In this paper an evolving Neuro–Fuzzy Network Modeling based on recursive parameter estimation with fuzzy instrumental variable method, is proposed. The proposed methodology presents an online evolving clustering algorithm composed of participatory learning based on the maximum likelihood norm. To avoid the curse of dimensionality in relation to the number of evolving rules, the algorithm uses an online adaptive norm strategy in the creation of fuzzy rules. The performance of the proposed methodology is concerned to benchmark problems: experiments considering the convergence analysis, by proposal of three Lemmas and one Theorem, of the fuzzy instrumental variable applied to the parametric estimation of nonlinear systems in a noise environment; nonlinear systems identification are performed and compared to evaluate the performance of the approach proposed with other models of evolving systems widely cited in the literature and statistical analysis of experimental results from black box modeling of a helicopter with two degrees of freedom are used for the purpose of show the performance and efficiency the proposed approach.
Abdul RahmanR.Z. and ShoumyN.J., Neural Network Controller for Two-Degree-Freedom Helicopter Control System, 2012 12th International Conference on Control, Automation and Systems (ICCAS), 2012, pp. 101–106.
2.
AcamporaG., PedryczW. and VasilakosA.V., Efficient modeling of MIMO systems through timed automata based neuro-fuzzy inference engine, International Journal of Approximate Reasoning55(6) (2014), 1336–1356. Neuro-fuzzy systems; Timed Automata based Fuzzy Systems.
3.
AngelovP. and ZhouX., Evolving fuzzy systems from data streams in real-time, IEEE (2006), 29–35.
4.
AngelovP., Autonomous Learning Systems, From Data Streams to Knowledge in Real-time, IEEE Press Series on Computational Intelligence, Willey, ISBN 9781119951520, 2013.
5.
AngelovP., FilevD. and KasabovN., Evolving Intelligent Systems: Methology and applications, IEEE Press Series on Computational Intelligence, Willey-Blackwell, ISBN 9780470287194, 2010.
6.
AryaV. and RathyR.K., An Efficient Neuro-Fuzzy Approach for Classification of Iris Dataset, International Conference on Reliability, Optimization and Information Technology, 2014, pp. 161–165. doi: 10.1109/ICROIT.2014.6798304
7.
BabuskaR., SchutterB., LendekZs. and GuerraT.M., Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models, Springer Publishing Company, Incorporated, vol. 262, 2010. doi: 10.1007/978-3-642-16776-8
8.
BaruahR.D., AngelovP. and BaruahD., Dynamically evolving clustering for data streams, Evolving and Adaptive Intelligent Systems (EAIS), 2014 IEEE Conference on, 2014, pp. 1–6. doi: 10.1109/TFUZZ.2013.2264938
9.
BaruahR.D. and AngelovP., Evolving local means method for clustering of streaming data, in Fuzzy Systems (FUZZIEEE), 2012 IEEE International Conference on, 2012,pp. 1–8. doi: 10.1109/FUZZ-IEEE.2012.6251366
10.
BenzaouiaA. and HajjajiA.E., Advanced Takagi Sugeno Fuzzy Systems, Delay and Saturation, Springer, ISBN 9783319056388, 2014.
11.
BodyanskiyY., TyshchenkoO. and KoplianiD., An Evolving Neuro-Fuzzy System for Online Fuzzy Clustering, Computer Science and Information Technologies, 2015, pp. 158–161. doi: 10.1109/STC-CSIT.2015.7325456
12.
BodyanskiyY., VynokurovaO., SetlakG. and PlissI., Hybrid Neuro-Neo-Fuzzy System and Its Adaptive Learning Algorithm, Computer Science and Information Technologies, 2015, pp. 111–114. doi: 10.1109/STC-CSIT.2015.7325445
13.
BordignonF. and GomideF., Uninorm based evolving neural networks and approximation capabilities, ELSEVIER: Neurocomputing127 (2014), 13–20.
14.
CostaB.S., AngelovP.P. and GuedesL.A., Fully unsupervised fault detection and identification based on recursive density estimation and self-evolving cloud-based classifier, Neurocomputing150(A) (2015), 289–303. doi: 10.1016/j.neucom.2014.05.086
15.
DaneshawarM.A. and NohN.M., Adaptive Neuro-Fuzzy Inference System Identification Model for Smart Control Valves with Static Friction, IEEE Conference on Control System, Computing and Engineering, 2013, pp. 122–126. doi: 10.1109/ICCSCE.2013.6719944
16.
DovzanD., LogarV. and SkrjancI., Implementation of an evolving fuzzy model (eFuMo) in a monitoring system for a waste-water treatment process, Fuzzy Systems, IEEE Transactions on23(5) (2015), 1761–1776. doi: 10.1109/TFUZZ.2014.2379252
17.
