SİSTEM KİMLİKLENDİRME İÇİN GELİŞTİRİLEN BİR WIENER MODEL

Wiener blok yapısı doğrusal ve doğrusal olmayan modellerin kaskad bağlanması ile oluşturulmaktadır. Bu çalışmada sistemkimliklendirme alanı için yeni ve geliştirilmiş bir Wiener model yapısı sunulmuştur. Önerilen yapıda, doğrusal kısım olarakSonlu Darbe Cevaplı model, doğrusal olmayan kısım olarak Esnek Anahtarlama Temelli Hibrit (EATH) model kullanılmıştır.EATH yapısı, doğrusal olmayan ikinci derece bir Volterra model, doğrusal olmayan hafızasız bir polinom model ve bir bulanıksinir ağı temelli esnek anahtarlama mekanizmasından oluşmaktadır. Simülasyonlarda, önerilen model ile dört farklı sistem tipi kimliklendirilmiştir. İlave olarak, bu sistemleri kimliklendirmek için literatürde yeralan Volterra ve Wiener modellerde ayrıcakullanılarak önerilen modelin performansı ile karşılaştırılmıştır. Simülasyon sonuçları, önerilen modelin başarısını ortayakoymaktadır.

AN IMPROVED WIENER MODEL FOR SYSTEM IDENTIFICATION

Wiener block structure is formed by cascade of linear and nonlinear models. A novel and improved Wiener model structure for system identification area is proposed in this study. In proposed Wiener model, Finite Impulse Response (FIR) model is used as linear part and Soft Switching based Hybrid (SSH) model is used as nonlinear part. The SSH structure consists of a Second Order Volterra (SOV) nonlinear model, a Memoryless Polynomial (MP) nonlinear model, and a soft-switching part through a Neuro-Fuzzy (NF) network. In simulation studies, different types systems are identified by presented novel model. In addition to the mentioned identified systems, the performance of the improved model is also compared with Volterra model and Wiener models presented in the literature. Simulation results find out the success of the proposed model.

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[1] S. Bagis, “System modelling by using artificial intelligence algorithms,” M. S. thesis, Erciyes University, Kayseri, Turkey, 2009.
[2] F. Guo, “A new identification method for wiener and hammerstein systems,” Dissertation thesis, Karlsruhe University, Germany, 2004.
[3] T. Schweickhardt and F. Allgower, “On system gains, nonlinearity measures, and linear models for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 54, pp. 62-78, 2009.
[4] N.B. Hızır, M.Q. Phan, R. Betti and R.W. Longman, “Identification of discrete-time bilinear systems through equivalent linear models,” Nonlinear Dynamics, vol. 69, pp. 2065-2078, 2012.
[5] Ö. Erçin and R. Çoban, “Identification of linear dynamic systems using the artificial bee colony algorithm,” Turk J Elec Eng & Comp Sci., vol. 20, pp. 1175-1188, 2012.
[6] X. Hong, R.J. Mitchell, S. Chen, C.J. Harris, K. Li and G.W. Irwin, “Model selection approaches for nonlinear system identification: a review,” International Journal of Systems Sci., vol. 39, pp. 925-946, 2008.
[7] Ş. Özer and H. Zorlu, “Identification of bilinear systems using differential evolution algorithm,” Sadhana Academy Proceedings in Engineering Sciences, vol. 36, pp. 281-292, 2011.
[8] C.S. Manohar and D. Roy, “Monte Carlo filters for identification of nonlinear structural dynamical systems,” Sadhana Academy Proceedings in Engineering Sciences, vol. 31, pp. 399-427, 2006.
[9] A. Rahrooh and S. Shepard, “Identification of nonlinear systems using NARMAX model,” Nonlinear Analysis, vol. 71, pp. 1198-1202, 2009.
[10]A. Naitali and F. Giri, “Wiener–Hammerstein system identification an evolutionary approach,” International Journal of Systems Science, vol. 47, pp. 45-61, 2015.
[11]F. Ding, Y. Wang and J. Ding, “Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model,” Digital Signal Processing, vol. 37, pp. 100-108, 2015.
[12]F. Ding, X.P. Liu and G. Liu, “Identification methods for Hammerstein nonlinear systems,” Digital Signal Processing, vol. 21, pp. 215-238, 2011.
