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DOĞRUSAL OLMAYAN PAR SİSTEMLER KULLANILARAK KAOTİK ZAMAN SERİSİ KESTİRİMİ

CHAOTIC TIME SERIES PREDICTION USING THE NONLINEAR PAR SYSTEMS

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Abstract (2. Language): 
In this work, the nonlinear polynomial autoregressive (PAR) system has been applied to predict chaotic time series. For this purpose, different mathematical model structures based on nonlinear PAR time series have been presented to prediction of Mackey-Glass and Lorenz chaotic time series. As adaptive algorithms, Genetic algorithm (GA), differential evolution algorithm (DEA) and clonal selection algorithm (CSA) in heuristic algorithms, recursive least square algorithm (RLS) in classic algorithms have been used to determine the parameter values in the presented models and compared its performances. The simulation results have shown that both the presented mathematical models for chaotic systems and optimization works using the different algorithms to determine the parameters of these model structures have been highly successful.
Abstract (Original Language): 
Bu çalışmada kaotik zaman serilerinin kestirimi için doğrusal olmayan polinomsal özbağlanım (polynomial autoregressive – PAR) sistemler kullanılmıştır. Bu amaçla literatürde yer alan Mackey-Glass ve Lorenz kaotik sistemlerine ait zaman serilerinin kestirimi için doğrusal olmayan PAR zaman serilerine dayalı çeşitli matematiksel model yapıları sunulmuştur. Sunulan modellerdeki parametre değerlerinin belirlenmesi amacıyla sezgisel algoritmalardan genetik algoritma (GA), diferansiyel gelişim algoritması (DGA) ve klonal seçme algoritması (KSA), klasik algoritmalardan ise içsel en küçük kareler (recursive least square-RLS) algoritması uyarlanır algoritmalar olarak kullanılmış ve başarımları karşılaştırılmıştır. Benzetim sonuçlarına göre hem kaotik sistemler için sunulan matematiksel model yapıları hem de bu model yapılarına ait parametrelerin belirlenmesi için farklı algoritmalarla yapılan optimizasyon işlemleri oldukça başarılı olmuştur.
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