1.1 Linear dynamic system with disturbance . . . 9
1.2 General principle od system modeling . . . 9
1.3 Correlation based weight function identification . . . 10
1.4 Example of membership functions: Gaussian . . . 15
1.5 Example of membership functions . . . 15
1.6 Multilayer neural network . . . 16
1.7 The basic principle of the radial basis network . . . 18
1.8 General regression neural network . . . 19
1.9 Neuro-fuzzy network . . . 23
2.1 GRNN probability density function . . . 26
2.2 Signal pass through the GRNN . . . 27
2.3 Dependence of generalization ability on the smoothness parameter . . 29
2.4 Fuzzy GRNN block diagram . . . 32
2.5 Fuzzification of the neuron functions . . . 33
2.6 Fuzzification of the neuron functions . . . 34
2.7 Fuzzification of the neuron functions . . . 35
2.8 Fuzzy general regression neural network for MIMO system . . . 35
3.1 1D thread blocks of GRNN distributed in a 1D grid . . . 38
3.2 Array of streaming multiprocessors . . . 40
3.3 2D thread blocks distributed in 3D grid . . . 41
3.4 1D thread blocks of GRNN distributed in a 1D grid . . . 43
4.1 Measurement on the miniaturized model of aircraft EV 55. . . 45
4.2 Dependence of network error on the training dataset size . . . 47
4.3 Comparison of measured data and network output; left: FGRNN, right: MLP . . . 48
4.4 Comparison of measured data and network output computed using MLP . . . 49
4.5 Comparison of measured data and network output computed using FGRNN . . . 49
4.6 Comparison of measured data with a significant ¨outlier and network output computed using FGRNN . . . 50
BIBLIOGRAPHY
[1] LJUNG, L. System identification: Theory for the user. Prentice Hall, London, 1999.
[2] NELLES, O. Nonlinear system identification: From classical approaches to neu-ral network and fuzzy models. Springer, Berlin, 2001.
[3] SÖDERSTRÖM, T; STOICA, P. System identification. Prentice Hall, Uppsala, 2001.
[4] BODYANSKIY, Y.; TESLENKO, N. General regression neuro-fuzzy network for identifiaction of nonstationary plants.In International Journal "Information Technologies and Knowledge" Vol.2 / 2008. p. 136-142.
[5] SPECHT, D. A General Regression Neural NetworkIEEE Transactions on Neu-ral Networks, vol. 2, p. 568-576, 1991.
[6] HAYKIN, S. Neural networks: A comprehensive foundation. Pearson Educa-tion, Ontario, 1999.
[7] GUPTA, M.; JIN, L.; HOMMA, N. Static and dynamic neural networks: from fundamentals to advanced theory. Wiley, New Jersey, 2003.
[8] NVIDIA Corp. NVIDIA CUDA C Programming guide.NVIDIA Corporation, 2006.
[9] WEEKS, J. R. The Shape of Space: how to visualize surfaces and three-dimensional manifolds. 2nd edition Marcel Dekker, Inc., New York, 2002.
[10] MathWorks, Inc.Parallel Computing Toolbox User’s Guide, Natick, 2011.
[11] JOERGENSEN, B. GOEGEBEUR, Y. Prediction and validation, http://statmaster.sdu.dk/courses/ST02, [online]. [cit. 10. 8. 2012]
[12] CANETE, J. F.; GONZALEZ-PEREZ, S.; SAZ-OROSCO, P. Software tools for system identification and control using neural networks in process engineering. World Academy of Science, Engineering and Technology 47, 2008. p 59-63.
[13] KIM, I.; FOK, S.; FREGENE, K.; LEE, D.; OH, T.; WANG, D. W. L. Neural network-based system identification and controller synthesis for an industrial sewing machine. International Journal of Control, Automation, and Systems Vol. 2, No. 1, March 2004. p. 83-91.
[14] FEKIH, A. Neural networks based system identification techniques for model based faultdetection of nonlinear systems. International Journal of Innovative Computing, Information and Control Volume 3, Number 5, October 2007. p.
1073-1085.
[15] BABUŠKA, R.; VERBRUGGEN, H. Neuro-fuzzy methods for nonlinear system identification. Annual Reviews in Control 27, 2003. p. 73–85.
[16] SENG, T. L.; KHALID, M.; YUSOF, R.; OMATU, S. Adaptive neuro-fuzzy control system by RBF and GRNN neural networks. Journal of Intelligent and Robotic Systems Vol. 23, Kluwer Academic, 1998. p. 267-289.
[17] NOSSAIR, Z. B.; MADKOUR, A. A.; AWADALLA, M. A.; ABDULHADY, M.
M. System identification using intelligent algorithms. 13th International Con-ference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT-13, May 26 – 28, 2009.
[18] NOCEDAL, J.; WRIGHT, S. J. Numerical optimization. Springer, New York, 1999.
[19] ANTONIOU, A.; LU, W. Practical optimization: Algorithms and engineering applications. Springer, New York, 2007.
[20] HAATAJA, K. Sumean logiikan ja neuroverkkojen työkaluselvitys. VTT Elek-troniikka, Espoo 1998.
[21] BABUŠKA, R., VERBRUGGEN, H. Neuro-fuzzy methods for nonlinear system identificationAnnual Reviews in Control 27, 2003.
