AN IMPROVED WIENER MODEL FOR SYSTEM IDENTIFICATION

Year 2020, Volume: 9 Issue: 2, 796 - 810, 07.08.2020

Selçuk Mete , Hasan Zorlu , Şaban Özer

https://doi.org/10.28948/ngumuh.553279

Abstract

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.

Keywords

system identification, wiener, hybrid model, optimization

SİSTEM KİMLİKLENDİRME İÇİN GELİŞTİRİLMİŞ BİR WIENER MODEL

Abstract

Wiener blok yapısı doğrusal ve doğrusal olmayan modellerin kaskad
bağlanması ile oluşturulmaktadır. Bu çalışmada sistem kimliklendirme alanı için
yeni ve geliştirilmiş bir Wiener model yapısı sunulmuştur. Önerilen yapıda,
doğrusal kısım olarak Sonlu 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 bulanık sinir 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 ayrıca kullanılarak
önerilen modelin performansı ile karşılaştırılmıştır. Simülasyon sonuçları,
önerilen modelin başarısını ortaya koymaktadır.

Keywords

sistem kimliklendirme, wiener, hibrit model, optimizasyon

References

• BAGIS, S., System modelling by using artificial intelligence algorithms, Master Tezi, Erciyes Üniversitesi, Fen Bilimleri Enstitüsü, Kayseri, Turkey, 2009
• GUO, F., A new identification method for wiener and hammerstein systems, Doktora Tezi, Karlsruhe Üniversitesi, Angewandte Informatik Bölümü, Germany, 2004.
• SCHWEICKHARDT, T., ALLGOWER, F., “On system gains, nonlinearity measures, and linear models for nonlinear systems”, IEEE Transactions on Automatic Control, 54, 62-78, 2009.
• HIZIR, N.B., PHAN, M.Q., BETTI, R., Longman, R.W., “Identification of discrete-time bilinear systems through equivalent linear models”, Nonlinear Dynamics, 69, 2065-2078, 2012.
• ERÇİN, Ö., ÇOBAN, R., “Identification of linear dynamic systems using the artificial bee colony algorithm”, Turk J Elec Eng & Comp Sci., 20, 1175-1188, 2012.
• HONG, X., MITCHELL, R.J., CHEN, S., HARRIS, C.J., LI, K., IRWIN, G.W., “Model selection approaches for nonlinear system identification: a review”, International Journal of Systems Sci., 39, 925-946, 2008
• ÖZER, Ş., ZORLU, H., “Identification of bilinear systems using differential evolution algorithm”, Sadhana Academy Proceedings in Engineering Sciences, 36, 281-292, 2011
• MANOHAR, C.S., ROY, D., “Monte Carlo filters for identification of nonlinear structural dynamical systems”, Sadhana Academy Proceedings in Engineering Sciences, 31, 399-427, 2006.
• RAHROOH, A., SHEPARD, S., “Identification of nonlinear systems using NARMAX model”, Nonlinear Analysis, 71, 1198-1202, 2009.
• NAITALI, A., GIRI, F., “Wiener–Hammerstein system identification an evolutionary approach”, International Journal of Systems Science, 47, 45-61, 2015.
• DING, F., WANG, Y., DING, J., “Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model”, Digital Signal Processing, 37, 100-108, 2015.
• DING, F., LIU, X.P., LIU, G., “Identification methods for Hammerstein nonlinear systems”, Digital Signal Processing, 21, 215-238, 2011.
• CELKA, P., BERSHAD, N.J., VESIN, J.M., “Fluctuation analysis of stochastic gradient identification of polynomial Wiener systems”, IEEE Transactions on Signal Processing, 48, 1820-1825, 2000.
• ZHIJUN, C., ER-WEI, B., “How nonlinear parametric Wiener system identification is under Gaussian inputs ?”, IEEE Transactions on Automatic Control, 57, 738-742, 2011.
• HWANG, S.H., HSIEH, C.Y., CHEN, H.T., HUANG, Y.C., “Use of discrete laguerre expansions for noniterative identification of nonlinear Wiener models”, Ind. Eng. Chem. Res., 50, 1427-1438, 2011.