[13]P. Chelka, N.J. Bershad and J.M. Vesin, “Fluctuation analysis of stochastic gradient identification of polynomial Wiener systems,” IEEE Transactions on Signal Processing, vol. 48, pp. 1820-1825, 2000.
[14]C. Zhijun and B. Er-Wei, “How nonlinear parametric Wiener system identification is under Gaussian inputs ?,” IEEE Transactions on Automatic Control, vol. 57, pp. 738-742, 2011.
[15]S.H. Hwang, C.Y. Hsieh, H.T. Chen and Y.C. Huang, “Use of discrete laguerre expansions for noniterative identification of nonlinear Wiener models,” Ind. Eng. Chem. Res., vol. 50, pp.1427-1438, 2011.
[16]E. Abd-Elrady, "A recursive prediction error algorithm for digital predistortion of FIR Wiener systems,” In 6th International Symposium on Communication Systems, Networks and Digital Signal Processing (CNSDSP), Graz, 2008, pp. 698-701.
[17]S. Zhenwei and J. Zhicheng, “Identification of Wiener nonlinear systems using the key-term separation principle and the filtering approach,” In Proceedings of the 34th Chinese Control Conference, China, 2015, pp. 1878-1885.
[18]S. Hafsi, K. Laabidi and M.K. Lahmari, “Identification of wiener-hammerstein model with multi segment piecewiselinear characteristic,” In IEEE Mediterranean Electrotechnical Conference (MELECON), Tunisia, 2012, pp. 5-10.
[19]L.A. Aguirre, M.C.S. Coelhoand and M.V. Correa, “On the interpretation and practice of dynamical differences between Hammerstein and Wiener models,” IEE P-Contr Theor Ap., vol. 152, pp. 349-356, 2005.
[20]J. Lee, W. Cho and T.F. Edgar, “Control system design based on a nonlinear first-order plus time delay model,” J Process Contr., vol. 7, pp. 65-73, 1997.
[21]G. Shafiee, M. Arefi, M. Jahed-Motlagh and A. Jalali, “Nonlinear predictive control of a polymerization reactor based on piecewise linear Wiener model,” Chemical Engineering Journal, vol. 143, no. 1, pp. 282-292, 2008.
[22]I.W. Hunter and M.J. Korenberg, “The identification of nonlinear biological systems: Wiener and Hammerstein cascade models,” Biological Cybernetics, vol. 55, no. 2, pp. 135-144, 1986.
[23]T.Y. Kuc and K.H. You, “Dynamic state feedback and its application to linear optimal control,” International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 667-674, 2012.
[24]D.T. Westwick and R.E. Kearney, “Nonparametric identification of nonlinear biomedical systems, Part I. Theory,” Crit. Rev. Biomed. Eng., vol. 26, pp. 153-226, 1998.
[25]R.K.H. Galvao, A. Izhac, S. Hadjiloucas, V.M. Becerra and J.W. Bowen, “MIMO Wiener model identification for large scale fading of wireless mobile communications links,” IEEE Communications Letters, vol. 11, no. 6, pp. 513-515, 2007.
[26]S.J. Norquay, A. Palazoglu and J.A. Romagnoli, “Model predictive control based on Wiener models,” Chem. Eng. Sci. vol. 53, no. 1, pp. 75-84, 1998.
[27]A.L. Cervantes, O.E. Agamennoni and J.L. Figueroa, “A nonlinear model predictive control based on Wiener piecewise linear models,” J. Proc. Control, vol. 13, pp. 655-666, 2003.
[28]M. Lawrynczuk, “Practical nonlinear predictive control algorithms for neural Wiener models,” J. Proc. Control, vol. 23, pp. 696-714, 2013.
[29]M. Lawrynczuk, Eds., Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach. Switzerland: Springer, 2014.
[30]S. Mahmoodi, J. Poshtan, M.R. Jahed-Motlagh and A. Montazeri, “Nonlinear model predictive control of a pH neutralization process based on Wiener-Laguerre model,” Chem. Eng. J., vol. 146, pp. 328-337, 2009.
[31]S. Oblak and I. Skrjanc, “Continuous-time Wiener-model predictive control of a pH process based on a PWL approximation,” Chem. Eng. Sci., vol 65, pp. 1720-1728, 2010.
[32]J. Peng, R. Dubay, J.M. Hernandez and M. Abu-Ayyad, “A Wiener neural network-based iden tification and adaptive Generalized Predictive Control for nonlinear SISO systems,” Ind. Eng. Chem. Res., vol. 50, pp. 7388-7397, 2011.
