Entropy Analysis and Fault Diagnosis in Complex Time Series
Summary
Complex time series arise in domains as diverse as mechanical engineering, power systems and biomedical monitoring. Entropy analysis provides quantitative measures of unpredictability and complexity by mapping patterns in data sequences. Classical metrics such as approximate entropy and sample entropy assess the regularity of fluctuations, while multiscale approaches capture dynamics across temporal scales. These entropy measures serve as sensitive indicators of subtle changes in signal structure, enabling early detection of anomalies. Fault diagnosis frameworks harness entropy features in conjunction with signal decomposition techniques and machine learning classifiers to identify and isolate malfunctions in rotating machinery, hydraulic systems and other industrial contexts. Advances in composite and fluctuation‐based entropy methods have improved robustness against noise and limited data length, enhancing reliability in real‐world applications. Integrated workflows now combine adaptive mode decomposition, entropy feature extraction and optimisation algorithms for automated monitoring. This synergy between information theory and data-driven diagnostics underpins a growing repertoire of tools for condition monitoring, predictive maintenance and risk assessment in complex systems.
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Entropy Analysis and Fault Diagnosis in Complex Time Series publication trend
The graph below shows the total number of articles in entropy analysis and fault diagnosis in complex time series across all publications each year (not limited to Nature Index journals).
Technical terms
Approximate entropy (ApEn): A statistic measuring the likelihood that similar patterns in a time series remain similar at subsequent points.
Sample entropy (SampEn): A refinement of approximate entropy that reduces bias by excluding self-matches when computing pattern regularity.
Multiscale entropy (MSE): The entropy of coarse-grained representations of a time series evaluated over multiple temporal scales.
Composite multiscale entropy (CMSE): An enhancement of MSE that aggregates entropy estimates across overlapping segments to improve reliability at large scales.
Dispersion entropy (DispEn): An entropy measure that quantifies complexity by mapping amplitude values into dispersion patterns.
Refined composite multiscale fluctuation dispersion entropy (RCMFDE): A composite entropy metric extending DispEn to characterise fluctuations over multiple scales with enhanced stability.
Variational mode decomposition (VMD): An adaptive signal decomposition technique that separates a time series into modes via constrained variational optimisation.
Particle swarm optimisation (PSO): A population-based heuristic algorithm inspired by social behaviour for tuning model parameters and optimising feature selection.
References
- Approximate Entropy and Sample Entropy: A Comprehensive Tutorial. Entropy (2019).
- The Multiscale Entropy Algorithm and Its Variants: A Review. Entropy (2015).
- Time Series Analysis Using Composite Multiscale Entropy. Entropy (2013).
- Amplitude- and Fluctuation-Based Dispersion Entropy. Entropy (2018).
- Fault Diagnosis of Hydraulic Pumps Using PSO‐VMD and Refined Composite Multiscale Fluctuation Dispersion Entropy. Shock and Vibration (2020).
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