End-effects mitigation in empirical mode decomposition using a new correlation-based expansion model

Abstract

The real-time analysis of time-varying data has become extremely significant in mechanical systems. The Hilbert–Huang transform (HHT) is a recent development in signal processing based on time–frequency distribution for analyzing complex signals. The HHT permits instantaneous attributes to be used to study signals that display complex behavior and stochastically vary with time. This transform combines empirical mode decomposition (EMD) and Hilbert transform (HT). The EMD converts a signal of time into various intrinsic mode functions (IMF), which are subsequently used by the HT to insert into the same time–frequency space. However, the restriction of the end-effect is an important problem when employing the EMD method. End-effect causes several issues such as changing the shapes of envelopes, deviating IMF, computational instabilities at the signal borders, and modal aliasing. To mitigate the end-effects, this study presents a correlation-based expansion model at both ends of the signal. Motivated by end-effects mitigation, data outside of the signal boundaries are predicted based on the similarity of the signal’s start and end segments with the signal's inner segment. Correlation techniques are a reliable method to find signal pattern similarities. Seven simulated signals are used to verify the method's performance. The seven signals include six monovarietal signals with various amplitude modulation-frequency modulation behaviors and a one-channel functional near-infrared spectroscopy (fNIRS) signal. The comparison results of the proposed technique with standard EMD and EMD coupled with other expansion methods show that the end-effect in the EMD method by correlation expansion can effectively reduce.