A signal processing method of generating intrinsic mode functions using wavelet packet decomposition


The research into fault diagnosis system of machine and equipment is of great significance in modernizing and putting the national economy on an IT basis.

The Faculty of Mechanics of Kim Il Sung University has made achievements in the researches to newly develop the vibration signal processing algorithm, an important component of the fault diagnosis system, to meet the world standards and apply it to production sites.

Empirical mode decomposition, a signal processing method that decomposes time series data into Intrinsic Mode Functions(IMFs) satisfying several specific conditions and then performs its Hilbert spectral analysis according to the purpose of interest, has been widely used in signal processing in different fields such as system identification, structural condition monitoring, seismic and ocean observation since its first introduction by N. E. Huang and other researchers more than 20 years ago.

Although empirical mode decomposition has many advantages in the analysis and processing of stationary and nonstationary signals, there are still problems that need to be solved, such as mode mixing and endpoint effects, and efforts to improve it with its wide application have been constantly made.

For example, the EEMD method proposed a new noise additive data analysis method to overcome the mode mixing phenomenon, while the FFDSI method uses fast Fourier transform to separate IMFs from the original signal.

We propose a new method to decompose a given vibration signal into IMFs based on wavelet packet decomposition and demonstrate the effectiveness of the proposed method by performing Hilbert spectral analysis based on this method for several vibration and speech signals.

This method generates IMFs so that the frequency bands do not overlap each other and have maximum bandwidth when decomposing the vibration signal into IMFs. Since we obtain IMFs using a special filtering algorithm based on wavelet packet decomposition instead of the filtering process of the empirical mode decomposition method, the generated IMFs are strictly orthogonal to each other.

Our proposed method is more reliable for the decomposition of IMFs of a signal under some bad conditions than the existing method, especially by decomposing linear structure vibration response signals into natural vibration modes, which can be useful for the modal analysis of machinery and structures. Several application examples have shown that this method is an effective and valuable method for both stationary and nonstationary signal processing and Hilbert spectral analysis.

Our research achievements have already been reviewed in the journal of "Applied Mathematics and Mechanics" (English Edition) 34(7) published by Shanghai University and Springer-Verlag, under the title of "Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition".