Improved DCT-based method for online detection of oscillations in univariate time series

Automatic oscillation detection for univariate time series is the very first step in detection and compensation of oscillations in process industries. This paper is motivated by our industrial experience of applying the discrete cosine transform (DCT)-based method for oscillation detection. An improved DCT-based method is proposed with three main modifications, namely, a revised hypothesis test based on the confidence interval of coefficient of variation, a fitness index to determine a dominant oscillation component, and a hypothesis test on the regularity of oscillation magnitudes. These modifications are also applicable to other oscillation detection methods in the literature. Moreover, an online oscillation detection method is proposed, with a mechanism by which the size of a supervision time window is adaptive to frequency variation of process variables. Industrial examples are provided to demonstrate the effectiveness of the two proposed methods.