YAPAY ARI KOLONİSİ ALGORİTMASI İLE OPTİMİZE EDİLEN HAMMERSTEIN MODEL KULLANARAK SİSTEMLERİN KİMLİKLENDİRİLMESİ

Year 2018, , 83 - 98, 31.01.2018

Hasan Zorlu , Selçuk Mete Şaban Özer

https://doi.org/10.28948/ngumuh.386351

Cited By: 1

Abstract

   Hammerstein model, doğrusal olmayan alt
model çıkışının doğrusal olan bir alt modelin girişine seri bağlanması ile
oluşan bir blok model yapısıdır. Literatürde, Hammerstein modellerde çoğunlukla
doğrusal olmayan bölümler için doğrusal olmayan hafızasız polinom (MPN - memoryless polynomial nonlinear) model
ve doğrusal bölümler için sonlu darbe cevaplı (FIR- finite impulse response) ya da sonsuz darbe cevaplı (IIR- infinite impulse response) model tercih edilmektedir. Literatürden farklı
olarak bu çalışmada doğrusal olmayan bölüm için MPN yerine ikinci derece
volterra (SOV -
Second Order Volterra)
model tercih edilmiştir. Bu açıdan doğrusal olmayan SOV ve doğrusal FIR modelin
kaskat bağlanmasından oluşan yeni bir Hammerstein model sunulmuştur.
Simulasyonlarda, yapay arı kolonisi (ABC- artificial bee colony) algoritmasıyla optimize edilen Hammerstein model ile
farklı sistemler kimliklendirilmiştir. Simulasyon sonuçlarında ABC algoritması
ile önerilen modelin etkili ve güçlü olduğu görülmüştür.

Keywords

Sistem kimliklendirme, Hammerstein model, yapay arı koloni algoritması, klonal seçim algoritması, yenilemeli en küçük kareler algoritması

SYSTEM IDENTIFICATION USING HAMMERSTEIN MODEL OPTIMIZED WITH ARTIFICIAL BEE COLONY ALGORITHM

Abstract

   Hammerstein model is formed
by cascade of linear and nonlinear parts. In literature, memoryless polynomial
nonlinear (MPN) model for nonlinear part and finite impulse response (FIR)
model or infinite impulse response (IIR) model for linear part are mostly
preferred for Hammerstein models. This paper different from the studies in
literature, focuses on the success of Hammerstein block model that Second Order
Volterra (SOV) is preferred instead of MPN as nonlinear part. In this context, a new Hammerstein model is presented which is obtained by
cascade form of a nonlinear SOV and a linear FIR model.
In simulations, different types of system are identified by proposed
Hammerstein model which is optimized with ABC (artificial bee colony)
algorithm. The simulation results reveal effectiveness and robustness of the
proposed model with ABC algorithm.

Keywords

System identification, Hammerstein model, artificial bee colony algorithm, clonal selection algorithm, recursive least square algorithm

