Variational mode decomposition denoising combined with the Hausdorff distance

Variational mode decomposition (VMD) is a recently introduced adaptive signal decomposition algorithm with a solid theoretical foundation and good noise robustness compared with empirical mode decomposition (EMD). However, there is still a problem with this algorithm associated with the selection of relevant modes. To solve this problem, this paper proposes a novel signal-filtering method that combines VMD with Hausdorff distance (HD) in the VMD-HD method. A noisy signal is first decomposed into a given number K of band-limited intrinsic mode functions by VMD. The probability density function is then estimated for each mode. The aim of this method is to reconstruct the signal using the relevant modes, which are selected on the basis of noticeable similarities between the probability density function of the input signal and that of each mode. Various similarity measures are investigated and compared, and the HD is shown to offer the best performance. The results of filtering of simulation signals illustrate the validity of the proposed method when compared with EMD-based methods under comprehensive quantitative evaluation criteria. As a specific example, the proposed method is successfully used for filtering the pipeline leakage signal as evaluated by the de-trended fluctuation analysis algorithm.