• ABD-ELRADY, E., "A recursive prediction error algorithm for digital predistortion of FIR Wiener systems”, 6th International Symposium on Communication Systems, Networks and Digital Signal Processing (CNSDSP), 698-701, Graz, 2008.
• ZHENWEI, S., ZHICHENG, J., “Identification of Wiener nonlinear systems using the key-term separation principle and the filtering approach”, Proceedings of the 34th Chinese Control Conference, 1878-1885, China, 2015.
• HAFSI, S., LAABIDI, K., LAHMARI, M.K., “Identification of wiener-hammerstein model with multi segment piecewise-linear characteristic”, IEEE Mediterranean Electrotechnical Conference (MELECON), 5-10, Tunisia, 2012.
• AGUIRRE, L.A., COELHOAND, M.C.S., CORREA, M.V., “On the interpretation and practice of dynamical differences between Hammerstein and Wiener models”, IEE P-Contr Theor Ap., 152, 349-356, 2005.
• LEE, J., CHO, W., EDGAR, T.F., “Control system design based on a nonlinear first-order plus time delay model”, J Process Contr., 7, 65-73, 1997.
• SHAFIEE, G., AREFI, M., JAHED-MOTLAGH, M., JALALI, A., “Nonlinear predictive control of a polymerization reactor based on piecewise linear Wiener model”, Chemical Engineering Journal, 143(1), 282–292, 2008.
• HUNTER, I.W., KORENBERG, M.J., “The identification of nonlinear biological systems: Wiener and Hammerstein cascade models”, Biological Cybernetics, 55(2), 135-144, 1986.
• KUC, T.Y., YOU, K.H., “Dynamic state feedback and its application to linear optimal control”, International Journal of Control, Automation and Systems, 10(4), 667-674, 2012.
• WESTWICK, D.T., KEARNEY, R.E. “Nonparametric identification of nonlinear biomedical systems, Part I. Theory”, Crit. Rev. Biomed. Eng., 26, 153-226, 1998
• GALVAO, R.K.H., IZHAC, A., HADJILOUCAS, S., BECERRA, V.M., BOWEN, J.W., “MIMO Wiener model identification for large scale fading of wireless mobile communications links”, IEEE Communications Letters, 11(6), 513-515, 2007.
• NORQUAY, S.J., PALAZOGLU, A., ROMAGNOLI, J.A., “Model predictive control based on Wiener models”, Chem. Eng. Sci. 53(1), 75-84, 1998
• CERVANTES, A.L., AGAMENNONI, O.E., FIGUEROA, J.L., “A nonlinear model predictive control based on Wiener piecewise linear models”, J. Proc. Control, 13, 655-666, 2003
• LAWRYNCZUK, M., “Practical nonlinear predictive control algorithms for neural Wiener models”, J. Proc. Control, 23, 696-714, 2013.
• LAWRYNCZUK, M., Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach, Springer, 3, Switzerland, 2014
• MAHMOODI, S., POSHTAN, J., JAHED-MOTLAGH, M.R., MONTAZERI, A., “Nonlinear model predictive control of a pH neutralization process based on Wiener-Laguerre model”, Chem. Eng. J., 146, 328-337, 2009
• OBLAK, S., SKRJANC, I., “Continuous-time Wiener-model predictive control of a pH process based on a PWL approximation”, Chem. Eng. Sci., 65, 1720-1728, 2010
• PENG, J., DUBAY, R., HERNANDEZ, J.M., ABU-AYYAD, M., “A Wiener neural network-based iden tification and adaptive Generalized Predictive Control for nonlinear SISO systems”, Ind. Eng. Chem. Res,. 50, 7388-7397, 2011
• GOMEZ, J.C., JUTAN, A., BAEYENS, E., “Wiener model identification and predictive control of a pH neutralisation process”, IEE Proc. Control Theory Appl., 151(3), 329-338, 2004
• CELKA, P., COLDITZ, P., “Nonlinear nonstationary Wiener model of infant EEG seizures”, IEEE Transactions On Biomedical Engineering, 49(6), 556-564, 2002
