An improved multiscale distribution entropy for analyzing complexity of real-world signals

Assessment of the dynamical complexity of signals or systems is very crucial in medical diagnostics, fault analysis of mechanical systems, astrophysics and many more. Although there have been tremendous improvements in entropy measures as complexity estimator, most of these measures are affected by short data length and are highly sensitive to predetermined parameters. These issues are addressed quite successfully by distribution entropy (DistEn), a robust estimator of complexity for many signals. However, it fails to discriminate random noise, pink noise and Henon map-based chaotic signals. Furthermore, it underestimates the complexity of chaotic signals at higher scales. To circumvent these problems, we propose an improved distribution entropy (ImDistEn), which utilizes embedded vectors' orientation, ordinality and ℓ 1 -norm distance information for its computation. Simulation results show that ImDistEn can provide clear distinction of different classes of real-world signals, besides accurately assessing the complexity of various synthetic signals. • Dynamical complexity of synthetic and real-world signals are analysed by the proposed “ImDistEn” entropy measure. • Impacts of data length, embedding dimension, noise, and sampling frequency on the proposed entropy measure are demonstrated. • Comparative analysis of the state-of-the-art with the proposed entropy measure is done using real and synthetic signals. • Hypothesis tests showed that the meditative state and normal heart conditions have more complex heart beat dynamics.