[33]J.C. Gomez, A. Jutan and E. Baeyens, “Wiener model identification and predictive control of a pH neutralisation process,” IEE Proc. Control Theory Appl., vol. 151, no. 3, pp. 329-338, 2004.
[34]P. Celka and P, Colditz, “Nonlinear nonstationary Wiener model of infant EEG seizures,” IEEE Transactions On Biomedical Engineering, vol. 49, no. 6, pp. 556-564, 2002.
[35]T. Wigren, “Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model,” IEEE Transactions on Automatic Control, vol. 39, pp. 2191-2206, 1994.
[36]A.E. Nordsjo and L.H. Zetterberg, “Identification of certain time-varying nonlinear Wiener and Hammerstein systems,” IEEE Transactions on Signal Processing, vol. 49, pp. 577-792, 2001.
[37]H.N. Al-Duwaish, “Identification of Wiener model using genetic algorithms,” In 5th IEEE GCC Conference & Exhibition, Kuwait City, 2009, pp. 1-4.
[38]Ş. Özer, H. Zorlu and S. Mete, “System identification using Wiener model,” In Conference on Electrical, Electronics and Computer Engineering (ELECO), Turkey, Bursa, 2014, pp. 543-547.
[39]X. Weili, Y. Xianqiang, K. Liang and X. Baoguo, “EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data,” Nonlinear Dynamics, vol. 80, pp. 329–339, 2015.
[40]C.L. Chena and C.Y. Chiub, “A fuzzy neural approach to design of a Wiener printer model incorporated into modelbased digital halftoning,” Applied Soft Computing, vol. 12, pp. 1288-1302, 2012.
[41]S. Mete, Ş. Özer and H. Zorlu, “System identification using Hammerstein model,” In 22nd Signal Processing and Communications Appllica. Conf. (SIU), Turkey, 2014, pp. 1303-1306.
[42]J.T.R. Jang, C.T. Sun and E. Mizutani, Eds., Neuro-Fuzzy and Soft Computing. PTR: Prentice Hall, 1997.
[43]M.E. Yuksel and A. Basturk, “Efficient removal of impulse noise from highly corrupted digital images by a simple neuro-fuzzy operator,” Int. J. Electron. Commun. (AEU), vol. 57, pp. 214-219, 2003.
[44]M.E. Yuksel and E. Besdok, “A simple neuro-fuzzy impulse detector for efficient blur reduction of impulse noise removal operators for digital images,” IEEE Trans. Fuzzy Syst., vol. 12, pp. 854-865, 2004.
[45]H. Zorlu, “Identification of nonlinear systems with soft computing techniques”, Dissertation thesis, Erciyes University, Kayseri, Turkey, 2011.
[46]R. Yanyan, W. Dongfeng, L. Changliang and H. Pu, “PSO and RBF network-based Wiener model and Its application to system identification,” In 24th Chinese Control and Decision Conference (CCDC), Taiyuan, 2012, pp. 2063-2068.
[47]L. Yong and T. Ying-Gan, “Chaotic system identification based on a fuzzy Wiener model with particle swarm optimization,” Chin. Phys. Lett., vol. 27, pp. 090503/1-090503/4, 2010.
[48]O.M. Mohamed Vall and M. Radhi, “An approach to the closed loop identification of the Wiener systems with variable structure controller using an hybrid neural model,” In IEEE International Symposium on Industrial Electronics, Montreal, Que, 2006, pp. 2654-2658.
[49]T. Yinggan and L. Zhonghui, “Identification of nonlinear system using fuzzy Wiener model through self-adaptive differential evolution algorithm,” In 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, Shanghai, 2013, pp. 575-580.
[50]B. Chen, Y. Zhu, J. Hu and J.C. Principe, “A variable step-size SIG algorithm for realizing the optimal adaptive FIR filter,” International Journal of Control, Automation, and Systems, vol. 9, pp. 1049-1055, 2011.
[51]P.S.R. Diniz, Eds., Adaptive Filtering Algorithms and Practical Implemantations. USA: Springer Verlag, 2008.
[52]F. Sbeity, J.M. Girault, S. Menigot and J. Charara, J., “Sub and ultra harmonic extraction using several Hammerstein models,” Int Conf Comp Syst (ICCS), Morocco, 2012, pp. 1-5.
