A queued Variational Mode Decomposition method

The restoration of a non-stationary composite signal to its original components is a challenging and intriguing task in the field of signal processing. Various methods have been developed to tackle this problem. A traditional method for this problem is Singular Spectrum Analysis (SSA), while it needs to know the component number and costs too much time. Empirical Mode Decomposition (EMD) is also frequently applied, which decomposes the composite signal into a set of components known as Intrinsic Mode Functions (IMFs). However, the EMD method has been criticized for lacking a strong theoretical foundation and being more of a mathematical trick. Another popular method, Empirical Wavelet Transform (EWT), divides the frequency spectrum of the target signal into predefined segments and applies wavelet transforms using specific wavelet bases. Recently, a new method called Variational Mode Decomposition (VMD) has been proposed. This method is based on the variational principle and transforms the decomposition problem into an optimization problem. VMD has a robust mathematical foundation and exhibits excellent performance. However, it does have some limitations, such as the requirement for prior information on the modal number and the existence of a serious deviation in the end regions (named "end effect"). In this paper, we propose a novel method for sequentially separating non-stationary composite signals. Our method is inspired by the variational principle and can accurately and adaptively recover the original modes one by one from the raw mixture, without any prior knowledge or assumptions regarding the modal number. Moreover, our method can determine the modal number during the separation process, providing significant convenience in realworld applications. Additionally, we address the issue of end effects by conducting a new end elongation for the composite signal before the decomposition operation. This approach effectively reduces the end effect to a much lower level compared to the VMD method. To further enhance the accuracy of our method, we introduce a refinement approach after the coarse extraction. Combined these techniques, the final decomposition results demonstrate that our novel method outperforms VMD, EMD, EWT and SSA methods in most cases.