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DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ

Yıl 2012, Cilt: 27 Sayı: 2, 0 - , 19.02.2013

Şaban Özer Hasan Zorlu

Öz

Bu çalışmada kaotik zaman serilerinin kestirimi için doğrusal olmayan polinomsal özbağlanım (polynomialautoregressive – PAR) sistemler kullanılmıştır. Bu amaçla literatürde yer alan Mackey-Glass ve Lorenz kaotiksistemlerine ait zaman serilerinin kestirimi için doğrusal olmayan PAR zaman serilerine dayalı çeşitlimatematiksel model yapıları sunulmuştur. Sunulan modellerdeki parametre değerlerinin belirlenmesi amacıylasezgisel algoritmalardan genetik algoritma (GA), diferansiyel gelişim algoritması (DGA) ve klonal seçmealgoritması (KSA), klasik algoritmalardan ise içsel en küçük kareler (recursive least square-RLS) algoritmasıuyarlanır algoritmalar olarak kullanılmış ve başarımları karşılaştırılmıştır. Benzetim sonuçlarına göre hem kaotiksistemler için sunulan matematiksel model yapıları hem de bu model yapılarına ait parametrelerin belirlenmesiiçin farklı algoritmalarla yapılan optimizasyon işlemleri oldukça başarılı olmuştur.

Anahtar Kelimeler

Kaotik zaman serisi kestirimi Kaotik sistemler PAR sistem Esnek Hesaplama Algoritmaları.

