The Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) has been used to propose a new method for filtering time series originating from nonlinear systems. The filtering method is based on fuzzy entropy and a new waveform. A new waveform is defined wherein Intrinsic Mode Functions (IMFs)—which are obtained by CEEMDAN algorithm—are firstly sorted in ascending order (the sorted IMFs is symmetric about center point, because at any point, the mean value of the envelope line defined by the local maxima and the local minima is zero), and the energy of the sorted IMFs are calculated, respectively. Finally, the new waveform with axial symmetry can be obtained. The complexity of the new waveform can be quantified by fuzzy entropy. The relevant modes (noisy signal modes and useful signal modes) can be identified by the difference between the fuzzy entropy of the new waveform and the next adjacent new waveform. To evaluate the filter performance, CEEMDAN and sample entropy, Ensemble Empirical Mode Decomposition (EEMD) and fuzzy entropy, and EEMD and sample entropy were used to filter the synthesizing signals with various levels of input signal-to-noise ratio (SNRin
). In particular, this approach is successful in filtering impact signal. The results of the filtering are evaluated by a de-trended fluctuation analysis (DFA) algorithm, revised mean square error (RMSE), and revised signal-to-noise ratio (RSNR), respectively. The filtering results of simulated and impact signal show that the filtering method based on CEEMDAN and fuzzy entropy outperforms other signal filtering methods.
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