DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ

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

1. Ljung, L., System Identification: Theory For
2. The User, Englewood Cliffs, NJ, Prentice Hall,
3. -
4. Gauss, K. F., Theory of the Motion of Heavenly
5. Bodies, Dover, 1963.
6. Zadeh, L.A., “From Circuit Theory to System
7. Theory”, Proc IRE, 50, 856-865, 1962.
8. Töderstrom S., System Identification, Prentice-

9. Hall, 1989.
10. Ljung L., Söderström T., Theory and Practice Of
11. Recursive Identification, Cambridge, MA, MIT
12. Press, 1983.
13. Makhoul, J., “Linear Prediction: A Tutorial
14. Review”, Proc. IEEE, Cilt 63, 561-580, 1975.
15. Lim, Y.C., Parker, S.R., “On The Identification Of
16. Systems From Data Measurements Using ARMA
17. Lattice Models”, IEEE TRANS. ASSP, Cilt 4,
18. -827, 1986.
19. Özer, Ş., Taşpınar, N., Güney, K., “ARMA modeli
20. ile Ayrık Zamanlı Lineer Sistemlerin
21. Modellenmesi”, Bilkent Üni. Elektrik-
22. Elektronik ve Bilgisayar Mühendisliği
23. Konferansı Bildiri kitabı, 195-198, 1991.
24. Özer, Ş., Sağıroğlu, Ş., “Kaplan, A., Performance
25. Analysis of Algorithms on Linear ARMA
26. Models”, Proc. Of the Int. Symposium
27. Computer and Information Science XVI, 445-
28. , 2001.
29. Widrow, B, Stearns, D., Adaptive Signal
30. Processing, Prentice Hall, 1985.
31. Honig, H.L., Messerschmitt, D.G., Adaptive
32. Filters Structures, Algorithms and applications,
33. Kluwer Academic Publishers, 1984
34. Isidori A., “Nonlinear Control Systems: An
35. Introduction”, Lecture Notes in Control An
36. Information Science, Cilt 72, Springer-Verlag,
37. Berlin, 1985.
38. Prochazka, A., Neumann, R., “High Frequency
39. Distortion Analysis Of A Semiconductor Diode
40. For CATV Applications”, IEEE Trans. on
41. Consumer Electronics, Cilt CE-21, 120-129, 1975.
42. Nam, S.W., Powers, E.J., “Application Of Higher
43. Order Spectral Analysis To Cubically Nonlinear
44. System Identification”, IEEE Trans. on Signal
45. Processing, Cilt 42, 2124-2135, 1994.
46. Özgunel, S., Kayran, A. H., Panayirci, E.,
47. “Nonlinear Channel Equalization and
48. Identification”, Proc. Of Int. Conf. on Digital
49. Signal Proc., 260-265, Florence,1991.
50. Özden, M. T., Kayran, A. H., Panayirci, E.,
51. “Adaptive Volterra Filtering with Complete
52. Lattice Orthogonalization”, IEEE Trans. On
53. Signal Proc., Cilt 44, 2092-2098, 1996.
54. Griffith, D.W., Arce, G.R., “Partially Decoupled
55. Volterra Filters: Formulation and LMS
56. Adaptation”, IEEE Trans. on Signal Processing,
57. Cilt 45, 1485-1494, 1997.
58. Lee, J., Mathews, V.J., “A Stability Condition For
59. Certain Bilinear Systems”, IEEE Trans. on
60. Signal Processing, Cilt 42, 1871-1873, 1994.
61. Cowan, C.F, Grant, P.M., “Nonlinear System
62. Modelling - Concept and Application”,
63. Proceedings Of IEEE Int. Conference On
64. Acoustic Speech and Signal Processing, 1-4, San
65. Diego, California, 1984.
66. Priestley, M. B., Nonlinear and Non-Stationary
67. Time Series Analysis, Academic Press,1988.
68. Rauf, F., Nonlinear Adaptive Filtering : A
69. Unified Approach, Ph.D. Thesis, Boston
70. University, Boston, 1993.
71. Giannakis, G.B., Serpedin, E., “A Bibliography on
72. Nonlinear System Identification”, Signal
73. Processing, Cilt 81, 533-580, 2001.
74. Khurram, M. U., Fast Learning Nonlinear
75. Adaptive Filtering Structures, Ph.D. Thesis,
76. University Of Boston, 1994.
77. Koh, T., Powers, E. J., “Scond Order Volterra
78. Filtering and Its Application to nonlinear system
79. identification”, IEEE Trans. on ASSP, Cilt 33,
80. -1455, 1985.
