Online detrended fluctuation analysis and improved empirical wavelet transform for real-time oscillations detection in industrial control loops

Abstract

Detrended Fluctuation Analysis (DFA) is a reliable and assumption-free approach for gauging the complexity of a time series. In this paper, an online oscillations detection paradigm is presented, which integrates the potential of DFA in detecting abnormal coherent fluctuations with the Empirical Wavelet Transform (EWT) efficiency in extracting the characteristics of oscillations. However, the standard EWT fails to separate modes oscillating at close frequencies, resulting in an incorrect decomposition. Furthermore, the lack of an appropriate stopping criterion frequently results in the signal being over-decomposed into several inconsequential components. Therefore, owing to the capability of DFA to differentiate between fluctuations stemming from noise and coherent fluctuations arising from genuine oscillations, an Improved EWT (IEWT) is presented to mitigate these issues and accurately extract only compelling oscillating modes. The proposed DFA-based IEWT framework is verified on simulated applications and data from real industrial processes, illustrating its effectiveness.