Kaynakça

  • Ljung, L., System Identification: Theory For
  • The User, Englewood Cliffs, NJ, Prentice Hall,
  • -
  • Gauss, K. F., Theory of the Motion of Heavenly
  • Bodies, Dover, 1963.
  • Zadeh, L.A., “From Circuit Theory to System
  • Theory”, Proc IRE, 50, 856-865, 1962.
  • Töderstrom S., System Identification, Prentice-
  • Hall, 1989.
  • Ljung L., Söderström T., Theory and Practice Of
  • Recursive Identification, Cambridge, MA, MIT
  • Press, 1983.
  • Makhoul, J., “Linear Prediction: A Tutorial
  • Review”, Proc. IEEE, Cilt 63, 561-580, 1975.
  • Lim, Y.C., Parker, S.R., “On The Identification Of
  • Systems From Data Measurements Using ARMA
  • Lattice Models”, IEEE TRANS. ASSP, Cilt 4,
  • -827, 1986.
  • Özer, Ş., Taşpınar, N., Güney, K., “ARMA modeli
  • ile Ayrık Zamanlı Lineer Sistemlerin
  • Modellenmesi”, Bilkent Üni. Elektrik-
  • Elektronik ve Bilgisayar Mühendisliği
  • Konferansı Bildiri kitabı, 195-198, 1991.
  • Özer, Ş., Sağıroğlu, Ş., “Kaplan, A., Performance
  • Analysis of Algorithms on Linear ARMA
  • Models”, Proc. Of the Int. Symposium
  • Computer and Information Science XVI, 445-
  • , 2001.
  • Widrow, B, Stearns, D., Adaptive Signal
  • Processing, Prentice Hall, 1985.
  • Honig, H.L., Messerschmitt, D.G., Adaptive
  • Filters Structures, Algorithms and applications,
  • Kluwer Academic Publishers, 1984
  • Isidori A., “Nonlinear Control Systems: An
  • Introduction”, Lecture Notes in Control An
  • Information Science, Cilt 72, Springer-Verlag,
  • Berlin, 1985.
  • Prochazka, A., Neumann, R., “High Frequency
  • Distortion Analysis Of A Semiconductor Diode
  • For CATV Applications”, IEEE Trans. on
  • Consumer Electronics, Cilt CE-21, 120-129, 1975.
  • Nam, S.W., Powers, E.J., “Application Of Higher
  • Order Spectral Analysis To Cubically Nonlinear
  • System Identification”, IEEE Trans. on Signal
  • Processing, Cilt 42, 2124-2135, 1994.
  • Özgunel, S., Kayran, A. H., Panayirci, E.,
  • “Nonlinear Channel Equalization and
  • Identification”, Proc. Of Int. Conf. on Digital
  • Signal Proc., 260-265, Florence,1991.
  • Özden, M. T., Kayran, A. H., Panayirci, E.,
  • “Adaptive Volterra Filtering with Complete
  • Lattice Orthogonalization”, IEEE Trans. On
  • Signal Proc., Cilt 44, 2092-2098, 1996.
  • Griffith, D.W., Arce, G.R., “Partially Decoupled
  • Volterra Filters: Formulation and LMS
  • Adaptation”, IEEE Trans. on Signal Processing,
  • Cilt 45, 1485-1494, 1997.
  • Lee, J., Mathews, V.J., “A Stability Condition For
  • Certain Bilinear Systems”, IEEE Trans. on
  • Signal Processing, Cilt 42, 1871-1873, 1994.
  • Cowan, C.F, Grant, P.M., “Nonlinear System
  • Modelling - Concept and Application”,
  • Proceedings Of IEEE Int. Conference On
  • Acoustic Speech and Signal Processing, 1-4, San
  • Diego, California, 1984.
  • Priestley, M. B., Nonlinear and Non-Stationary
  • Time Series Analysis, Academic Press,1988.
  • Rauf, F., Nonlinear Adaptive Filtering : A
  • Unified Approach, Ph.D. Thesis, Boston
  • University, Boston, 1993.
  • Giannakis, G.B., Serpedin, E., “A Bibliography on
  • Nonlinear System Identification”, Signal
  • Processing, Cilt 81, 533-580, 2001.
  • Khurram, M. U., Fast Learning Nonlinear
  • Adaptive Filtering Structures, Ph.D. Thesis,
  • University Of Boston, 1994.
