Feng Zhou

Feng Zhou, Antonio Cicone, Haomin Zhou

The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decomposition methods led by the empirical mode decomposition, which was pioneered by Huang et al. in 1998, have been proposed by different research groups. However, they still have some limitations. For example, they are generally prone to boundary and mode mixing effects and are not very robust to noise. Inspired by the successful applications of deep learning in fields like image processing and natural language processing, and given the lack in the literature of works in which deep learning techniques are used directly to decompose non-stationary signals into simple oscillatory components, we use the convolutional neural network, residual structure and nonlinear activation function to compute in an innovative way the local average of the signal, and study a new non-stationary signal decomposition method under the framework of deep learning. We discuss the training process of the proposed model and study the convergence analysis of the learning algorithm. In the experiments, we evaluate the performance of the proposed model from two points of view: the calculation of the local average and the signal decomposition. Furthermore, we study the mode mixing, noise interference, and orthogonality properties of the decomposed components produced by the proposed method. All results show that the proposed model allows for better handling boundary effect, mode mixing effect, robustness, and the orthogonality of the decomposed components than existing methods.

Feng Zhou, Antonio Cicone, Haomin Zhou

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when applied to nonlinear and non-stationary signals. To address this challenge, a series of nonlinear and adaptive methods, pioneered by the empirical mode decomposition method, have been proposed. The goal of these methods is to decompose a non-stationary signal into quasi-stationary components that enhance the clarity of features during time-frequency analysis. Recently, inspired by deep learning, we proposed a novel method called iterative residual convolutional neural network (IRCNN). IRCNN not only achieves more stable decomposition than existing methods but also handles batch processing of large-scale signals with low computational cost. Moreover, deep learning provides a unique perspective for non-stationary signal decomposition. In this study, we aim to further improve IRCNN with the help of several nimble techniques from deep learning and optimization to ameliorate the method and overcome some of the limitations of this technique.