A Globally Convergent Method for Finding the Number of Intrinsic Modes on Narrow-Banded Signals

Abstract: Variational Mode Decomposition (VMD) plays an important role in many scientific areas, especially for the area of signal processing. Unlike the traditional Fourier paradigm, it makes decomposition of a signal possible without any predefined function basis, which gives unprecedented flexibilities while handling narrow-banded signals of varieties. However, determining the number and central frequencies of intrinsic mode functions are still open questions in that few studies has been proposed to give a complete method that can theoretically guarantee the global convergence during decomposition. In this article, we propose a globally convergent numerical optimization method based on variational convex optimization to automatically determine the number and central frequency of IMFs without any prior knowledge for narrow banded signals, as long as the spectra of each sub-band are identifiable. Our method focuses on finding the support baseline of the spectral function, and further separating the significant frequency band regions above the support baseline. Unlike pioneer works that focus on optimizations on complex field, our method achieves obtaining the number of decomposed IMFs and center frequencies in real field by combining variational calculus, convex optimization, and numerical solutions of differential equations in real field and theoretical analysis shows our algorithm is guaranteed terminate to one of the optimum as close as possible. Experiments also shows that our algorithm converges quickly and can be used in practical engineering to determine the prior information of the number of intrinsic modes and evaluate initial center frequency as prior information to continue the VMD procedure.