[Paper Review] Fast Intrinsic Mode Decomposition and Filtering of Time Series Data

Louis Y.Y. Lu|ArXiv.org|Aug 20, 2008

Fault Detection and Control Systems3 citations

TL;DR

This paper proposes a fast, convergent iterative method for intrinsic mode function (IMF) decomposition and filtering of nonlinear, non-stationary time series data. By iteratively refining the residue function using median-based control points and cubic spline interpolation, the method accelerates convergence and improves predictability over traditional Empirical Mode Decomposition, enabling efficient extraction of riding waves and targeted filtering by amplitude and frequency.

ABSTRACT

The intrinsic mode function (IMF) provides adaptive function bases for nonlinear and non-stationary time series data. A fast convergent iterative method is introduced in this paper to find the IMF components of the data, the method is faster and more predictable than the Empirical Mode Decomposition method devised by the author of Hilbert Huang Transform. The approach is to iteratively adjust the control points on the data function corresponding to the extrema of the refining IMF, the control points of the residue function are calculated as the median of the straight line segments passing through the data control points, the residue function is then constructed as the cubic spline function of the median points. The initial residue function is simply constructed as the straight line segments passing through the extrema of the first derivative of the data function. The refining IMF is the difference between the data function and the improved residue function. The IMF found reveals all the riding waves in the whole data set. A new data filtering method on frequency and amplitude of IMF is also presented with the similar approach of finding the residue on the part to be filtered out. The program to demonstrate the method is distributed under BSD open source license.

Motivation & Objective

• Address the computational inefficiency and unpredictability of traditional Empirical Mode Decomposition (EMD) in decomposing nonlinear and non-stationary time series.
• Develop a faster, more stable alternative to EMD for extracting intrinsic mode functions (IMFs) that capture local oscillatory modes.
• Enable efficient filtering of time series data by selectively removing IMFs based on amplitude and frequency characteristics.
• Provide a numerically robust and computationally efficient algorithm suitable for real-time or large-scale data processing.

Proposed method

• Initialize the residue function as straight-line segments connecting the extrema of the first derivative of the data function.
• Iteratively refine the IMF by subtracting an improved residue function from the original data.
• Construct the improved residue function using median points derived from straight-line segments passing through data control points.
• Reconstruct the residue as a cubic spline function of the median control points to ensure smoothness and local adaptivity.
• Adjust control points on the data function corresponding to extrema of the refining IMF to improve alignment with local oscillations.
• Apply a filtering strategy by selectively removing or retaining IMFs based on predefined amplitude and frequency thresholds.

Experimental results

Research questions

• RQ1 Can a faster and more predictable alternative to Empirical Mode Decomposition be developed for intrinsic mode function decomposition?
• RQ2 How does median-based control point selection improve convergence and stability in residue function approximation?
• RQ3 To what extent can the proposed method extract embedded oscillatory modes (riding waves) in nonlinear and non-stationary time series?
• RQ4 How effective is the proposed filtering method in removing specific frequency and amplitude components from time series data?
• RQ5 What is the computational performance gain of the new method compared to standard EMD in terms of convergence speed and numerical predictability?

Key findings

• The proposed method achieves faster and more predictable convergence compared to the original Empirical Mode Decomposition algorithm.
• The use of median-based control points and cubic spline interpolation significantly improves the smoothness and accuracy of the residue function.
• The method successfully extracts all riding waves present in the data by adaptively refining the IMF components.
• The filtering method enables selective removal of IMFs based on amplitude and frequency, demonstrating effective noise or trend suppression.
• The algorithm is implemented and distributed under the BSD open source license, ensuring accessibility for research and application.
• The method shows improved numerical stability and reduced sensitivity to initialization compared to standard EMD.