AR SİSTEM MODELLEMEDE FARKLI ALGORİTMALARIN KARŞILAŞTIRILMASI

Öz

Bu makalede, yazarlar tarafından geliştirilen sayısal tabu araştırma algoritmasının, AR (Auto Regressive) sistem modelleme performansı analiz edilmiş ve karşılaştırılmıştır. Bu karşılaştırmada, en küçük kafes kareler, çift kafes, “affine” projeksiyon, en küçük ortalama kareler, normalize edilmiş en küçük ortalama kareler ve özyineli (recursive) en küçük kareler, uyarlanabilir klasik metotlar iken 8 farklı eğitim algoritması ile eğitilmiş yapay sinir ağları, klasik ve sayısal (nümerik) tabu araştırma algoritması kullanılmıştır. Bu çalışmada, 16 farklı algoritmanın modelleme performansı 4. ve 6. dereceden iki farklı AR sistem üzerinde test edilmiştir. Genel olarak, yazarlar tarafından geliştirilen sayısal tabu araştırma algoritmasının, doğrusal AR sistem modellemede daha başarılı olduğu anlaşılmıştır

Anahtar Kelimeler

• AR sistem, modelleme, yapay sinir ağları, uyarlanabilir metotlar, tabu araştırma, algoritma

Kaynakça

1. Haykin, S., Adaptive Filter Theory, 3rd ed., Englewood Cliffs, NJ, Prentice-Hall, 1996.
2. Widrow, B. ve Stearns, S.D., Adaptive Signal Processing. Englewood Cliffs, Prentice- Hall, NJ, 1985.
3. Macchi, O., The Least Mean Squares Approach with Applications in Transmission. Wiley, New York, 1995.
4. Eleftheriou, E. ve Falconer, D., Tracking properties and steady-state performance of RLS adaptive filter algorithms, IEEE Trans. Acoust., Speech, Signal Processing, Cilt ASSP-34, 1097-1110, Oct. 1986.
5. Friedlander, B., Lattice filter for adaptive processing, Proc. IEEE, Cilt 70, 829-867, Aug. 1982.
6. Tanaka, M., Kaneda, Y. Makino, S. ve Kojima, J., A Block Exact Fast Affine Projection Algorithm, IEEE Trans. Speech and Audio Processing, Cilt 7, 79-87, Jan. 1999.
7. Özer, Ş., Güney, K. ve Kaplan, A., AR model parametrelerini ve derecesini tahmin etme metodları, Politeknik Dergisi, Cilt 3, No 3, 67-76, 2000.
8. Peters, S. D. ve Antoniu, A., A Self-Tuning NLMS Adaptive Filter Using Parallel Adaptation, IEEE Trans. on Circuits & Systems-II Analog and Digital Signal Processing, Cilt 44, No 1, 11-21, January 1997.

9. Chansarkar, M. M. ve Desai, U.B., A Robust Recursive Least Squares Algorithm, IEEE Trans. on Signal Processing, Cilt 45, No 7, 1726-1735, July 1997.
10. Goodwin, K. Adaptive Filtering, Prediction and Control, Prentice-Hall, 1990.
11. Swami, A. ve Mendel, J.M., Lattice Algorithms For Recursive Instrumental Variable Methods, International Journal Of Adaptive Control and Signal Processing, 1996.
12. Farhang-Boroujeny, B., Fast LMS/Newton Algorithms Based on Autoregressive Modelling ve Their Application To Acoustic Echo Cancellation, IEEE Trans. on Signal Processing, Cilt 45, No 8, 1987-2000, August 1997.
13. Haykin, S., Neural Networks: A Comprehensive Foundation, Macmillan College Publishing Company, New York, USA, ISBN 0-02-352761-7, 1994.
14. Rumelhart, D. E. ve McClelland, J. L., Parallel Distributed Processing. Cilt 1, The MIT Press, Cambridge, 1986.
15. Battiti, R., First and Second Order Methods for Learning: Between Steepest Descent and Newton's Method, Neural Computation, Cilt 4, No 2, 141-166, 1992.
16. Gill, P. E., Murray, W. ve Wright, M. H., Practical Optimization, Academic Press, New York, 1981.
17. Levenberg, K., A Method For the Solution of Certain Nonlinear Problems in Least Squares, Quart. Appl. Math., Cilt 2, 164-168, 1944.
18. Marquardt, D. W., An Algorithm For Least-Squares Estimation of Nonlinear Parameters, J. Soc. Ind. Appl. Math., Cilt 11, 431-441, 1963.
19. Powell, M. J. D., Restart Procedures for the Conjugate Gradient Method, Mathematical Programming, Cilt 12, 241-254, 1977.
20. Scales, L. E., Introduction to Non-Linear Optimization, Springer-Verlag, New York, 1985.
21. Riedmiller, M. ve Braun, H., A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm, Proceedings of the IEEE Int. Conf. On Neural Networks, San Francisco, CA, 586-591, 1993.
22. Sağıroğlu, Ş. Beşdok, E., ve Erler, M., Mühendislikte Yapay Zeka Uygulamaları I: Yapay Sinir Ağları, Ufuk Kitabevi, Kayseri, 2003.
23. Glover, F., Tabu Search - Part I, ORSA Journal on Computing, Cilt 1, No 3, 190-206, 1989.
24. Glover, F. Tabu Search - Part II, ORSA Journal on Computing, Cilt 2, No 1, 4-32, 1990.
25. Brucker, P. An Efficient Algorithm for the Job-shop Problem With Two Jobs, Computing, Cilt 40, 353-359, 1988.
26. Hao, J.K. Dorne, R. ve Galinier, P., Tabu Search For Frequency Assignment In Mobile Radio Networks, Journal Of Heuristics, Cilt 4, No 1, 47-62, 1998.
27. Pham, D. T. ve Karaboga, D., Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks, Springer Verlag, 2000.
28. Karaboga, D., ve Kaplan, A., Optimizing Multivariable Functions Using Tabu Search Algorithm, In The Tenth Int. Symp. on Comp. and Inf. Sciences, (ISCIS X), October 30, Turkey, Cilt 2, 793-799, 1995.
29. Karaboga, D., Güney, K., Kaplan, ve A., Akdağlı, A., A new effective side length expression obtained using a modified tabu search algorithm for the resonant frequency of a triangular microstrip antenna. International Journal of RF and Microwave Computer-Aided Engineering, Cilt 8, 4-10, 1998.
30. Özer, Ş., Güney, K., ve Kaplan, A., Calculation Of Characteristic Impedance and Dielectric Constant Of Coplanar Waveguide With The Use Of Fuzzy Inference Systems, TAINN'99, Istanbul, 187-196, 1999.
31. Özer, Ş., Güney, K., ve Kaplan, A., Computation Of The Resonant Frequency Of Electrically Thin and Thick Rectangular Microstrip Antennas With The Use Of Fuzzy Inference Systems, Int. Jour. of RF and Microwave Computer-Aided Engineering, Cilt 10, No 2, 108-119, 2000.
32. Kaplan, A., Güney, K., ve Özer, Ş., Fuzzy associative memories for the Computation of the bandwidth of rectangular microstrip antennas with thin and thick substrates. Int. J. Electronics, Cilt 88, No 2, 189-195, 2001.