FilevD., GeorgievaO., An extended version of the Gustafson–Kessel algorithm for evolving data stream clustering. In: AngelovP., FilevD., KasabovA., (eds), Evolving Intelligent Systems: Methodology and Applications, Willey, IEEE Press Series on Computational Intellegence, 2010, pp. 273–300.
18.
HanL., YiD., LifanZ. and DingL., Neuro-Fuzzy Control Based on Online Least Square Support Vector Machines, Proceedings of the 34th Chinese Control Conference, 2015, pp. 3411–3416.
19.
KasabovN., Evolving fuzzy neural networks-algorithms, applications and biological motivation. Methodologies for the conception, design and application of soft computing, World Scientific, v. 1, 1998, pp. 271–274.
20.
LeiteD., GomideF., BalliniR. and CostaP., Fuzzy Granular Evolving Modeling for Time Series Prediction, IEEE International Conference on Fuzzy Systems, 2011, pp. 2794–2801. doi: 10.1109/FUZZY.2011.6007452
21.
LemosA., CaminhasW. and GomideF., Evolving fuzzy linear regression trees, Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, Barcelona, 2010, pp. 1–8. doi: 10.1109/FUZZY.2010.5583970
22.
LemosA., CaminhasW. and GomideF., Multivariable gaussian evolving fuzzy modeling system, in Fuzzy Systems, IEEE Transactions on19(1) (2011), 91–104. doi: 10.1109/TFUZZ.2010.2087381
23.
LimaE., HellM., BalliniR. and GomideF., Evolving fuzzy modeling using participatory learning, Evolving intelligent systems, methodology and applications, Wiley-Interscience-IEEE Press, 2010, pp. 67–86. ISBN 0470287195.
24.
LiuY., ZhangW. and ZhangY., Data Driven Modeling of HumanWelder Intelligence, A Neuro-Fuzzy Approach, IEEE International Conference on Automation Science and Engineering, 2013, pp. 663–668. doi: 10.1109/CoASE.2013.6653890
25.
LiuX., WangJ. and ZhengW.X., Convergence analysis of refined instrumental variable method for continuous-time system identification, IET Control Theory and Applications5(7) (2011), 868–877.
26.
LughoferE.D., Flexfis: A robust incremental learning approach for evolving takagi-sugeno fuzzy models, IEEE Transactions on Fuzzy Systems16(6) (2008), 1393–1410.
27.
LughoferE., Evolving Fuzzy Systems, Methodologies, Advanced Concepts and Applications, Springer, 2011, ISBN 9783642180866.
28.
LughoferE. and Sayed-MouchawehM., Autonomous data stream clustering implementing incremental split-and-merge techniques–towards a plug-and-play approach, Information Sciences204(C) (2015), 54–79. doi: 10.1016/j.ins.2015.01.010
MacielL., GomideF. and BalliniR., MIMO evolving participatory learning fuzzy modeling, Fuzzy Systems (FUZZIEEE), 2012 IEEE International Conference on, 2012, pp. 1–8. doi: 10.1109/FUZZ-IEEE.2012.6251170
31.
PapoulisA. and PilaiS.U., Probability, Random, Variables, and Stochastic Processes, McGraw–Hill series in electrical engineering, Communications and signal processing, McGraw-Hill, 2002, ISBN 9780070486584.
32.
PratamaM., AnavattiS.G. and LughoferE., Evolving fuzzy rule-based classifier based on GENEFIS, Fuzzy Systems (FUZZ), 2013 IEEE International Conference on, 2013, pp. 1–8. doi: 10.1109/FUZZ-IEEE.2013.6622526
33.
PratamaM., AnavattiS.G. and LughoferE., GENEFIS, toward an effective localist network, in, IEEE Transactions on Fuzzy Systems22(3) (2014), 547–562.
34.
PetelinD. and KocijanJ., Evolving Gaussian process models for predicting chaotic time-series, Evolving and Adaptive Intelligent Systems (EAIS), 2014 IEEE Conference on, 2014, pp. 1–8. doi: 10.1109/EAIS.2014.6867476
35.
RajabS. and SharmaV., Performance Evaluation of ANN and Neuro-Fuzzy System in Business Forecasting, Computing for Sustainable Global Development (INDIACom), 2015 2nd International Conference on, 2015, pp. 749–754.
36.
RongH., SundararajanN., HuangG. and SaratchandranP., Sequential adaptive fuzzy inference system (safis) for nonlinear system identification and prediction, Fuzzy Sets and Systems157(9) (2006), pp. 1260–1275.
Sayed-MouchawehM. and LughoferE., Learning in Non-stationary Environments, Methods and Applications, Springer, 2012, ISBN 9781441980199.
