Simplified coded dispersion entropy: a nonlinear metric for signal analysis

Recently, coded permutation entropy has been proposed, which enhances the noise immunity by quadratic partitioning on the basis of permutation entropy. However, coded permutation entropy and permutation entropy only consider the order of amplitude values and ignore some information related to amplitude. To overcome these defects, this paper applies the concept of quadratic partitioning to dispersion entropy (DE), takes advantage of the fact that DE can effectively measure amplitude information, and proposes coded DE (CDE), which increases the number of patterns and improves the divisibility by further coding the dispersion patterns in DE. Moreover, to reduce the computational consumption of CDE, we simplify the division criterion in quadratic partitioning while guaranteeing that no effective information is lost and propose simplified CDE (SCDE). Several simulation experiments demonstrate the advantages of SCDE and CDE over DE, permutation entropy, and coded permutation entropy in detecting the nonlinear dynamic changes within chaotic and synthetic signals. In addition, real-world experiments on electroencephalogram signals, bearing signals, and ship signals show that SCDE has better performance in medical diagnosis, fault diagnosis and signal classification, and the accuracy of SCDE-based classification methods is higher than that of other entropy-based methods.