Detection and Comparative Evaluation of Noise Perturbations in Simulated Dynamical Systems and ECG Signals Using Complexity-Based Features

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Abstract
Noise contamination is a common challenge in the analysis of time series data, where stochastic perturbations can obscure deterministic dynamics and complicate the interpretation of signals from chaotic and physiological systems. Reliable identification of noise regimes and their intensity is therefore essential for robust analysis of dynamical and biomedical signals, where incorrect attribution of stochastic perturbations can lead to misleading interpretations of system behavior. For this reason, the present study examines the role of complexity-based descriptors for identifying stochastic perturbations in time series and analyzes how these metrics respond to different noise regimes across heterogeneous dynamical systems. A supervised learning approach based on complexity descriptors was developed to analyze controlled perturbations in multiple signal types. Gaussian, pink, and low-frequency noise disturbances were injected at predefined intensity levels into the Rössler and Lorenz chaotic systems, the Hénon map, and synthetic electrocardiogram signals, while AR(1) processes were used for validation on inherently stochastic signals. From these systems, eighteen entropy-based, fractal, statistical, and singular value decomposition-based complexity metrics were extracted from either raw signals or reconstructed phase spaces. These features were used to perform three classification tasks that capture different aspects of noise characterization, including detecting the presence of noise, identifying the perturbation type, and discriminating between different noise intensities. In addition to predictive modeling, the study evaluates the complexity profiles and feature relevance of the metrics under varying perturbation regimes. The results show that no single complexity metric consistently discriminates noise regimes across all systems. Instead, system-specific relevance patterns emerge. Under given experimental constraints (data partitioning, machine learning algorithm, etc.), Approximate Entropy provides the strongest discrimination for the Lorenz system and the Hénon map, the Coefficient of Variation, Sample and Permutation Entropy dominate classification for ECG signals, and the Condition Number and Variance of first derivative together with Fisher Information are most informative for the Rössler system. Across all datasets, the proposed framework achieves an average accuracy of 99% for noise presence detection, 98.4% for noise type classification, and 98.5% for noise intensity classification. These findings demonstrate that complexity metrics capture structural and statistical signatures of stochastic perturbations across a diverse set of dynamic systems.
Funding Information
  • BMK, BMAW, and the federal state of Vienna (COMET - SBA Research)
  • Austrian Federal Ministry of Labour and Economy, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association (CDL - AsTra)

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