Three-dimensional causal complementary complexity: a new measure for time series complexity analysis

The empirical mode decomposition (EMD) energy entropy plane is an effective tool for analysing the complexity of time series, but mode mixing caused by EMD affects the accuracy of experimental results. To overcome this shortcoming, we propose a new complexity-entropy causal plane named the complete ensemble EMD with adaptive noise analysis (CEEMDAN) energy entropy plane, which is a combination of CEEMDAN energy entropy and the statistical complexity metric. Among the existing methods of entropy planes, no method has been proposed that can reflect the randomness and complexity of time series from both the internal mode of time series and the original signal. To further improve its signal classification ability and time series complexity analysis skills, we introduce dispersion entropy into the CEEMDAN energy entropy plane as a complementary feature and propose three-dimensional causal complementary complexity so that this representation space expands from two-dimensional to three-dimensional. Simulation experiments show that the proposed three-dimensional causal complementary complexity can better distinguish different states of the logistic map. In addition, real-world experiments show that the proposed three-dimensional causal complementary complexity has better performance in ship signal classification and bearing fault diagnosis.