The DCT-based oscillation detection method for a single time series

This paper proposes a new method based on the discrete cosine transform (DCT), named as the DCT-based method, to detect oscillations for a single time series. The main idea is to isolate different frequency components of the time series via the DCT, and to detect oscillations by checking the regularity of zero-crossings of these isolated components. This method has the following features: (i) usage of only time series information of process variables without additional process knowledge, (ii) ability to deal with slowly varying trends, (iii) robustness to both white and colored noises, (iv) capability to handle the presence of multiple oscillations, and (v) amenability to complete automation without human intervention. Simulation examples and industrial case studies are presented to demonstrate the effectiveness and the above features of the DCT-based method.