Variational mode decomposition denoising combined with the Hausdorff distance

Area of Science:

• Signal Processing
• Data Analysis
• Noise Reduction Techniques

Background:

• Variational Mode Decomposition (VMD) offers advantages over Empirical Mode Decomposition (EMD) in noise robustness and theoretical foundation.
• A key limitation of VMD is the challenge in selecting appropriate modes for signal reconstruction.
• Existing methods require improvement for accurate and reliable signal filtering.

Purpose of the Study:

• To propose a novel signal-filtering method, VMD-HD, that enhances mode selection in Variational Mode Decomposition.
• To address the limitations of VMD in identifying relevant intrinsic mode functions for signal reconstruction.
• To validate the efficacy of the VMD-HD method in filtering noisy signals and detecting anomalies.

Main Methods:

• Signal decomposition using Variational Mode Decomposition (VMD) into K band-limited intrinsic mode functions.
• Estimation of probability density functions (PDFs) for the input signal and each decomposed mode.
• Selection of relevant modes based on similarity between the input signal's PDF and individual mode PDFs, utilizing Hausdorff distance (HD).

Main Results:

• The VMD-HD method demonstrates superior performance in filtering simulation signals compared to EMD-based techniques.
• Hausdorff distance (HD) proved to be the most effective similarity measure for relevant mode selection.
• Successful application of VMD-HD for filtering pipeline leakage signals, validated by de-trended fluctuation analysis.

Conclusions:

• The VMD-HD method provides a robust and effective solution for signal filtering by improving mode selection.
• The integration of Hausdorff distance significantly enhances the accuracy of VMD in practical signal processing applications.
• This approach offers a promising tool for identifying and filtering noise in complex signals, with demonstrated utility in engineering diagnostics.