SVMD: Spearman Variational Mode Decomposition

In practice, it is difficult to determine the number of decomposition modes, K, for Variational Mode Decomposition (VMD). To overcome this issue, this study offers Spearman Variational Mode Decomposition (SVMD), a method that uses the Spearman correlation coefficient to calculate the ideal mode number. Unlike the Pearson correlation coefficient, which only returns a perfect value when X and Y are linearly connected, the Spearman correlation can be calculated without knowing the probability distributions of X and Y. The Spearman correlation coefficient, also called Spearman's rank correlation coefficient, is a subset of a wider correlation coefficient. As VMD decomposes a signal, the Spearman correlation coefficient between the reconstructed and original sequences rises as the mode number K increases. Once the signal has been fully decomposed, subsequent increases in K cause the correlation to gradually level off. When the correlation reaches a specific level, VMD is said to have adequately decomposed the signal. Numerous experiments revealed that a threshold of 0.997 produces the best denoising effect, so the threshold is set at 0.997. This package has been developed using concept of Yang et al. (2021)<doi:10.1016/j.aej.2021.01.055>.

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