Wavelets and irregular time series
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In this thesis we study time series containing pressure measurements from a three phase flow pipeline at the Ekofisk oil field. The pipeline transports a mixture of oil, water and gas from $15$ wells for approximately 2.5km to a production facility. Our aim is to develop techniques that allow the selection and (to some extent) prediction of "non-standard" behavior in the system (sharp pressure changes and other type of instabilities). To advice this aim we perform a scalewise decomposition of the input signal/time series and investigate the behavior of each scale separately. We introduce the Sliding Window Wavelet Transform (SWWT) method. The method evaluate the variability on different scales within the time interval of a characteristic length (a window) and then trace these characteristics as the window slides in time.We use the discrete wavelet transform (DWT) in order to obtain the scalewise decomposition within the window. Using orthonormal discrete wavelets, we show that the variability of such sequences can be decomposed into their corresponding scales. Based on this, a thresholding algorithm is applied, characterizing the state of the system any given time. The results we find are promising and we show that different parameters in the thresholding algorithm extracts different types of special events. We also show that in some cases, this approach allows to predict special events before they really occur.While we investigate one particular system in this thesis, the procedures developed can be applied to other complicated systems where instability in system parameters is important.