39.
SalihbegovicA., SokicE., OsmicN. and HebibovicM., High Performance Disturbance Observer based Control of the Nonlinear 2DOF Helicopter System, Information, Communication and Automation Technologies (ICAT), XXIV International Symposium on, 2013, pp. 1–7. doi: 10.1109/ICAT.2013.6684038
40.
SerraG. and BotturaC., An IV-QR algorithm for neuro-fuzzy multivariable online identification, Fuzzy Systems, IEEE Transactions on15(2) (2007), 200–210. doi: 10.1109/TFUZZ.2006.879997
41.
SerraG. and BotturaC., Fuzzy Instrumental Variable approach for nonlinear discrete–time systems identification in a noisy environment, Science Direct, Fuzzy Sets and Systems, ELSEVIER160(4) (2009), 500–520. doi: 10.1016/j.fss.2008.06.020
42.
SerraG., Frontiers in Advanced Control Systems, InTech, ISBN 9789535106777, 2012, doi: 10.5772/1267
43.
SilvaA., CaminhasW., LemosA. and GomideF., Real-time nonlinear modeling of a twin rotor MIMO system using evolving neuro-fuzzy network, Computational Intelligence in Control and Automation (CICA), 2014 IEEE Symposium on, 2014, pp. 1–8. doi: 10.1109/CICA.2014.7013229
44.
Soleimani-BH., LucasC. and ArrabiN., Recursive Gath-Geva Clustering as Basis for Envolving Neuro-Fuzzy Modeling, Fuzzy Systems 2010 IEEE Conference1, 2010, pp. 1–7. doi: 10.1109/ICSSSM.2014.6874031
45.
SkrjancI., DovzanD. and GomideF., Evolving fuzzymadel-based on c-regression clustering, Evolving and Adaptive Intelligent Systems (EAIS), 2014 IEEE Conference on, 2014, pp. 1–7. doi: 10.1109/EAIS.2014.6867481
46.
SkrjancI., Evolving fuzzy-model-based design of experiments with supervised hierarchical clustering, Fuzzy Systems, IEEE Transactions on23(4) (2015), 861–871. doi: 10.1109/TFUZZ.2014.2329711
47.
SmithS.W., The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, 2002, 0-9660176-3-3.
48.
SunZ., MaoK.Z., TangW., MakL.O., XianK. and LiuY., Knowledge-based evolving clustering algorithm for data stream, Service Systems and Service Management (ICSSSM), 2014 11th International Conference on, 2014, pp. 1–6.
49.
VelagicJ. and OsmicN., Identification and Control of2DOF Nonlinear Helicopter Model Using Intelligent Methods, Control and Fault-Tolerant Systems (SysTol), Systems Man and Cybernetics (SMC), 2010 IEEE International Conference on, 2010, pp. 2267–2275.
50.
VelasquezJ.D., Adaptive multidimenisonal neuro-fuzzy inference system for time series prediction, IEEE Latin America Transactions13(8) (2015), 2694–2699. doi: 10.1109/TLA.2015.7332151
51.
VishnupriyanJ., ManoharanP.S. and RamalakshmiA.P.S., Uncertainty Modeling of Nonlinear 2-DOF Helicopter Model, 2014 International Conference on Computer Communication and Informatics (ICCCI -2014), 2014, pp. 1–6. doi: 10.1109/ICCCI.2014.6921840
52.
WangL. and GarnierH., System Identification, Environmental Modelling, and Control System Design, Springer Publishing Company, Incorporated, ISBN 1447158458, 2013.
53.
YilmazS. and OysalY., Nonlinear System Modeling with Dynamic Adaptive Neuro-Fuzzy Inference System, Innovations in Intelligent Systems and Applications (INISTA) Proceedings, 2014 IEEE International Symposium on, 2014, pp. 205–211. doi: 10.1109/INISTA.2014.6873619
54.
YoungP., Refined instrumental variable estimation: Maximum likelihood optimization of a unified box–jenkings model, Automatica52 (2015), 35–46. ELSEVIER, doi: 10.1016/j.automatica.2014.10.126
55.
ZaeriA.H., Mohd-NoorS.B., IsaM.M., TaipF.S. and MarnaniA.E., Disturbance Rejection for a 2-DOF Nonlinear Helicopter Model by Using MIMO Fuzzy Sliding Mode Control with Boundary Layer, 2012 Third International Conference on Intelligent Systems Modelling and Simulation, 2012, pp. 411–416. doi: 10.1109/ISMS.2012.129
56.
ZhuY., A Box–Jenkins method that is asymptotically globally convergent for open loop data. In Proceedins of the IFAC World Congress, Milano, Italy, 2010, pp. 9047–9051.