• WIGREN, T., “Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model”, IEEE Transactions on Automatic Control, 39, 2191-2206, 1994
• NORDSJO, A.E., ZETTERBERG, L.H., “Identification of certain time-varying nonlinear Wiener and Hammerstein systems”, IEEE Transactions on Signal Processing, 49, 577-792, 2001
• AL-DUWAISH, H.N., “Identification of Wiener model using genetic algorithms”, 5th IEEE GCC Conference & Exhibition, 1-4, Kuwait City, 2009.
• ÖZER, Ş., ZORLU, H., METE, S., “System identification using Wiener model”, Conference on Electrical, Electronics and Computer Engineering (ELECO), 543-547, Turkey, Bursa, 2014
• WEILI, X., XIANQIANG, Y., LIANG, K., BAOGUO, X., “EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data”, Nonlinear Dynamics, 80, 329–339, 2015
• CHENA, C.L., CHIUB, C.Y., “A fuzzy neural approach to design of a Wiener printer model incorporated into model-based digital halftoning”, Applied Soft Computing, 12, 1288-1302, 2012
• METE, S., ÖZER, Ş., ZORLU, H., “System identification using Hammerstein model”, 22nd Signal Processing and Communications Appllica. Conf. (SIU), 1303-1306, Turkey, 2014
• JANG, J.T.R., SUN, C.T., MIZUTANI, E., Neuro-Fuzzy and Soft Computing, PTR, Prentice Hall, 1997.
• YUKSEL, M.E., BASTURK, A., “Efficient removal of impulse noise from highly corrupted digital images by a simple neuro-fuzzy operator”, Int. J. Electron. Commun. (AEU), 57, 214-219, 2003
• YUKSEL, M.E., BESDOK, E., “A simple neuro-fuzzy impulse detector for efficient blur reduction of impulse noise removal operators for digital images”, IEEE Trans. Fuzzy Syst., 12, 854-865, 2004
• ZORLU, H., Identification of nonlinear systems with soft computing techniques, Doktora Tezi, Erciyes Üniversitesi, Fen Bilimleri Enstitüsü, Kayseri, Turkey, 2011.
• YANYAN, R., DONGFENG, W., CHANGLIANG, L., PU, H., “PSO and RBF network-based Wiener model and Its application to system identification”, 24th Chinese Control and Decision Conference (CCDC), 2063-2068, Taiyuan, 2012
• YONG, L., YING-GAN, T., “Chaotic system identification based on a fuzzy Wiener model with particle swarm optimization”, Chin. Phys. Lett. 27, 090503/1-090503/4, 2010
• MOHAMED VALL, O.M., RADHI, M., “An approach to the closed loop identification of the Wiener systems with variable structure controller using an hybrid neural model”, IEEE International Symposium on Industrial Electronics, 2654-2658, Montreal, Que, 2006
• YINGGAN, T., ZHONGHUI, L., “Identification of nonlinear system using fuzzy Wiener model through self-adaptive differential evolution algorithm”, 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, 575-580, Shanghai, 2013
• CHEN, B., ZHU, Y., HU, J., PRINCIPE, J.C., “A variable step-size SIG algorithm for realizing the optimal adaptive FIR filter”, International Journal of Control, Automation, and Systems, 9, 1049-1055, 2011
• DINIZ, P.S.R., Adaptive Filtering Algorithms and Practical Implemantations, USA, Springer Verlag, 2008.
• SBEITY, F., GIRAULT, J.M., MENIGOT, S., CHARARA, J., “Sub and ultra harmonic extraction using several Hammerstein models”, Int Conf Comp Syst (ICCS), 1-5, Morocco, 2012
• DU, Z., WANG, X., “A novel identification method based on qdpso for Hammerstein error-output system”, Chinese Control Decis Conf (CCDC), 3335-3339, PRC, 2010