  • Koh, T., Powers, E. J., “Scond Order Volterra
  • Filtering and Its Application to nonlinear system
  • identification”, IEEE Trans. on ASSP, Cilt 33,
  • -1455, 1985.
  • Leuschen, M.L., Walker, I.D.; Cavallaro, J.R.;”
  • Fault residual generation via nonlinear analytical
  • redundancy”, IEEE Transactions on Control
  • Systems Technology, Cilt:13, 452-458, 2005.
  • Goldberger, AL., “Applications of chaos to
  • physiology and medicine”, In: Kim JH, Stringer
  • J, eds. Applied Chaos. New York: John Wiley &
  • Sons, 321-329, 1992.
  • Sağıroğlu, Ş., Özer, Ş., “A Neural Identifier for
  • Linear Dynamic Systems”, Journal of
  • Polytechnic, Cilt 4, 55-61, 2001.
  • Özer, Ş., Sağıroğlu Ş.,Zorlu H., “Arma Sistem
  • Modellemede Klasik ve Yapay Sinir Ağları
  • Algoritmalarının Karşılaştırılması”, Elektrik-
  • Elektronik-Bilgisayar Mühendisliği 10.Ulusal
  • Kongresi Bildiriler Kitabı, 434-437, 2003.
  • Narendra, K.S., Mukhopadhyay, S., “Adaptive
  • Control Using Neural Networks and Approximate
  • Models”, IEEE Trans. on Neural Networks, Cilt
  • , 475-485, 1997.
  • Kaplan, A., Nümerik Tabu Arama Algoritması,
  • Doktora Tezi, Erciyes Üniversitesi, Kayseri, 2001
  • Wang, Z., Gu, H., “Parameter Identification of
  • Bilinear System Based on Genetic Algorithm”,
  • LNCS 4688, 83 – 91, 2007.
  • Karaboga, N., “Digital IIR Filter Design Using
  • Differential Evolution Algorithm”, EURASIP
  • Journal on Applied Signal Processing, Cilt 8,
  • –1276, 2005.
  • Cheng, S. L., Hwang, C., “Optimal approximation
  • of linear systems by a differential algorithm”,
  • IEEE Trans Syst Man and Cybernet—Part A
  • Syst Humans, Cilt 31, 698–707, 2001.
  • Chang, W.D., “Parameter identification of
  • Rossler’s chaotic system by an evolutionary
  • algorithm”, Chaos, Solitons and Fractals, Cilt
  • , 1047–1053, 2006.
  • Chang, W.D., “Parameter identification of Chen
  • and Lü systems: A differential evolution
  • approach”, Chaos, Solitons and Fractals, Cilt 32,
  • –1476, 2007.
  • Price, K. V., An introduction to differential
  • evolution, in D. Corne, M. Dorigo, and F. Glover,
  • (Ed), New Ideas in Optimization, chapter 6,
  • McGraw Hill, London, UK, 1999.
  • Bağış, S., Yapay Zeka Algoritmaları
  • Kullanılarak Sistem Modelleme, Yüksek Lisans
  • Tezi, Erciyes Üniversitesi, Kayseri, 2009.
  • Kristinsson, K., Dumont, G.A., “System
  • Identification and Control using Genetic
  • Algorithms”, IEEE Trans. on Systems, Man,
  • and Cybernetics, Cilt 22-5, 1033-1046, 1992.
  • Pham, D.T., Karaboga, D., Intelligent
  • Optimisation Techniques: Genetic Algorithms,
  • Tabu Search, Simulated Annealing and Neural
  • Networks, Springer- Verlag, 2000.
  • Madar, J., Abonyi, J., Szeifert, F., “Genetic
  • Programming for the Identification of Nonlinear
  • Input−Output Models”, Ind. Eng. Chem. Res.,
  • Cilt 44-9, 3178-3186, 2005.
  • Bağış, A., Özçelik, Y., “Gerçek Kodlu Genetik
  • Algoritma Kullanılarak Sistem Kimliklendirme”,
  • Elektrik, Elektronik, Bilgisayar,
  • Biyomedikal Mühendisliği Ulusal Kongresi,
  • Eskişehir, 2007.
  • Bagis, A., “Performance Comparison of Genetic
  • and Tabu Search Algorithms for System
  • Identification”, Lecture Notes in Computer
  • Science (including subseries Lecture Notes in
  • Artificial Intelligence and Lecture Notes in
