A Minimum Arclength Method for Removing Spikes in Empirical Mode Decomposition

Abstract

Empirical mode decomposition (EMD) is an extensively utilized tool in a time-frequency analysis. However, disturbances, such as impulse noise, can result in a mode-splitting effect, in which one physically meaningful component is split into two or more intrinsic mode functions (IMFs). In this paper, we propose a novel method, minimum arclength EMD (MA-EMD), to robustly decompose time series data with impulse-like noises. The idea is to apply a minimum arclength criterion to adjust the knot positions of impulses during the sifting process in EMD. In this way, the impulse-like artifact is extracted with the first IMF, and the mode splitting effect of the latter decomposition is alleviated. Furthermore, when the first IMF contains the desired information, we separate the spikes and the first IMF by adding a pair of masking signals. For using this masking-aided MA-EMD (MAMA-EMD) method, we also mathematically derived the appropriate ranges of the frequency and the amplitude of the masking signal. The MAMA-EMD is utilized to deal with the simulated Duffing wave and four real-world data, including electrical current, vibration signals, the cyclic alternating pattern in sleep EEG (electroencephalography), and circadian of core body temperature. The results show that the MA-EMD and MAMA-EMD have a sound improvement when encountering impulse noises.

New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms

“…The proper identification of spikes position in signals has been already studied in the literature, for instance in 113,114 , and for the jumps the so called essentially non-oscillatory (ENO) technique was developed in computational fluid dynamics to capture shock positions 25,115 , and it can be adopted in this context. If on the one 110 .…”

“…Regarding the jumps and spikes identification and their localization, as we mentioned previously, many works have been published in the literature where different techniques have been proposed, e.g. 113,114 . Therefore in this work we assume that their localization is known.…”

“…Whereas, if one or more spikes are present, they can be localized and removed following what has been already suggested in the literature, e.g. 113,114 .…”

“…The proper identification of spikes position in signals has been already studied in the literature, for instance in 113 , 114 , and for the jumps the so called essentially non-oscillatory (ENO) technique was developed in computational fluid dynamics to capture shock positions 25 , 115 , and it can be adopted in this context. If on the one hand some approaches have been proposed on how to remove spikes, on the other hand the question of how to properly handle jumps have never been raised in the context of EMD- and IF-based methods decompositions, to the best of the authors knowledge.…”

Fault Diagnosis of Reciprocating Compressor Using Component Estimating Empirical Mode Decomposition and De-Dimension Template With Double-Loop Correction Algorithm

“…Several improved approaches based on EMD have been studied to solve the trend filtering problem [16], [17]. A minimum arclength EMD (MA-EMD) is proposed to remove impulse-like noises in time series data [18]. In this work, a novel method based on EMD is proposed to remove the random noises in a time series data.…”