81. Leuschen, M.L., Walker, I.D.; Cavallaro, J.R.;”
82. Fault residual generation via nonlinear analytical
83. redundancy”, IEEE Transactions on Control
84. Systems Technology, Cilt:13, 452-458, 2005.
85. Goldberger, AL., “Applications of chaos to
86. physiology and medicine”, In: Kim JH, Stringer
87. J, eds. Applied Chaos. New York: John Wiley &
88. Sons, 321-329, 1992.
89. Sağıroğlu, Ş., Özer, Ş., “A Neural Identifier for
90. Linear Dynamic Systems”, Journal of
91. Polytechnic, Cilt 4, 55-61, 2001.
92. Özer, Ş., Sağıroğlu Ş.,Zorlu H., “Arma Sistem
93. Modellemede Klasik ve Yapay Sinir Ağları
94. Algoritmalarının Karşılaştırılması”, Elektrik-
95. Elektronik-Bilgisayar Mühendisliği 10.Ulusal
96. Kongresi Bildiriler Kitabı, 434-437, 2003.
97. Narendra, K.S., Mukhopadhyay, S., “Adaptive
98. Control Using Neural Networks and Approximate
99. Models”, IEEE Trans. on Neural Networks, Cilt
100. , 475-485, 1997.
101. Kaplan, A., Nümerik Tabu Arama Algoritması,
102. Doktora Tezi, Erciyes Üniversitesi, Kayseri, 2001
103. Wang, Z., Gu, H., “Parameter Identification of
104. Bilinear System Based on Genetic Algorithm”,
105. LNCS 4688, 83 – 91, 2007.
106. Karaboga, N., “Digital IIR Filter Design Using
107. Differential Evolution Algorithm”, EURASIP
108. Journal on Applied Signal Processing, Cilt 8,
109. –1276, 2005.
110. Cheng, S. L., Hwang, C., “Optimal approximation
111. of linear systems by a differential algorithm”,
112. IEEE Trans Syst Man and Cybernet—Part A
113. Syst Humans, Cilt 31, 698–707, 2001.
114. Chang, W.D., “Parameter identification of
115. Rossler’s chaotic system by an evolutionary
116. algorithm”, Chaos, Solitons and Fractals, Cilt
117. , 1047–1053, 2006.
118. Chang, W.D., “Parameter identification of Chen
119. and Lü systems: A differential evolution
120. approach”, Chaos, Solitons and Fractals, Cilt 32,
121. –1476, 2007.
122. Price, K. V., An introduction to differential
123. evolution, in D. Corne, M. Dorigo, and F. Glover,
124. (Ed), New Ideas in Optimization, chapter 6,
125. McGraw Hill, London, UK, 1999.
126. Bağış, S., Yapay Zeka Algoritmaları
127. Kullanılarak Sistem Modelleme, Yüksek Lisans
128. Tezi, Erciyes Üniversitesi, Kayseri, 2009.
129. Kristinsson, K., Dumont, G.A., “System
130. Identification and Control using Genetic
131. Algorithms”, IEEE Trans. on Systems, Man,
132. and Cybernetics, Cilt 22-5, 1033-1046, 1992.
133. Pham, D.T., Karaboga, D., Intelligent
134. Optimisation Techniques: Genetic Algorithms,
135. Tabu Search, Simulated Annealing and Neural
136. Networks, Springer- Verlag, 2000.
137. Madar, J., Abonyi, J., Szeifert, F., “Genetic
138. Programming for the Identification of Nonlinear
139. Input−Output Models”, Ind. Eng. Chem. Res.,
140. Cilt 44-9, 3178-3186, 2005.
141. Bağış, A., Özçelik, Y., “Gerçek Kodlu Genetik
142. Algoritma Kullanılarak Sistem Kimliklendirme”,
143. Elektrik, Elektronik, Bilgisayar,
144. Biyomedikal Mühendisliği Ulusal Kongresi,
145. Eskişehir, 2007.
146. Bagis, A., “Performance Comparison of Genetic
147. and Tabu Search Algorithms for System
148. Identification”, Lecture Notes in Computer
149. Science (including subseries Lecture Notes in
150. Artificial Intelligence and Lecture Notes in
151. Bioinformatics), Cilt 4251 LNAI-I, 94-101, 2006.
152. Price, K., Storn, R., “Differential Evolution:
153. Numerical Optimization Made Easy”, Dr. Dobb’s
154. J., Cilt 78, 18–24, 1997.
155. Bağış, A., Özçelik, Y., “Farksal Evrim
156. Algoritması Kullanılarak Sistem Kimliklendirme”,
157. Otomatik Kontrol Ulusal Toplantısı (TOK’07),
158. -183, İstanbul, 2007.