  • Bioinformatics), Cilt 4251 LNAI-I, 94-101, 2006.
  • Price, K., Storn, R., “Differential Evolution:
  • Numerical Optimization Made Easy”, Dr. Dobb’s
  • J., Cilt 78, 18–24, 1997.
  • Bağış, A., Özçelik, Y., “Farksal Evrim
  • Algoritması Kullanılarak Sistem Kimliklendirme”,
  • Otomatik Kontrol Ulusal Toplantısı (TOK’07),
  • -183, İstanbul, 2007.
  • Hou, Z., “Wiener Model Identification based on
  • Adaptive Particle Swarm Optimization”,
  • Proceedings of the Seventh International
  • Conference on Machine Learning and
  • Cybernetics, 1041-1045, Kunming,12-15 July
  • -
  • Liu, L., Liu, W., Cartes, D.A., “Particle Swarm
  • Optimization based Parameter Identification
  • Applied to Permanent Magnet Synchronous
  • Motors”, Engineering Applications of Artificial
  • Intelligence, Cilt 21, 1092–1100, 2008.
  • Zorlu, H., Özer Ş., “Doğrusal Olmayan
  • Sistemlerin Klonal Seçme Algoritması
  • Kullanılarak Kimliklendirilmesi”, Sinyal İşleme
  • ve Uygulamaları Kurultayı (SİU), 2009.
  • Subudhi, B., Debashisha, J., “A Combined
  • Differential Evolution and Neural Network
  • Approach to Nonlinear System Identification”,
  • IEEE Region 10 Conference, TENCON 2008, 1-
  • , 19-21 Nov. 2008.
  • Subudhi, B., Jena, D., Gupta, M.M., “Memetic
  • Differential Evolution Trained Neural Networks
  • for Nonlinear System Identification”, Third
  • International Conference on Industrial and
  • Information Systems (ICIIS’2008), 1-6, 2008.
  • Karaboğa, D., Yapay Zeka Optimizasyon
  • Algoritmaları, Atlas yayın dağıtım, İstanbul,
  • -
  • Holland, J.H., Adaption in Natural and
  • Artificial Systems, MAMIT Press, Cambridge,
  • -
  • De Castro, L.N., Von Zuben, F.J., “The clonal
  • selection algorithm with engineering
  • applications”, In Workshop Proceedings of
  • GECCO’00, Workshop on Artificial Immune
  • Systems and their Applications, 36–37, Las
  • Vegas, 2000.
  • De Castro, L.N., Von Zuben, F.J.: “Learning and
  • optimization using clonal selection principle”,
  • IEEE Transactions on Evolutionary
  • Computation, Special Issue on Artificial
  • Immune Systems, Cilt 6-3, 239–251, 2001.
  • Aslantas, V., Ozer, S., and Ozturk, S., “A Novel
  • Clonal Selection Algorithm Based Fragile
  • Watermarking Method”, LNCS, Cilt 4628, 358-
  • , 2007.
  • Ada, G. L. and Nossal, G., “The clonal selection
  • theory”, Scientific American, Cilt 257, 50−57,
  • -
  • Lorenz, E.N., “Deterministic Nonperiodic Flow”,
  • Journal of the Athmosferic Sciences, Cilt 20,
  • -141, 1963.
  • González, O.A., Han, G., de Gyvez, J.P., and
  • Edgar, “CMOS Cryptosystem Using a Lorenz
  • Chaotic Oscillator”, Proceedings of the IEEE
  • International Symposium on Circuits and
  • Systems, ISCAS '99, Cilt 5, 442-445, 1999.
  • Chen Y. A., Yang B. A., Dong J. A., Abraham A.,
  • “Time-Series Forecasting Using Flexible Neural
  • Tree Model”, Information Sciences, Cilt 174,
  • –235, 2005.
  • Wang, L.X., Mendel, J.M., “Generating fuzzy
  • rules by learning from examples”, IEEE
  • Transactions on Systems, Man and
  • Cybernetics, Cilt 22, 1414–1427, 1992.
  • Cho, K.B., Wang, B.H., “Radial basis function
  • based adaptive fuzzy systems their application to
  • system identification and prediction”, Fuzzy Sets
  • and Systems, Cilt 83, 325–339, 1995.

