A modified variational mode decomposition method based on envelope nesting and multi-criteria evaluation

Abstract As an extensively applied signal decomposition method, Variational Mode Decomposition (VMD) has many favorable characteristics for addressing signals with noise interference. However, the requirement of presetting modal number K and balancing parameter α makes this method difficult to use in some cases where prior knowledge of the analyzed signal cannot be acquired. In this paper, a modified VMD method (MVMD) is proposed to overcome this drawback. First, an envelope nesting method is adopted to preliminarily guide the latent central frequencies. Then, a Permutation Entropy and orthogonality-based modal number adjusting process is conducted, after which the modal number can be determined. Finally, a coarse-to-fine search procedure aiming at the optimal α value is carried out, under the guidance of a multi-criteria target function. The effectiveness and practicability of the proposed method have been proven by experiments which adopt a synthetic signal and three different kinds of fault-bearing vibration signals. A comparison between the proposed method and conventional methods has been made to demonstrate the superiority of the proposed MVMD method on the accuracy of modal number estimation, the independence of individual modes and the robustness of decomposition under heavy noise conditions.