159. Hou, Z., “Wiener Model Identification based on
160. Adaptive Particle Swarm Optimization”,
161. Proceedings of the Seventh International
162. Conference on Machine Learning and
163. Cybernetics, 1041-1045, Kunming,12-15 July
164. -
165. Liu, L., Liu, W., Cartes, D.A., “Particle Swarm
166. Optimization based Parameter Identification
167. Applied to Permanent Magnet Synchronous
168. Motors”, Engineering Applications of Artificial
169. Intelligence, Cilt 21, 1092–1100, 2008.
170. Zorlu, H., Özer Ş., “Doğrusal Olmayan
171. Sistemlerin Klonal Seçme Algoritması
172. Kullanılarak Kimliklendirilmesi”, Sinyal İşleme
173. ve Uygulamaları Kurultayı (SİU), 2009.
174. Subudhi, B., Debashisha, J., “A Combined
175. Differential Evolution and Neural Network
176. Approach to Nonlinear System Identification”,
177. IEEE Region 10 Conference, TENCON 2008, 1-
178. , 19-21 Nov. 2008.
179. Subudhi, B., Jena, D., Gupta, M.M., “Memetic
180. Differential Evolution Trained Neural Networks
181. for Nonlinear System Identification”, Third
182. International Conference on Industrial and
183. Information Systems (ICIIS’2008), 1-6, 2008.
184. Karaboğa, D., Yapay Zeka Optimizasyon
185. Algoritmaları, Atlas yayın dağıtım, İstanbul,
186. -
187. Holland, J.H., Adaption in Natural and
188. Artificial Systems, MAMIT Press, Cambridge,
189. -
190. De Castro, L.N., Von Zuben, F.J., “The clonal
191. selection algorithm with engineering
192. applications”, In Workshop Proceedings of
193. GECCO’00, Workshop on Artificial Immune
194. Systems and their Applications, 36–37, Las
195. Vegas, 2000.
196. De Castro, L.N., Von Zuben, F.J.: “Learning and
197. optimization using clonal selection principle”,
198. IEEE Transactions on Evolutionary
199. Computation, Special Issue on Artificial
200. Immune Systems, Cilt 6-3, 239–251, 2001.
201. Aslantas, V., Ozer, S., and Ozturk, S., “A Novel
202. Clonal Selection Algorithm Based Fragile
203. Watermarking Method”, LNCS, Cilt 4628, 358-
204. , 2007.
205. Ada, G. L. and Nossal, G., “The clonal selection
206. theory”, Scientific American, Cilt 257, 50−57,
207. -
208. Lorenz, E.N., “Deterministic Nonperiodic Flow”,
209. Journal of the Athmosferic Sciences, Cilt 20,
210. -141, 1963.
211. González, O.A., Han, G., de Gyvez, J.P., and
212. Edgar, “CMOS Cryptosystem Using a Lorenz
213. Chaotic Oscillator”, Proceedings of the IEEE
214. International Symposium on Circuits and
215. Systems, ISCAS '99, Cilt 5, 442-445, 1999.
216. Chen Y. A., Yang B. A., Dong J. A., Abraham A.,
217. “Time-Series Forecasting Using Flexible Neural
218. Tree Model”, Information Sciences, Cilt 174,
219. –235, 2005.
220. Wang, L.X., Mendel, J.M., “Generating fuzzy
221. rules by learning from examples”, IEEE
222. Transactions on Systems, Man and
223. Cybernetics, Cilt 22, 1414–1427, 1992.
224. Cho, K.B., Wang, B.H., “Radial basis function
225. based adaptive fuzzy systems their application to
226. system identification and prediction”, Fuzzy Sets
227. and Systems, Cilt 83, 325–339, 1995.