Abstract
Abstract Detecting and localizing transient regime transitions in nonlinear and nonstationary time series remains a major challenge in monitoring and forecasting the behaviour of complex natural and engineered systems. In this work, we formalize and evaluate the D-index (Dynamic Energy Redistribution Index) as an energy-based dynamical diagnostic that quantifies the normalized temporal rate of change of an energy-like functional of a signal. The D-index is conceptually motivated by a quantity originally introduced within structured-systems mechanics to characterize irreversible internal energy production, but is used here strictly in an operational sense for empirical signal analysis. Rather than replacing probabilistic complexity measures derived from Shannon’s information theory, the D-index provides a complementary, energy-aware perspective by revealing localized activation and relaxation phases, burst-like episodes, and transient regime shifts that may remain weakly expressed in probability-based entropies. A computational framework with adaptive window selection is developed to ensure applicability across multiple temporal scales. Experiments on synthetic benchmarks and real observational data, including GOES x-ray flux and GNSS-derived vertical total electron content (VTEC), demonstrate that the D-index reliably identifies transitions between operating regimes, phase-change intervals, and ionospheric responses to solar terminator forcing while remaining robust to moderate and even severe noise contamination. These results confirm the practical value of the D-index as a diagnostic indicator for nonstationary signal analysis, with direct relevance to operational monitoring, early-warning detection, and predictive analytics in complex systems.