Interpretation of mechanical signals using an improved Hilbert–Huang transform

Abstract

Attribute to providing a more accurate ‘real-life’ representation of a signal without any artefacts imposed by the non-locally adaptive limitations of the fast Fourier transform (FFT) and wavelet processing, the Hilbert–Huang transform (HHT) has been regarded as a powerful tool for adaptive analysis of non-linear and non-stationary signals. The HHT allows direct algorithmic analysis of signals through the combined use of the empirical mode decomposition (EMD) and the Hilbert transform (HT). So, the HHT possesses a high efficiency in computation, which further strengthens its power in signal processing. The EMD is a non-constrained decomposition. It decomposes the signal into a finite number of intrinsic mode functions (IMFs), which have the same number of zero crossings and extrema and simultaneously have symmetric envelopes determined by local maxima and minima. Therefore, the resultant IMFs are a set of basic oscillatory functions whose instantaneous frequencies may be extracted readily by using the HT. But this does not mean that the derived IMFs are certain to be monocomponent functions. In fact, as the EMD cannot decompose narrowband multi-harmonic signal very well, most IMFs are still multi-harmonic functions. Consequently, the instantaneous frequencies extracted from them usually show irregularities, which raise difficulties in interpreting the signal. The situation becomes worse especially when inspecting a signal with complex frequency composition. In order to make up for this deficiency of the HHT, an improved method is developed in this paper. Firstly, the signal is pre-processed and the ‘monocomponent’ functions in the signal are extracted with the aid of an adaptive band-pass filter. Then, the ‘monocomponent’ functions are decomposed by using the EMD. Among the resultant IMFs, the IMF with the same frequency as the central frequency of the filter is taken as a new IMF for feature extraction. The other IMFs are regarded as part of the residue of the whole EMD. Finally, the instantaneous frequencies and amplitudes of the signal are extracted from new IMFs by means of the HT. The novelty of this technique is that the HT is performed on a number of carefully selected ‘monocomponent’ functions rather than on the IMFs possibly with multiple numbers of frequency components. So, the irregularities presented in instantaneous frequencies are minimized and the accuracy of the time–frequency analysis is therefore guaranteed. In order to further increase the reliability of the analysis, the role of every new IMF is estimated and applied to refining the final results. Experiments prove that the proposed technique does improve the HHT and provide a more precise description of the signal being inspected.