• SCHMIDT, C.A., BIAGIOLA, S.I., COUSSEAU, J.E., FIGUEROA, J.L., “Volterra-type models for nonlinear systems identification”, Applied Mathematical Modelling, 38, 2414-2421, 2014
• MAACHOU, A., MALTI, R., MELCHIOR, P., BATTAGLIA, J.L., OUSTALOUP, A., HAY, B., “Nonlinear thermal system identification using fractional Volterra series”, Control Engineering Practice, 29, 50-60, 2014
• BAŞTURK, A., Noise removal from digital images and image enhancement by soft computing based methods, Doktora Tezi, Erciyes Üniversitesi, Fen Bilimleri Enstitüsü, Kayseri, Turkey, 2006.
• YUKSEL, M.E., BASTURK, A., “A simple generalized neuro–fuzzy operator for efficient removal of impulse noise from highly corrupted digital images”, AEU International Journal of Electronics and Communications, 59(1), 1-7, 2005
• YUKSEL, M.E., BASTURK, A., “Efficient distortion reduction of mixed noise filters by neuro–fuzzy processing”, Lecture Notes in Artificial Intelligence (LNAI), 4252, 331–339, 2006
• TAKAGI, T., SUGENO, M., “Fuzzy identification of systems and its applications to modeling and control”, IEEE Transactions on Systems, Man, and Cybernetics, 15, 116–132, 1985
• SUGENO, M., KANG, G.T., “Structure identification of fuzzy model”, Fuzzy Sets and Systems, 28 15-33, 1988
• LEVENBERG, K., “A method for the solution of certain problems in least squares”, Quan. Appl. Math., 2, 164-168, 1944
• MARQUARDT, D.W., “An algorithm for least squares estimation of nonlinear parameters”, J. Soc. Industrial and Applied Mathematics, 31, 431–441, 1963
• ÖZER, Ş., ZORLU, H., “Neuro-Fuzzy soft-switching hybrid filter for impulsive noisy environments”, Turk J Elec Eng & Comp., 19, 73-85, 2011
• BASTURK, A., YUKSEL, M.E., “Neuro-Fuzzy soft switching hybrid filter for impulse noise removal from digital images”, Proceedings of the IEEE 13th Signal Proces Com Ap Conf (SIU), 13-16, Kayseri, 2005
• SOYTURK, M.A., BASTURK, A., YUKSEL, M.E., “A novel fuzzy filter for speckle noise removal”, Turk J Elec Eng & Comp., 22, 1367-1381, 2014
• YILDIRIM, M.T., BASTURK, A., YUKSEL, M.E., “Impulse noise removal from digital images by a detail-preserving filter based on type-2 fuzzy logic”, IEEE Transactions on Fuzzy Systems, 16, 920- 928, 2008
• WANG, Z., SHEN, Y., JI, Z., DING, R., “Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems”, Nonlinear Dynamics, 73, 1045-1054, 2013
• NANDA, S.J., PANDA, G., MAJHI, B., “Development of immunized PSO algorithm and its application to Hammerstein model identification”, IEEE Congress on Evolutionary Computation, 3080-3086, Trondheim, 2009
• CHON, K.H., COHEN, R.J., “Linear and nonlinear arma model parameter estimation using an artificial neural network”, IEEE T Bio-Med Eng., 44, 168-174, 1997
• METE, S., ZORLU, H., OZER, S., “A New Hybrid Model Based On Neuro Fuzzy Network Soft Switching Mechanism For System Identification”, Bilişim Teknolojileri Dergisi, 12(1), 1-8, 2019.
• METE, S., OZER, S., ZORLU, H., “System identification using Hammerstein model optimized with differential evolution algorithm”, International Journal of Electronics and Communications (AEU),70, 1667-1675, 2016
• METE, S., OZER, S., ZORLU, H., “System identification application using hammerstein model”, Sadhana-Academy Proceedings in Engineering Sciences, 41, 597-605, 2016
• METE, S., ZORLU, H., OZER, S., An Improved Hammerstein Model for System Identification, Information Innovation Technology in Smart Cities, pp.47-61, Springer-Verlag, Singapur, Part I, 2018