References

• [1] UPADHYAY, P., KAR, R., MANDAL, D., GHOSHAL, S.P., “Craziness Based Particle Swarm Optimization Algorithm for IIR System Identification Problem”, AEU- International Journal of Electronics and Communications, 68(5), 369-378, 2014.
• [2] ADEL MOHSEN, A.K., ABU EL-YAZEED, M.F., “Selection of Input Stimulus for Fault Diagnosis of Analog Circuits Using ARMA Model”, AEU- International Journal of Electronics and Communications, 58(3), 212-217, 2004.
• [3] SCHWEICKHARDT, T., ALLGOWER, F., “On System Gains, Nonlinearity Measures, and Linear Models for Nonlinear Systems”, IEEE Transactions on Automatic Control, 54(1), 62-78, 2009.
• [4] HIZIR, N.B., PHAN, M.Q., BETTI, R., LONGMAN, R.W., “Identification of Discrete-Time Bilinear Systems Through Equivalent Linear Models”, Nonlinear Dynamics, 69(4), 2065-2078, 2012.
• [5] ERCIN, O., COBAN, R., “Identification of Linear Dynamic Systems Using The Artificial Bee Colony Algorithm”, Turk. J. Elec. Eng. & Comp. Sci., 20(1), 1175-1188, 2012.
• [6] HONG, X., MITCHELL, R.J., CHEN, S., HARRIS, C.J., LI, K., IRWIN, G.W., “Model Selection Approaches for Non-Linear System Identification: A Review”, International Journal of Systems Science, 39(10), 925–946, 2008.
• [7] ZONG-XIANG, L., LI-JUAN, L., WEI-XIN, X., LIANG-QUN, L., “Two Implementations of Marginal Distribution Bayes Filter for Nonlinear Gaussian Models”, AEU- International Journal of Electronics and Communications, 69(9), 1297-1304, 2015.
• [8] VIPIN, B.V., PARTHASARATHY, H., “Parameter Estimation for Nonlinear Circuits Using Variants of LMS”, AEU- International Journal of Electronics and Communications, 64(5), 465-468, 2010.
• [9] MANOHAR, C.S., ROY, D., “Monte Carlo Filters for Identification of Nonlinear Structural Dynamical Systems”, Sadhana Academy Proceedings in Engineering Sciences, 31(4), 399-427, 2006.
• [10] RAHROOH, A., SHEPARD, S., “Identification of Nonlinear Systems Using NARMAX Model”, Nonlinear Analysis: Theory, Methods & Applicatons, 71(12), 1198-1202, 2009.
• [11] NAITALI, A., GIRI, F., “Wiener–Hammerstein System Identification an Evolutionary Approach”, International Journal of Systems Science, 47(1), 45-61, 2015.
• [12] 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.
• [13] DING, F., LIU, X.P., LIU, G., “Identification Methods for Hammerstein Nonlinear Systems”, Digital Signal Processing, 21(2), 215-238, 2011.
• [14] 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.
• [15] OZER, S., ZORLU, H., “Identification of Bilinear Systems Using Differential Evolution Algorithm”, Sadhana-Acad. P. Eng. S., 36, 281-292, 2011.
• [16] DINIZ, P.S.R., Adaptive Filtering Algorithms and Practical Implemantations, Springer Verlag, USA, 2008.
• [17] ZORLU, H., Identification of Nonlinear Systems with Soft Computing Techniques, Thesis (PhD), Erciyes University, Kayseri, Turkey, 2011.
• [18] OZER, S., ZORLU, H., “Chaotic Time Series Prediction Using The Nonlinear Par Systems”, J. of The Faculty of Engineering and Architecture of Gazi University, 27, 323-331, 2012.
• [19] SCHMIDT, C.A., BIAGIOLA, S.I., COUSSEAU, J.E., FIGUEROA, J.L., “Volterra-Type Models for Nonlinear Systems Identification”, Applied Mathematical Modelling, 38(9), 2414-2421, 2014.
• [20] 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.
• [21] COELHO, L.D.S., PESSOA, M.W., “Nonlinear Model Identification of an Experimental Ball-And-Tube System Using a Genetic Programming Approach”, Mechanical Systems and Signal Processing, 23(5), 1434-1446, 2009.
• [22] BAO, C., HAO, H., LI, Z.X., “Integrated ARMA Model Method for Damage Detection of Subsea Pipeline System”, Engineering Structures, 48, 176-192, 2013.
• [23] CAILLEC, J.M.L., “Hypothesis Testing for Nonlinearity Detection Based on an MA Model”, IEEE Transactions on Signal Processing, 56(2), 816-821, 2008.