Yıl 2012, Cilt: 27 Sayı: 2, 0 - , 19.02.2013

Şaban Özer Hasan Zorlu

Öz

Kaynakça

  • Ljung, L., System Identification: Theory For
  • The User, Englewood Cliffs, NJ, Prentice Hall,
  • -
  • Gauss, K. F., Theory of the Motion of Heavenly
  • Bodies, Dover, 1963.
  • Zadeh, L.A., “From Circuit Theory to System
  • Theory”, Proc IRE, 50, 856-865, 1962.
  • Töderstrom S., System Identification, Prentice-
  • Hall, 1989.
  • Ljung L., Söderström T., Theory and Practice Of
  • Recursive Identification, Cambridge, MA, MIT
  • Press, 1983.
  • Makhoul, J., “Linear Prediction: A Tutorial
  • Review”, Proc. IEEE, Cilt 63, 561-580, 1975.
  • Lim, Y.C., Parker, S.R., “On The Identification Of
  • Systems From Data Measurements Using ARMA
  • Lattice Models”, IEEE TRANS. ASSP, Cilt 4,
  • -827, 1986.
  • Özer, Ş., Taşpınar, N., Güney, K., “ARMA modeli
  • ile Ayrık Zamanlı Lineer Sistemlerin
  • Modellenmesi”, Bilkent Üni. Elektrik-
  • Elektronik ve Bilgisayar Mühendisliği
  • Konferansı Bildiri kitabı, 195-198, 1991.
  • Özer, Ş., Sağıroğlu, Ş., “Kaplan, A., Performance
  • Analysis of Algorithms on Linear ARMA
  • Models”, Proc. Of the Int. Symposium
  • Computer and Information Science XVI, 445-
  • , 2001.
  • Widrow, B, Stearns, D., Adaptive Signal
  • Processing, Prentice Hall, 1985.
  • Honig, H.L., Messerschmitt, D.G., Adaptive
  • Filters Structures, Algorithms and applications,
  • Kluwer Academic Publishers, 1984
  • Isidori A., “Nonlinear Control Systems: An
  • Introduction”, Lecture Notes in Control An
  • Information Science, Cilt 72, Springer-Verlag,
  • Berlin, 1985.
  • Prochazka, A., Neumann, R., “High Frequency
  • Distortion Analysis Of A Semiconductor Diode
  • For CATV Applications”, IEEE Trans. on
  • Consumer Electronics, Cilt CE-21, 120-129, 1975.
  • Nam, S.W., Powers, E.J., “Application Of Higher
  • Order Spectral Analysis To Cubically Nonlinear
  • System Identification”, IEEE Trans. on Signal
  • Processing, Cilt 42, 2124-2135, 1994.
  • Özgunel, S., Kayran, A. H., Panayirci, E.,
  • “Nonlinear Channel Equalization and
  • Identification”, Proc. Of Int. Conf. on Digital
  • Signal Proc., 260-265, Florence,1991.
  • Özden, M. T., Kayran, A. H., Panayirci, E.,
  • “Adaptive Volterra Filtering with Complete
  • Lattice Orthogonalization”, IEEE Trans. On
  • Signal Proc., Cilt 44, 2092-2098, 1996.
  • Griffith, D.W., Arce, G.R., “Partially Decoupled
  • Volterra Filters: Formulation and LMS
  • Adaptation”, IEEE Trans. on Signal Processing,
  • Cilt 45, 1485-1494, 1997.
  • Lee, J., Mathews, V.J., “A Stability Condition For
  • Certain Bilinear Systems”, IEEE Trans. on
  • Signal Processing, Cilt 42, 1871-1873, 1994.
  • Cowan, C.F, Grant, P.M., “Nonlinear System
  • Modelling - Concept and Application”,
  • Proceedings Of IEEE Int. Conference On
  • Acoustic Speech and Signal Processing, 1-4, San
  • Diego, California, 1984.
  • Priestley, M. B., Nonlinear and Non-Stationary
  • Time Series Analysis, Academic Press,1988.
  • Rauf, F., Nonlinear Adaptive Filtering : A
  • Unified Approach, Ph.D. Thesis, Boston
  • University, Boston, 1993.
  • Giannakis, G.B., Serpedin, E., “A Bibliography on
  • Nonlinear System Identification”, Signal
  • Processing, Cilt 81, 533-580, 2001.
  • Khurram, M. U., Fast Learning Nonlinear
  • Adaptive Filtering Structures, Ph.D. Thesis,
  • University Of Boston, 1994.
  • Koh, T., Powers, E. J., “Scond Order Volterra
  • Filtering and Its Application to nonlinear system
  • identification”, IEEE Trans. on ASSP, Cilt 33,
  • -1455, 1985.
  • Leuschen, M.L., Walker, I.D.; Cavallaro, J.R.;”
  • Fault residual generation via nonlinear analytical
  • redundancy”, IEEE Transactions on Control
