. 29–46.

3. Jiang X, Adeli H. Dynamic Wavelet Neural Network for Nonlinear Identification of Highrise Buildings. Computer-Aided Civil and Infrastructure Engineering. 2005;20(5):316–30. doi: 10.1111/j.1467-8667.2005.00399.x

4. Abiyev RH, Kaynak O. Fuzzy Wavelet Neural Networks for Identification and Control of Dynamic Plants—A Novel Structure and a Comparative Study. IEEE Transactions on Industrial Electronics. 2008;55(8):3133–40. doi: 10.1109/TIE.2008.924018

5. Singh M, Srivastava S, Hanmandlu M, Gupta JRP. Type-2 fuzzy wavelet networks (T2FWN) for system identification using fuzzy differential and Lyapunov stability algorithm. Applied Soft Computing. 2009;9(3):977–89. doi: 10.1016/j.asoc.2008.03.017

6. Tzeng S-T. Design of fuzzy wavelet neural networks using the GA approach for function approximation and system identification. Fuzzy Sets and Systems. 2010;161(19):2585–96. doi: 10.1016/j.fss.2010.06.002

7. Bodyanskiy Y, Vynokurova O. Hybrid adaptive wavelet-neuro-fuzzy system for chaotic time series identification. Information Sciences. 2013;220:170–9. doi: 10.1016/j.ins.2012.07.044

8. Zekri M, Sadri S, Sheikholeslam F. Adaptive fuzzy wavelet network control design for nonlinear systems. Fuzzy Sets and Systems. 2008;159(20):2668–95. doi: 10.1016/j.fss.2008.02.008

9. Huang M, Zhang T, Ruan J, Chen X. A New Efficient Hybrid Intelligent Model for Biodegradation Process of DMP with Fuzzy Wavelet Neural Networks. Scientific Reports. 2017;7:41239. doi: 10.1038/srep41239 28120889

10. Ganjefar S, Tofighi M. Single-hidden-layer fuzzy recurrent wavelet neural network: Applications to function approximation and system identification. Information Sciences. 2015;294:269–85. doi: 10.1016/j.ins.2014.09.054

11. Cheng R, Bai Y. A novel approach to fuzzy wavelet neural network modeling and optimization. International Journal of Electrical Power & Energy Systems. 2015;64:671–8. doi: 10.1016/j.ijepes.2014.07.067

12. Ho DWC, Ping-Au Z, Jinhua X. Fuzzy wavelet networks for function learning. IEEE Transactions on Fuzzy Systems. 2001;9(1):200–11. doi: 10.1109/91.917126

13. Ong P, Zainuddin Z. Calibrating wavelet neural networks by distance orientation similarity fuzzy C-means for approximation problems. Applied Soft Computing. 2016;42:156–66. doi: 10.1016/j.asoc.2016.01.042

14. Huang M, Tian D, Liu H, Zhang C, Yi X, Cai J, et al. A Hybrid Fuzzy Wavelet Neural Network Model with Self-Adapted Fuzzy -Means Clustering and Genetic Algorithm for Water Quality Prediction in Rivers. Complexity. 2018;2018:11. doi: 10.1155/2018/8241342

15. Zarkogianni K, Mitsis K, Litsa E, Arredondo M-T, Ficο G, Fioravanti A, et al. Comparative assessment of glucose prediction models for patients with type 1 diabetes mellitus applying sensors for glucose and physical activity monitoring. Medical & Biological Engineering & Computing. 2015;53(12):1333–43. doi: 10.1007/s11517-015-1320-9 26049412

16. Kumar R, Srivastava S, Gupta JRP, Mohindru A. Self-recurrent wavelet neural network–based identification and adaptive predictive control of nonlinear dynamical systems. International Journal of Adaptive Control and Signal Processing. 2018;32(9):1326–58. doi: 10.1002/acs.2916

