A Comparative Study of Empirical Mode Decomposition-Based Filtering for Impact Signal
2. Related Works
2.1. Improved Empirical Mode Decomposition
- Decompose signal to obtain the first mode by using EMD algorithm.
- Compute the difference signal
- Decompose to obtain the first mode and define the second mode by
- For k = 2, …, K, calculate the k-th residue and obtain the first mode. Define the (k + 1)-th mode as follows:
- Repeat step (4) until the residue contains no more than two extremes. The residual mode is then defined as:
2.2. Fuzzy Entropy
- Given a time sequence ( is the sample size) to form a sequence segment by choosing consecutive values in time sequenceThe expression is shown as follows:
- The distance between the vector and is defined
- The similarity degree between and is expressed by the fuzzy function . The expression of similarity is as follows:
- Definition function
- For dimension function, repeat steps (1) to (4), and obtain
- The fuzzy entropy is defined by:
3. Filtering Method
3.1. Identifying the Relevant Mode
- The noisy signal x(t) is decomposed to obtain IMFi (i = 1, …, N) by EMD or the improved version.
- Each IMF is sorted in ascending order, and the energy of the sorted data is calculated and then normalized to obtain a new waveform (the normalized new waveform is defined as NNW).
- The complexity of each NNWi (except residue) is calculated by fuzzy entropy, and the value of fuzzy entropy is marked as Ei (i = 1, …, M − 1). Here, M is the number of modes by EMD or the improved version.
- The difference of adjacent Ei is obtained, and the absolute value of the difference is calculated.
- The relevant mode is identified.
- The filtered signal is obtained.
4. Results and Discussion
4.1. Simulated Signal Filtering
4.2. Impact Signal Filtering
Conflicts of Interest
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|Order||Signal||Length of Data|
|Filter Method||RSNRout||RMSE||Fractal Scaling Index (α)|
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Zhan, L.; Li, C. A Comparative Study of Empirical Mode Decomposition-Based Filtering for Impact Signal. Entropy 2017, 19, 13. https://doi.org/10.3390/e19010013
Zhan L, Li C. A Comparative Study of Empirical Mode Decomposition-Based Filtering for Impact Signal. Entropy. 2017; 19(1):13. https://doi.org/10.3390/e19010013Chicago/Turabian Style
Zhan, Liwei, and Chengwei Li. 2017. "A Comparative Study of Empirical Mode Decomposition-Based Filtering for Impact Signal" Entropy 19, no. 1: 13. https://doi.org/10.3390/e19010013