• [24] WANG, Y.J., DING, F., “Iterative Estimation for a Nonlinear IIR Filter with Moving Average Noise by Means of The Data Filtering Technique”, IMA Journal of Mathematical Control and Information, 2016. doi: 10.1093/imamci/dnv067
• [25] 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(6), 1049-1055, 2011.
• [26] ANTARI, J., ZEROUAL, A., “Modelling Video Packet Transmission in IP Networks Using Hammerstein Series and Higher Order Cumulants”, AEU - International Journal of Electronics and Communications, 63(5), 406-411, 2009.
• [27] TANG, Y., LI, Z., GUAN, X., “Identification of Nonlinear System Using Extreme Learning Machine Based Hammerstein Model”, Communications in Nonlinear Science and Numerical Simulation, 19(9), 3171-3183, 2014.
• [28] GOTMARE, A., PATIDAR, R., GEORGE, N.V., “Nonlinear System Identification Using a Cuckoo Search Optimized Adaptive Hammerstein Model”, Expert Systems with Applications, 42(5), 2538-2546, 2015.
• [29] CUI, M., LIU, H., LI, Z., TANG, Y., GUAN, X., “Identification of Hammerstein Model Using Functional Link Artificial Neural Network”, Neuro Computing, 2014. doi:10.1016/ j.neucom.2014.03.051
• [30] KHANI, F, HAERI, M., “Robust Model Predictive Control of Nonlinear Processes Represented by Wiener or Hammerstein Models”, Chemical Engineering Science, 2015. doi:10 .1016/j.ces.2015.02.021
• [31] JERAJ, J., MATHEWS, V.J., “Stochastic Mean-Square Performance Analysis of an Adaptive Hammerstein Filter”, IEEE Transactions on Signal processing, 54(6), 2168-2177, 2006.
• [32] SBEITY, F., GIRAULT, J.M., MENIGOT, S., CHARARA, J., “Sub and Ultra Harmonic Extraction Using Several Hammerstein Models”, International Conference on Complex Systems (ICCS), Morocco, 2012.
• [33] JERAJ, J., MATHEWS, V.J., DUBOW, J., “A Stable Adaptive Hammerstein Filter Employing Partial Orthogonalization of The Input Signals”, IEEE Transactions on Signal Processing, 54(4), 1412-1420, 2006.
• [34] 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.
• [35] 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.
• [36] 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.
• [37] NARENDRA, K.S., GALMAN, P.G., “An Iterative Method for The Identification of Nonlinear Systems Using a Hammerstein Model”, IEEE T. Automat. Contr., 11, 546-550, 1966.
• [38] YU, L., ZHANG, J., LIAO, Y., DING, J., “Parameter Estimation Error Bounds for Hammerstein Nonlinear Finite Impulsive Response Models”, Appl. Math. Comput., 202, 472-480, 2008.
• [39] GUO, F., A New Identification Method for Wiener and Hammerstein Systems, Thesis (PhD), Karlsruhe University, Germany, 2004.
• [40] KALAFATIS, A., ARIFIN, N., WANG, L., CLUETT, W.R., “A New Approach To The Identification of Ph Processes Based on The Wiener Model”, Chem. Eng. Sci., 50, 3693-3701, 1995.
• [41] SAPPAL, A.S., To Develop A Linearization Technique for Mitigating The Rf Power Amplifier’s Nonlinearity Effects in a Multi Carrier W-CDMA Base Station, Thesis (PhD), Punjabi University, India, 2011.
• [42] WANG, D.Q., ZHANG, W., “Improved Least Squares Identification Algorithm for Multivariable Hammerstein Systems”, Journal of the Franklin Institute-Engineering and Applied Mathematics., 352(11), 5292–5307, 2015.
• [43] KOZEK, M., HAMETNER, C., “Block-Oriented Identification of Hammerstein/Wiener Models Using The RLS Algorithm”, International Journal of Applied Electromagnetics and Mechanics, 25(1-4), 529-535, 2007.
• [44] DING, F., WANG, X.H., CHEN, Q.J., XIAO, Y.S., “Recursive Least Squares Parameter Estimation for a Class of Output Nonlinear Systems Based on The Model Decomposition”, Circuits, Systems and Signal Processing, 2016. doi:10.1007/s00034-015-0190-6
