Dalgacık Dönüşümü Tekniği Kullanılarak Akım Serilerinin Modellenmesi
Dalgacık Dönüşümü Tekniği Kullanılarak Akım Serilerinin Modellenmesi
Dosyalar
Tarih
Yazarlar
Küçük, Murat
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Tabi olaylar kararsız yapılarına rağmen, aslında içlerinde farklı zamanlarda oluşmuş bir çok periyodik bileşen barındırırlar. Dalgacık dönüşümü tekniği son yirmi yıldır kullanılmakta ve özellikle yer bilimleri sahasındaki bir çok ölçüm serisinin analizinde eski tekniklere göre iyi sonuçlar vermektedir. Kararsız seriler olarak akım serilerinin analizi, su kaynakları sistemlerinin planlaması ve tasarımında büyük rol oynar. Bu çalışmada ilk defa nehir akımlarının modellenmesinde dalgacık dönüşümü teknikleri uygulanmıştır. Tez çalışmasında, istasyonlar arası akım tahminlerinde kullanılan regresyon modelinde ki ölçüm serileri yerine ayrık dalgacık dönüşümünden elde edilen bileşenler kullanılarak yüksek başarımlı bir teknik ortaya konulmuştur. Kullanılan teknik farklı iklim koşullarına sahip iki ayrı bölgeye uygulanmıştır. Sonuçlar hata ve enerji değerlerine göre karşılaştırılmıştır. Çalışmada akım serilerinin modellenmesinde de yine ayrık dalgacık dönüşümü sonucunda elde edilen bileşenlerden uygun olanları kullanılarak zaman serisi modellemesi yapılmış ve başarılı sonuçlar elde edilmiştir. Zaman serileri öncelikle Fourier, kısa süreli Fourier, sürekli dalgacık dönüşümü ve global dalgacık spektrumu yardımıyla analiz edilmiştir. Daha sonra farklı dalgacık dönüşümü bileşenleri kullanılarak bir çok model oluşturulmuştur. Sonuçlar farklı hata kriterleri ile test edilmiştir. Sonuç olarak ilk defa bu çalışmada dalgacık dönüşümü tekniği, akarsu akım modellemelerinde kullanılmış ve başarılı sonuçlar elde edilmiştir.
Even though earth science phenomena have nonstationary characteristics, they actually include many different secret periodic events occurred in different time periods. Wavelet transform technique, which is widely used last two decades, gives better result than former techniques for analyzing of earth science phenomena and for feature detection of real measurements. Analysis results can reveal information related to the past period as well as a period in the future. As a nonstationary series, analysis of streamflow records takes a significant role in design and planning of water resources systems. In this study, a new modeling technique is offered for streamflow time series modeling by using discrete wavelet transform technique. The new technique was applied to streamflow models, which are constituted between two measurement stations. Instead of response and explanatory series in a linear regression model, discrete wavelet components of such series are used in this study. The new technique was tested by applying two different geographical locations. Results were compared with energy variation, and error values of models. The new technique was also applied to streamflow time series modeling. Time series was firstly analyzed by Fourier transform, short time Fourier transform, continuous wavelet transform, and global wavelet spectrums. Numerous models were constructed by discrete wavelet components of time series. Results were compared by error values of models. The new technique was also compared by results of Fourier filtered technique. The new technique offers good advantage with physical interpretation for streamflow modeling.
Even though earth science phenomena have nonstationary characteristics, they actually include many different secret periodic events occurred in different time periods. Wavelet transform technique, which is widely used last two decades, gives better result than former techniques for analyzing of earth science phenomena and for feature detection of real measurements. Analysis results can reveal information related to the past period as well as a period in the future. As a nonstationary series, analysis of streamflow records takes a significant role in design and planning of water resources systems. In this study, a new modeling technique is offered for streamflow time series modeling by using discrete wavelet transform technique. The new technique was applied to streamflow models, which are constituted between two measurement stations. Instead of response and explanatory series in a linear regression model, discrete wavelet components of such series are used in this study. The new technique was tested by applying two different geographical locations. Results were compared with energy variation, and error values of models. The new technique was also applied to streamflow time series modeling. Time series was firstly analyzed by Fourier transform, short time Fourier transform, continuous wavelet transform, and global wavelet spectrums. Numerous models were constructed by discrete wavelet components of time series. Results were compared by error values of models. The new technique was also compared by results of Fourier filtered technique. The new technique offers good advantage with physical interpretation for streamflow modeling.
Açıklama
Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2004
Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2004
Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2004
Anahtar kelimeler
Akım serileri,
dalgacık dönüşümü teknikleri,
eksik veri tamamlama,
zaman serisi modelleri,
Streamflow series,
wavelet transforms,
data reconstruction,
time series modeling