[22] JOELIANTO, E., RAHMAT, B. Adaptive Neuro Fuzzy Inference Sys-tem (ANFIS) with Error Backpropagation Algorithm using Mapping Func-tionInternational journal of artificial intelligence A08, 2008.
[23] SENG, T., MARZUKI, K., RUBIAH, Y., OMATU, S. Adaptive neuro-fuzzy control system by RBF and GRNN neural networksJournal of Intelligent and robotic systems, vol. 23, pp 267-289, 1998.
[24] JIMENEZ, J., GIRON-SIERRA, J., INSAURRALDE, C., SEMINARIO, M.
A simulation of aircraft fuel management systemSimulation modelling practice and theory 15, 2007.
[25] BAUER, M. General Regression Neural Network, GRNN- A Neural Network for Technical UseDiploma thesis, University of Wisconsin-Madison
[26] ŠTEFAN, M. Identifkace nelineárních systémů pomocí neurofuzzy mod-elůBulletin of Applied Mechanics 2, p.121-131 (2005).
[27] HAYASHI, K., KAWADA, K., YAMAMOTO, T. Evolutionary modeling of a process systemICROS-SICE International Joint Conference 2009, Fukuoka, Japan, 2009.
[28] BOYEON, K., PARK, K. A study on the modeling of nonlinear system using ge-netic programming18th annual conference of the IEEE Engineering in medicine and biology society, Amsterdam, 1996.
[29] LEUNG, H., VARADAN, V. System Modeling and Design using Genetic Pro-grammingirst IEEE International Conference on Cognitive Informatics, 2002.
Proceedings. pp. 88-97, 2002.
[30] SCHWUNG, A.Nonlinear System Modeling via Hybrid System Representation of Recurrent Fuzzy SystemsIEEE International Conference on Fuzzy Systems (FUZZ), 2010.
[31] YOSHIO, K., HATANAKA, T. Nonlinear System Identification Based on Evo-lutionary Fuzzy Modeling
[32] ÜBEYLI, E., GÜLLER, I. Adaptive neuro-fuzzy inference systems for analysis of internal carotid arterial Doppler signalsComputers in Biology and Medicine, Elsevier, 2005.
[33] PANCHARIYA, P., PALIT, A. Nonlinear System Identification using Takagi-Sugeno Type Neuro-Fuzzy ModelSecond IEEE international conference on in-telligent systems, 2004.
[34] ABDELRAHIM, P., YAHAGI, T. A New Transformed Input-Domain ANFIS for Highly Nonlinear System Modeling and predictionCanadian Conference on Electrical and Computer Engineering, 2001.
[35] PANCHARIYA, P., PALIT, A. Nonlinear System Identification using ARX and SVM with Advanced PS0SThe 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON), Taipei, Taiwan, 2007.
[36] PARK, H., DIBAZAR, A. Discrete Synapse Recurrent Neural Network for Non-linear System Modeling and Its Application on Seismic Signal ClassificationThe International Joint Conference on Neural Networks (IJCNN), 2010
[37] MIZUKAMI, Y., SATOH, T., TANAKA, K. A new framework of neural systems for non-linear system modelingProceedings of the 9th International Conference on Neural Information Processing (ICONIP’OZ), 2004.
[38] SCHETZEN, M.Nonlinear System Modeling Based on the Wiener The-oryProceedings of the IEEE, vol. 69, 1981.
[39] TRUNG, N., WANG, L., YOUNG, P. Nonlinear System Modeling BAsed on Mon-Parametric Identification and Linear Wavelet Estimation of SDP Mod-elsProceedings of 45th Conference on Decision and Control, 2006.
[40] OHSAKI, H., IWASE, M., HATAKEYAMA, S. A Consideration of Nonlinear System Modeling using the Projection MethodSICE Annual Conference 2007, Kagawa University, Japan, 2007.
[41] SILVA, C. Polyspectral Techniques for Nonlinear System Modeling and Distor-tion CompensaDistor-tionVacuum Electronics Conference, Third IEEE International, 2002.
[42] SAN, L., MING, G. An Effective Learning Approach for Nonlinear System Mod-elingProceeding of teh 2004 IEEE International Symposium on Intelligent Con-trol, Taipei, Taewan, 2004.
[44] BÄCK, T.; FOGEL, D. B.; MICHALEVICZ, Z. Handbook of evolutionary com-putation.Taylor & Francis, New York, 1997.
[44] EL BARDINI, H., KHALIL, H., EL RABIE, N., SHARAF, M. Offline Modeling of Nonlinear Systems Based on Least Squares Support Vector Ma-chinesInternational Conference on Computer Engineering and Systems, 2009.
[45] DEEM, B., ZANNINI, T. Electronics and Computer Math8th Edition, Pearson Education, New Jersey, 2006.
[46] KRÖSE, B.; van der SMAGT, P. An introduction to neural networks. The University of Amsterdam, 1996.
[47] GONZALES-OLVERA, M. A.; TANG, Y. Nonlinear system identication and control using an input-output recurrent neurofuzzy network. Proceedings of the 17th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008. p.7480-7485.
[48] COOLEN, A. C. C. A beginner’s guide to the mathematics of neural networks.
King’s College London, 1998.