  • Systems Technology, Cilt:13, 452-458, 2005.
  • Goldberger, AL., “Applications of chaos to
  • physiology and medicine”, In: Kim JH, Stringer
  • J, eds. Applied Chaos. New York: John Wiley &
  • Sons, 321-329, 1992.
  • Sağıroğlu, Ş., Özer, Ş., “A Neural Identifier for
  • Linear Dynamic Systems”, Journal of
  • Polytechnic, Cilt 4, 55-61, 2001.
  • Özer, Ş., Sağıroğlu Ş.,Zorlu H., “Arma Sistem
  • Modellemede Klasik ve Yapay Sinir Ağları
  • Algoritmalarının Karşılaştırılması”, Elektrik-
  • Elektronik-Bilgisayar Mühendisliği 10.Ulusal
  • Kongresi Bildiriler Kitabı, 434-437, 2003.
  • Narendra, K.S., Mukhopadhyay, S., “Adaptive
  • Control Using Neural Networks and Approximate
  • Models”, IEEE Trans. on Neural Networks, Cilt
  • , 475-485, 1997.
  • Kaplan, A., Nümerik Tabu Arama Algoritması,
  • Doktora Tezi, Erciyes Üniversitesi, Kayseri, 2001
  • Wang, Z., Gu, H., “Parameter Identification of
  • Bilinear System Based on Genetic Algorithm”,
  • LNCS 4688, 83 – 91, 2007.
  • Karaboga, N., “Digital IIR Filter Design Using
  • Differential Evolution Algorithm”, EURASIP
  • Journal on Applied Signal Processing, Cilt 8,
  • –1276, 2005.
  • Cheng, S. L., Hwang, C., “Optimal approximation
  • of linear systems by a differential algorithm”,
  • IEEE Trans Syst Man and Cybernet—Part A
  • Syst Humans, Cilt 31, 698–707, 2001.
  • Chang, W.D., “Parameter identification of
  • Rossler’s chaotic system by an evolutionary
  • algorithm”, Chaos, Solitons and Fractals, Cilt
  • , 1047–1053, 2006.
  • Chang, W.D., “Parameter identification of Chen
  • and Lü systems: A differential evolution
  • approach”, Chaos, Solitons and Fractals, Cilt 32,
  • –1476, 2007.
  • Price, K. V., An introduction to differential
  • evolution, in D. Corne, M. Dorigo, and F. Glover,
  • (Ed), New Ideas in Optimization, chapter 6,
  • McGraw Hill, London, UK, 1999.
  • Bağış, S., Yapay Zeka Algoritmaları
  • Kullanılarak Sistem Modelleme, Yüksek Lisans
  • Tezi, Erciyes Üniversitesi, Kayseri, 2009.
  • Kristinsson, K., Dumont, G.A., “System
  • Identification and Control using Genetic
  • Algorithms”, IEEE Trans. on Systems, Man,
  • and Cybernetics, Cilt 22-5, 1033-1046, 1992.
  • Pham, D.T., Karaboga, D., Intelligent
  • Optimisation Techniques: Genetic Algorithms,
  • Tabu Search, Simulated Annealing and Neural
  • Networks, Springer- Verlag, 2000.
  • Madar, J., Abonyi, J., Szeifert, F., “Genetic
  • Programming for the Identification of Nonlinear
  • Input−Output Models”, Ind. Eng. Chem. Res.,
  • Cilt 44-9, 3178-3186, 2005.
  • Bağış, A., Özçelik, Y., “Gerçek Kodlu Genetik
  • Algoritma Kullanılarak Sistem Kimliklendirme”,
  • Elektrik, Elektronik, Bilgisayar,
  • Biyomedikal Mühendisliği Ulusal Kongresi,
  • Eskişehir, 2007.
  • Bagis, A., “Performance Comparison of Genetic
  • and Tabu Search Algorithms for System
  • Identification”, Lecture Notes in Computer
  • Science (including subseries Lecture Notes in
  • Artificial Intelligence and Lecture Notes in
  • Bioinformatics), Cilt 4251 LNAI-I, 94-101, 2006.
  • Price, K., Storn, R., “Differential Evolution:
  • Numerical Optimization Made Easy”, Dr. Dobb’s
  • J., Cilt 78, 18–24, 1997.
  • Bağış, A., Özçelik, Y., “Farksal Evrim
  • Algoritması Kullanılarak Sistem Kimliklendirme”,
  • Otomatik Kontrol Ulusal Toplantısı (TOK’07),
  • -183, İstanbul, 2007.
  • Hou, Z., “Wiener Model Identification based on
  • Adaptive Particle Swarm Optimization”,
  • Proceedings of the Seventh International
  • Conference on Machine Learning and
  • Cybernetics, 1041-1045, Kunming,12-15 July
  • -
  • Liu, L., Liu, W., Cartes, D.A., “Particle Swarm
  • Optimization based Parameter Identification
  • Applied to Permanent Magnet Synchronous