17. Huang W, Oh S, Pedrycz W. Fuzzy Wavelet Polynomial Neural Networks: Analysis and Design. IEEE Transactions on Fuzzy Systems. 2017;25(5):1329–41. doi: 10.1109/TFUZZ.2016.2612267

18. Huang M, Ma Y, Wan J, Chen X. A sensor-software based on a genetic algorithm-based neural fuzzy system for modeling and simulating a wastewater treatment process. Applied Soft Computing. 2015;27:1–10. doi: 10.1016/j.asoc.2014.10.034

19. Huang M, Han W, Wan J, Ma Y, Chen X. Multi-objective optimisation for design and operation of anaerobic digestion using GA-ANN and NSGA-II. Journal of Chemical Technology & Biotechnology. 2016;91(1):226–33. doi: 10.1002/jctb.4568

20. Abraham A, Grosan C, Ramos V. Swarm Intelligence in Data Mining (Studies in Computational Intelligence): Springer-Verlag; 2006.

21. Chia-Feng J, Chin-Teng L. A recurrent self-organizing neural fuzzy inference network. IEEE Transactions on Neural Networks. 1999;10(4):828–45. doi: 10.1109/72.774232 18252581

22. Chia-Feng J. A TSK-type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms. IEEE Transactions on Fuzzy Systems. 2002;10(2):155–70. doi: 10.1109/91.995118

23. Elman JL. Finding structure in time. Cognitive Science. 1990;14(2):179–211. doi: 10.1016/0364-0213(90)90002-E

24. Madyastha RK, Aazhang B. An algorithm for training multilayer perceptrons for data classification and function interpolation. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1994;41(12):866–75. doi: 10.1109/81.340848

25. Narendra KS, Parthasarathy K. Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks. 1990;1(1):4–27. doi: 10.1109/72.80202 18282820

26. Patra JC, Kot AC. Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics). 2002;32(4):505–11. doi: 10.1109/TSMCB.2002.1018769 18238146

27. Zhao H, Zhang J. Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network. Neurocomputing. 2009;72(13):3046–54. doi: 10.1016/j.neucom.2009.04.001

28. Castro JR, Castillo O, Melin P, Rodríguez-Díaz A. A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks. Information Sciences. 2009;179(13):2175–93. doi: 10.1016/j.ins.2008.10.016

29. Tamura H, Koichi T, Hisasi T, Vairappan C, Zheng T, editors. Recurrent type ANFIS using local search technique for time series prediction. APCCAS 2008–2008 IEEE Asia Pacific Conference on Circuits and Systems; 2008 30 Nov.-3 Dec. 2008.

30. Jang JR. ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics. 1993;23(3):665–85. doi: 10.1109/21.256541

31. Oysal Y, Yilmaz S. An adaptive wavelet network for function learning. Neural Computing and Applications. 2010;19(3):383–92. doi: 10.1007/s00521-009-0297-4

32. Oysal Y, Yilmaz S. An adaptive fuzzy wavelet network with gradient learning for nonlinear function approximation. Journal of Intelligent Systems. 2014;23(2):201–12. doi: 10.1515/jisys-2013-0068

33. Gholipour A, Araabi BN, Lucas C. Predicting chaotic time series using neural and neuro-fuzzy models: a comparative study. Neural Processing Letters. 2006;24(3):217–39. doi: 10.1007/s11063-006-9021-x

34. Mackey M, Glass L. Oscillation and chaos in physiological control systems. Science. 1977;197(4300):287–9. doi: 10.1126/science.267326 267326

35. Box GEP, Jenkins G. Time Series Analysis, Forecasting and Control: Holden-Day, Inc.; 1990. 500 p.

36. Botter A, Marateb HR, Afsharipour B, Merletti R, editors. Solving EMG-force relationship using Particle Swarm Optimization. 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society; 2011 30 Aug.-3 Sept. 2011.

37. Afsharipour B. Estimation of load sharing among muscles acting on the same joint and Applications of surface electromyography: Politecnico di Torino; 2014.

