(183e) A Segmentation Approach for Oscillation Characterization
Given importance of oscillations across disciplines, several techniques have been developed to detect oscillations in data using time, frequency and time-frequency analysis techniques. A straightforward time domain analysis technique is visual inspection for presence of oscillations. Although simple, this makes the analysis subjective. The empirical mode decomposition  (a widely used time domain technique) can be used to reduce the effect of noise, and has been employed to analyze intermittent and elliptic oscillations at the atmospheric boundary layer. However, intermittent oscillation in data leads to presence of several modes in a single IMF, referred to as mode mixing. Moreover, a single mode of oscillation can also appear in multiple IMFs which makes mode mixing a serious concern for reliable detection of intermittent oscillations.
On the other hand, several frequency domain techniques exist that can be used for detection of oscillations. The most common frequency domain technique is the Fourier transform which transforms the time domain signal to frequency domain in which the power content at different frequencies can be examined to detect oscillations. However, phenomena such as spectral leakage make it difficult to correctly identify the frequencies of oscillations. An extension to Fourier Transform is the Short Time Fourier Transform for signals with time varying frequency that restricts the calculation of Fourier transform to a moving window of finite length. However, this approach suffers from the problem of fixed window size and hence fixed time and frequency resolution. The wavelet transforms use waveforms with certain desired characteristics (such as orthogonality) called (mother and daughter) wavelets as basis functions. However wavelet based techniques suffer from the fact that they lack clear definition of sinusoidal oscillations and there is a need to select appropriate mother wavelet for desired feature extraction.
Despite their limitations, the above techniques and many more have been extensively used for detection of oscillations in diverse applications. However, there is a lack of a common framework that can accommodate several important features in data such as non-stationarity, intermittent oscillation, measurement noise and multiple oscillations. In this paper, we report an approach that addresses all of the above stated problems. The proposed framework combines both time and frequency information for better oscillation characterization. A key segmentation idea that allows the localization of the oscillating regimes using template matching is used to overcome many of the difficulties with both time and frequency based oscillation characterization approaches. We show that the proposed approached is robust to non-stationarity, intermittency and noise while characterizing oscillations with multiple modes. The power of this approach is demonstrated using data from various disciplines.
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