  • Motors”, Engineering Applications of Artificial
  • Intelligence, Cilt 21, 1092–1100, 2008.
  • Zorlu, H., Özer Ş., “Doğrusal Olmayan
  • Sistemlerin Klonal Seçme Algoritması
  • Kullanılarak Kimliklendirilmesi”, Sinyal İşleme
  • ve Uygulamaları Kurultayı (SİU), 2009.
  • Subudhi, B., Debashisha, J., “A Combined
  • Differential Evolution and Neural Network
  • Approach to Nonlinear System Identification”,
  • IEEE Region 10 Conference, TENCON 2008, 1-
  • , 19-21 Nov. 2008.
  • Subudhi, B., Jena, D., Gupta, M.M., “Memetic
  • Differential Evolution Trained Neural Networks
  • for Nonlinear System Identification”, Third
  • International Conference on Industrial and
  • Information Systems (ICIIS’2008), 1-6, 2008.
  • Karaboğa, D., Yapay Zeka Optimizasyon
  • Algoritmaları, Atlas yayın dağıtım, İstanbul,
  • -
  • Holland, J.H., Adaption in Natural and
  • Artificial Systems, MAMIT Press, Cambridge,
  • -
  • De Castro, L.N., Von Zuben, F.J., “The clonal
  • selection algorithm with engineering
  • applications”, In Workshop Proceedings of
  • GECCO’00, Workshop on Artificial Immune
  • Systems and their Applications, 36–37, Las
  • Vegas, 2000.
  • De Castro, L.N., Von Zuben, F.J.: “Learning and
  • optimization using clonal selection principle”,
  • IEEE Transactions on Evolutionary
  • Computation, Special Issue on Artificial
  • Immune Systems, Cilt 6-3, 239–251, 2001.
  • Aslantas, V., Ozer, S., and Ozturk, S., “A Novel
  • Clonal Selection Algorithm Based Fragile
  • Watermarking Method”, LNCS, Cilt 4628, 358-
  • , 2007.
  • Ada, G. L. and Nossal, G., “The clonal selection
  • theory”, Scientific American, Cilt 257, 50−57,
  • -
  • Lorenz, E.N., “Deterministic Nonperiodic Flow”,
  • Journal of the Athmosferic Sciences, Cilt 20,
  • -141, 1963.
  • González, O.A., Han, G., de Gyvez, J.P., and
  • Edgar, “CMOS Cryptosystem Using a Lorenz
  • Chaotic Oscillator”, Proceedings of the IEEE
  • International Symposium on Circuits and
  • Systems, ISCAS '99, Cilt 5, 442-445, 1999.
  • Chen Y. A., Yang B. A., Dong J. A., Abraham A.,
  • “Time-Series Forecasting Using Flexible Neural
  • Tree Model”, Information Sciences, Cilt 174,
  • –235, 2005.
  • Wang, L.X., Mendel, J.M., “Generating fuzzy
  • rules by learning from examples”, IEEE
  • Transactions on Systems, Man and
  • Cybernetics, Cilt 22, 1414–1427, 1992.
  • Cho, K.B., Wang, B.H., “Radial basis function
  • based adaptive fuzzy systems their application to
  • system identification and prediction”, Fuzzy Sets
  • and Systems, Cilt 83, 325–339, 1995.
Toplam 227 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Şaban Özer Bu kişi benim

Hasan Zorlu Bu kişi benim

Yayımlanma Tarihi 19 Şubat 2013
Gönderilme Tarihi 19 Şubat 2013
Yayımlandığı Sayı Yıl 2012 Cilt: 27 Sayı: 2

Kaynak Göster

APA Özer, Ş., & Zorlu, H. (2013). DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 27(2).
AMA Özer Ş, Zorlu H. DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ. GUMMFD. Mart 2013;27(2).
Chicago Özer, Şaban, ve Hasan Zorlu. “DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 27, sy. 2 (Mart 2013).
EndNote Özer Ş, Zorlu H (01 Mart 2013) DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 27 2
IEEE Ş. Özer ve H. Zorlu, “DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ”, GUMMFD, c. 27, sy. 2, 2013.
ISNAD Özer, Şaban - Zorlu, Hasan. “DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 27/2 (Mart 2013).
JAMA Özer Ş, Zorlu H. DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ. GUMMFD. 2013;27.
MLA Özer, Şaban ve Hasan Zorlu. “DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 27, sy. 2, 2013.
Vancouver Özer Ş, Zorlu H. DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ. GUMMFD. 2013;27(2).