Issue 70

S.K. Shandiz et alii, Frattura ed Integrità Strutturale, 70 (2024) 24-54; DOI: 10.3221/IGF-ESIS.70.02

 The number of extrema and zero-crossings is exactly/nearly the same.  The mean value of the envelopes is defined by the local maxima and the local minima is zero at any point. The EMD procedure requires spline fitting to create the upper and lower envelopes of the signal and compute the mean of both envelopes. The signal is then subtracted from the mean, which is called the sifting process. The process is repeated until the resultant signal meets the mentioned requirements, at which point it is considered as an IMF. After subtracting the IMF from the original signal, the sifting process is repeated on the remaining signal to yield further IMFs [19,56] (see Fig. 1a).

(a)

(b)

Figure 1: (a) EMD, (b) VMD flowchart.

Variational Mode Decomposition A new method to break down the signal into its elemental components called VMD was introduced by Dragomiretskiy and Zosso [60]. This method is based on Wiener filtering, Hilbert transforms, analytic signal and frequency mixing, and heterodyne demodulation. In this method, a completely non-reversible VMD model is presented, in which the modes are extracted in one step (see Fig. 1b). The purpose of this method is to obtain a set of modes and their corresponding central frequencies so that the sum of the modes retrieves the input signal. Each sub-signal is supposed to be compressed around a corresponding central frequency  k which is extracted using the method. The decomposed signals are called IMF. An IMF is defined as an Amplitude-Modulated-Frequency-Modulated (AM-FM) adaptively in the frequency domain by VMD. By considering the adequate number of modes for VMD, the abnormality in the signals can be captured successfully.

27