Weighted Sliding Empirical Mode Decomposition

Abstract

The analysis of nonlinear and nonstationary time series is still a challenge, as most classical time series analysis techniques are restricted to data that is, at least, stationary. Empirical mode decomposition (EMD) in combination with a Hilbert spectral transform, together called Hilbert-Huang transform (HHT), alleviates this problem in a purely data-driven manner. EMD adaptively and locally decomposes such time series into a sum of oscillatory modes, called Intrinsic mode functions (IMF) and a nonstationary component called residuum. In this contribution, we propose an EMD-based method, called Sliding empirical mode decomposition (SEMD), which, with a reasonable computational effort, extends the application area of EMD to a true on-line analysis of time series comprising a huge amount of data if recorded with a high sampling rate. Using nonlinear and nonstationary toy data, we demonstrate the good performance of the proposed algorithm. We also show that the new method extracts component signals that fulfill all criteria of an IMF very well and that it exhibits excellent reconstruction quality. The method itself will be refined further by a weighted version, called weighted sliding empirical mode decomposition (wSEMD), which reduces the computational effort even more while preserving the reconstruction quality.

Ensemble Empirical Mode Decomposition Analysis of EEG Data Collected during a Contour Integration Task

“…The empirical nature of EMD offers the advantage over other signal decomposition techniques like Exploratory Matrix Factorization (EMF) [ 31 ] of not being constrained by conditions which often only apply approximately. Especially with biological signal processing, one often has only a rough idea about the underlying modes or component images, and frequently their number is unknown [ 32 , 33 ]. In addition, perfect reconstruction is hampered by intrinsic scaling indeterminacies.…”

A Signal Processing Approach with a Smooth Empirical Mode Decomposition to Reveal Hidden Trace of Corrosion in Highly Contaminated Guided Wave Signals for Concrete-Covered Pipes

“…It is worthy of mention that this method is different than some works with a similar names reported in [44,45,46,47]. …”

“…Replace x ( t ) with the residue and return to step 1; repeat the iteration process and continue until the residue r n ( t ) becomes too small or a monotonic function from which no more IMFs can be extracted. It is worthy of mention that this method is different than some works with a similar names reported in [ 44 , 45 , 46 , 47 ].…”

Time series anomaly detection for gravitational-wave detectors based on the Hilbert–Huang transform

“…In general, however, the use of an ensemble EMD in an online data analysis is inappropriate because of its expensive computing cost. This drawback can also be resolved using the SEMD [10] and/or its extension, the weighted SEMD [11]. The algorithm for the SEMD is somewhat simple (see Fig.…”

“…The weighted SEMD introduces a weighting function to the averaging process in step 2, which reduces the edge effects on both sides of each segment originating from the EMD and from the SEMD as well. [11] suggest a Gaussian weighting function, w(n) = exp 1 2 [2 n∕(L − 1)] 2 with = 2.5 and − 1 2 (L − 1) ≤ n ≤ 1 2 (L − 1) . This function, however, does not vanish at the ends of a segment, i.e., n = ± 1 2 (L − 1) ; thus, the edge effect from the SEMD remains and causes step function-like behaviors in the SEMD .…”