38. Jafari Z, Edrisi M, Marateb HR. An Electromyographic-driven Musculoskeletal Torque Model using Neuro-Fuzzy System Identification: A Case Study. Journal of medical signals and sensors. 2014;4(4):237–46. 25426427.

39. Kuriki HU, De Azevedo FM, Takahashi LSO, Mello EM, de Faria Negrão Filho R, Alves N. The relationship between electromyography and muscle force. EMG Methods for evaluating muscle and nerve function: InTech; 2012.

40. Kutz M. Biomedical engineering and design handbook. 2nd ed. ed. New York: McGraw-Hill; 2009.

41. Afsharipour BJIPdT. Estimation of load sharing among muscles acting on the same joint and Applications of surface electromyography. 2014.

42. Sadri AR, Zekri M, Sadri S, Gheissari N, Mokhtari M, Kolahdouzan F. Segmentation of Dermoscopy Images Using Wavelet Networks. IEEE Transactions on Biomedical Engineering. 2013;60(4):1134–41. doi: 10.1109/TBME.2012.2227478 23193305

43. Atashpaz-Gargari E, Lucas C, editors. Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition. 2007 IEEE Congress on Evolutionary Computation; 2007 25–28 Sept. 2007.

44. Abiyev RH, Kaynak O, Kayacan E. A type-2 fuzzy wavelet neural network for system identification and control. Journal of the Franklin Institute. 2013;350(7):1658–85. doi: 10.1016/j.jfranklin.2013.04.020

45. Karatepe E, Alcı M. A new approach to fuzzy wavelet system modeling. International Journal of Approximate Reasoning. 2005;40(3):302–22. doi: 10.1016/j.ijar.2005.06.003

46. Srivastava S, Singh M, Hanmandlu M, Jha AN. New fuzzy wavelet neural networks for system identification and control %J Appl. Soft Comput. 2005;6(1):1–17. doi: 10.1016/j.asoc.2004.10.001

47. Davanipoor M, Zekri M, Sheikholeslam F. Fuzzy Wavelet Neural Network With an Accelerated Hybrid Learning Algorithm. IEEE Transactions on Fuzzy Systems. 2012;20(3):463–70. doi: 10.1109/TFUZZ.2011.2175932

48. Zhao H, Gao S, He Z, Zeng X, Jin W, Li T. Identification of Nonlinear Dynamic System Using a Novel Recurrent Wavelet Neural Network Based on the Pipelined Architecture. IEEE Transactions on Industrial Electronics. 2014;61(8):4171–82. doi: 10.1109/TIE.2013.2288196

49. Han H-G, Ge L-M, Qiao J-F. An adaptive second order fuzzy neural network for nonlinear system modeling. Neurocomputing. 2016;214:837–47. doi: 10.1016/j.neucom.2016.07.003

50. Li C, Zhou J, Fu B, Kou P, Xiao J. T–S Fuzzy Model Identification With a Gravitational Search-Based Hyperplane Clustering Algorithm. IEEE Transactions on Fuzzy Systems. 2012;20(2):305–17. doi: 10.1109/TFUZZ.2011.2173693

51. Zhang R, Tao J. A Nonlinear Fuzzy Neural Network Modeling Approach Using an Improved Genetic Algorithm. IEEE Transactions on Industrial Electronics. 2018;65(7):5882–92. doi: 10.1109/TIE.2017.2777415

52. Clancy EA, Liu L, Liu P, Moyer DVZ. Identification of Constant-Posture EMG–Torque Relationship About the Elbow Using Nonlinear Dynamic Models. IEEE Transactions on Biomedical Engineering. 2012;59(1):205–12. doi: 10.1109/TBME.2011.2170423 21968709

Fuzzy jump wavelet neural network based on rule induction for dynamic nonlinear system identification with real data applications

Souhrn

Aim

Methods

Results

Conclusions

Klíčová slova:

Zdroje

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