[53]Z. Du and X. Wang, “A novel identification method based on qdpso for Hammerstein error-output system,” In Chinese Control Decis Conf (CCDC), PRC, 2010, pp. 3335-3339.
[54]C.A. Schmidt, S.I. Biagiola, J.E. Cousseau and J.L. Figueroa, “Volterra-type models for nonlinear systems identification,” Applied Mathematical Modelling, vol. 38, pp. 2414-2421, 2014.
[55]A. Maachou, R. Malti, P. Melchior, J.L. Battaglia, A. Oustaloup and B. Hay, “Nonlinear thermal system identification using fractional Volterra series,” Control Engineering Practice, vol. 29, pp. 50-60, 2014.
[56]A. Basturk, “Noise removal from digital images and image enhancement by soft computing based methods,” Dissertation thesis, Erciyes University, Kayseri, Turkey, 2006.
[57]M.E. Yuksel and A. Basturk, “A simple generalized neuro–fuzzy operator for efficient removal of impulse noise from highly corrupted digital images,” AEU International Journal of Electronics and Communications, vol. 59, no. 1, pp. 1- 7, 2005.
[58]M.E. Yuksel and A. Basturk, “Efficient distortion reduction of mixed noise filters by neuro–fuzzy processing,” Lecture Notes in Artificial Intelligence (LNAI), vol. 4252, pp. 331-339, 2006.
[59]T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 15, pp. 116-132, 1985.
[60]M. Sugeno and G.T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets and Systems, vol. 28, pp. 15-33, 1988.
[61]K. Levenberg, “A method for the solution of certain problems in least squares,” Quan. Appl. Math., vol. 2, pp. 164-168, 1944.
[62]D.W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” J. Soc. Industrial and Applied Mathematics, vol. 31, pp. 431-441, 1963.
[63]Ş. Özer and H. Zorlu, “Neuro-Fuzzy soft-switching hybrid filter for impulsive noisy environments,” Turk J Elec Eng & Comp., vol. 19, pp. 73-85, 2011.
[64]A. Basturk and M.E. Yuksel, “Neuro-Fuzzy soft switching hybrid filter for impulse noise removal from digital images,” In Proceedings of the IEEE 13th Signal Proces Com Ap Conf (SIU), Kayseri, 2005, pp. 13-16.
[65]M.A. Soyturk, A. Basturk and M.E. Yuksel, “A novel fuzzy filter for speckle noise removal,” Turk J Elec Eng & Comp., vol. 22, pp. 1367-1381, 2014.
[66]M.T. Yıldırım, A. Basturk and M.E. Yuksel, “Impulse noise removal from digital images by a detail-preserving filter based on type-2 fuzzy logic,” IEEE Transactions on Fuzzy Systems, vol. 16, pp. 920-928, 2008.
[67]Z. Wang, Y. Shen, Z. Ji and R. Ding, “Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems,” Nonlinear Dynamics, vol. 73, pp. 1045-1054, 2013.
[68]S.J. Nanda, G. Panda and B. Majhi, “Development of immunized PSO algorithm and its application to Hammerstein model identification,” In IEEE Congresson Evolutionary Computation, Trondheim, 2009, pp. 3080-3086.
[69]K.H. Chon and R.J. Cohen, “Linear and nonlinear arma model parameter estimation using an artificial neural network,” IEEE T Bio-Med Eng., vol. 44, pp. 168-174, 1997.
[70]S. Mete, H. Zorlu and S. Ozer, “A new hybrid model based on neuro fuzzy network soft switching mechanism for system identification,” Bilişim Teknolojileri Dergisi, vol. 12, no. 1, pp. 1-8, 2019.
[71]S. Mete, S. Ozer and H. Zorlu, “System identification using Hammerstein model optimized with differential evolution algorithm,” International Journal of Electronics and Communications (AEU), vol. 70, pp. 1667-1675, 2016.
[72]S. Mete, S. Ozer and H. Zorlu, “System identification application using hammerstein model,” Sadhana-Academy Proceedings in Engineering Sciences, vol. 41, pp. 597-605, 2016.
[73]S. Mete, H. Zorlu and S. Ozer, “An improved Hammerstein model for system identification,” in Information Innovation Technology in Smart Cities, L. Ismail and L. Zhang, Eds. Singapur: Springer-Verlag, Part I, 2018, pp.47-61.