• [45] HEGDE, V., RADHAKRSIHNAN, C., KRUSIENSKI, D., JENKINS, W.K., “Series Cascade Nonlinear Adaptive Filters”, 45th Midwest Symposium on Circuits and Systems (MWSCAS), 219-222, 2002.
• [46] NANDA, S.J., PANDA, G., MAJHI, B., “Improved Identification of Hammerstein Plants Using New CPSO and IPSO Algorithms”, Expert Systems with Applications, 37, 6818-6831, 2010.
• [47] GOUDOS, S. K., SIAKAVARA, K., SAHALOS, J.N., “Design of Load-Ended Spiral Antennas for RFID UHF Passive Tags Using Improved Artificial Bee Colony Algorithm”, AEU- International Journal of Electronics and Communications, 69(1), 206-214, 2015.
• [48] KARABOGA, D., An Idea Based on Honey Bee Swarm for Numerical Optimization, Technical Report-TR06, Erciyes University, Computer Engineering Department, Turkey, 2005.
• [49] KARABOGA, D., Artificial bee colony algorithm, Scholarpedia, http://www.scholarpedia.org /article/Artificial_bee_colony_algorithm (2010)
• [50] KARABOGA, D., BASTURK, B., “A Powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm”, Journal of Global Optimization, 39,459-471, 2007.
• [51] KARABOGA, N., KOCKANAT, S., DOGAN, H., “The Parameter Extraction of The Thermally Annealed Schottky Barrier Diode Using The Modified Artificial Bee Colony”, Applied Intelligence, 38,279-288, 2013.
• [52] KARABOGA, D., AKAY, B., “A Modified Artificial Bee Colony Algorithm for Constrained Optimization Problems”, Applied Soft Computing, 11, 3021-3031, 2011.
• [53] KARABOGA, N., ÇETINKAYA, M.B., “A Novel and Efficient Algorithm for Adaptive Filtering: Artificial Bee Colony Algorithm”, Turk. J. Elec. Eng. & Comp. Sci., 19,175-190, 2011.
• [54] KARABOGA, N., “A New Design Method Based on Artificial Bee Colony Algorithm for Digital IIR Filters”, Journal of the Franklin Institute, 346, 328-348, 2009.
• [55] SABAT, S., et al., “Artificial Bee Colony Algorithm for Small Signal Model Parameter Extraction of Mesfet”, Engineering Applications of Artificial Intelligence, 23,689–694, 2010.
• [56] ÇETINKAYA, M.B., Digital Filter Design by Using Artificial Bee Colony Algorithm, Thesis (PhD), Erciyes University, Kayseri, Turkey, 2010.
• [57] METE, S., OZER S., ZORLU, H., “System Identification Using Hammerstein Model”, IEEE Signal Proces. Com. Ap. Conf. (SIU), 1303-1306, Turkey, 2014.
• [58] UZUNHISARCIKLI, E., KARABOGA, N., LATIFOGLU, F., KOZA, T., KOCKANAT, S., “Mitral Kapak İşareti Üzerindeki Anatomik ve Elektronik Gürültülerin Abc Algoritması ile Tasarlanan IIR Süzgeçlerle Süzülmesi”, Electric-Elektronical and Computer Symposium, 288-292, Turkey, 2011.
• [59] KARABOGA, D., AKAY, B., “Yapay Arı Koloni (Artificial Bee Colony, ABC) Algoritması ile Yapay sinir Ağlarının Eğitilmesi”, IEEE Signal Proces. Com. Ap. Conf. (SIU), 1-4, Turkey, 2007.
• [60] KISI, O., OZKAN, C., AKAY B., “Modeling Discharge-Sediment Relationship Using Neural Networks with Artificial Bee Colony Algorithm”, Journal of Hydrology, 428-429, 94–103, 2012.
• [61] KARA, T., Adaptive Control of Nonlinear Systems with Applications, Thesis (PhD), Gaziantep University, Turkey, 2005.
• [62] METE, S., OZER, S., ZORLU, H., "System Identification Using Hammerstein Model Optimized with Differential Evolution Algorithm", AEU-International Journal of Electronics and Communications, 70, 1667-1675, 2016.
• [63] METE, S., OZER, S., ZORLU, H., "System Identification Application Using Hammerstein Model", Sadhana Academy Proceedings in Engineering Sciences, 41, 597-605, 2016.
• [64] DE MOOR, B.L.R.: DaISy, Database for The Identification of Systems. Department of Electrical Engineering, ESAT/ SISTA, K.U. Leuven, Belgium. http://homes.esat. kuleuven.be/~smc/daisy (2006)
• [65] FERON, E., BRENNER, M., PADUANO, J., TUREVSKY, A., “Time-Frequency Analysis for Transfer Function Estimation and Application to Fluetter Clearance”, J. on Guidance, Control & Dynamics, 21,375-382, 1998.