Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection

Abstract: This work proposes a novel method to construct weighted dynamic transfer network to map time series to complex networks. Firstly, we map time series into symbolic series by analyzing phase space characteristics. Then, we construct the complex network directly from the symbol sequence: symbol compositions correspond to network nodes, and the network edges are the temporal succession between nodes. Meanwhile, a novel method, spectral entropy, is proposed to quantify the local smoothness of complex networks. These two methods are demonstrated by simulation and applied to actual recorded data to confirm the advantages. The synthetic data study shows that the proposed method’s significant advantage is its reduced noise sensitivity. The methods can sense the topological structure change of the noise reconstruction network caused by weak acoustic signals. To further show the utility of these two methods, we provide new evidence of their application in actual recorded data collected in the south China sea. We can easily distinguish ship signals from the marine ambient noise by comparing the spectral entropy value. Meanwhile, compared with the existing network construction and characterization methods, both show that weighted dynamic transfer network and spectral entropy methods can distinguish nonlinear time series from noise more effectively. Graphical abstract: [Figure not available: see fulltext.].