A novel method to measure static and dynamic complexity of time series based on visualization curves

Area of Science:

• Complex Systems Analysis
• Information Theory
• Time Series Analysis

Background:

• Characterizing complex time series is crucial for understanding dynamic systems.
• Existing methods like RCMS-q-CECs have limitations in accuracy and identification capabilities.

Purpose of the Study:

• To propose a novel method, RCMS-RT-GFOCEC, for enhanced characterization and identification of complex time series.
• To improve upon existing complexity-entropy curve methods for time series analysis.

Main Methods:

• Introduction of reverse transition entropy (RTE) to extract temporal structure probabilities.
• Combination of RTE with refined composite multi-scale analysis and generalized fractional-order entropy.
• Utilizing visualization curves of RTE, Hαmin, and Cαmax for time series identification.

Main Results:

• The RCMS-RT-GFOCEC method demonstrated high accuracy (99.3% and 98.8%) in characterizing artificial and empirical time series.
• Successfully tracked dynamical changes in rolling bearing and turbine gearbox data.
• Outperformed the comparative RCMS-q-CEC method (95.7% and 97.8% accuracy).

Conclusions:

• The RCMS-RT-GFOCEC method offers superior performance in characterizing and identifying complex temporal systems.
• This approach provides a robust tool for analyzing dynamic changes in various industrial and scientific applications.