Dynamic Shannon entropy (DySEn): a novel method to detect the local anomalies of complex time series

In this paper, dynamic Shannon entropy (DySEn) is introduced as a novel method to detect the abnormal changes of signals. It is a combination of Shannon entropy and the permuted distribution entropy (PDE). Experiments have proved that Shannon entropy is not sensitive to local disorder, and there may be no response even if the amplitude changes significantly. PDE does not work well with chaotic sequences, unless the abnormal area and the normal one have obvious differences in periodicity. However, DySEn can deal with those problems at the same time based on both traditional statistical characteristics and dynamic characteristics. Our experiments show that it can provide an effective way to the anomaly detection for periodic signals, complex signals and the mixed signals. We also apply it to detect the rail corrugations. DySEn can effectively locate the abnormal areas, and, with the help of PDE, it can be seen that the periodicity of the abnormal areas has increased significantly, which is in line with the situation of rail corrugations.