Dispersion entropy-based Lempel-Ziv complexity: A new metric for signal analysis

Lempel-Ziv complexity (LZC) is one of the most important metrics for detecting dynamic changes in non-linear signals, but due to its dependence on binary conversion, LZC tends to lose some of the effective information of the time series, while the noise immunity is not guaranteed and cannot be applied to the detection of real-world signals. To address these limitations, we have developed a dispersion entropy-based LZC (DELZC) based on the normal cumulative distribution function (NCDF) and dispersion permutation patterns. In DELZC, the time series are first processed by NCDF to increase the number of classes and thus reduce the loss of information, and in addition, the dispersive entropy (DE) in terms of the ordinal number of the permutation pattern is considered to replace the binary conversion of LZC, thus improving the ability to capture the dynamic changes in the time series. In signal analysis using a set of time series, several easy-to-understand concepts are used to demonstrate the superiority of DELZC over other three LZC metrics in detecting the dynamic variability of the signals, namely LZC, dispersion LZC (DLZC) and permutation LZC (PLZC). The synthetic signal experiments demonstrate the superiority of DELZC in detecting the dynamic changes of time series and characterizing the complexity of signal, and also have lower noise sensitivity. Moreover, DELZC has the best performance in diagnosing four states of rolling bearing fault signals and classifying five types of ship radiation noise signals, with higher recognition rates than LZC, PLZC and DLZC.