Multifractal characterization of energy consumption in operating systems using empirical mode decomposition

Abstract

Multi-fractal Detrended Fluctuation Analysis (MF-DFA) is a reliable approach for determining long-range correlations and multifractal scaling properties in time series. In this work, MF-DFA is applied to study the multifractal properties of the software-hardware binomial by means of their energy performance. Specifically the energy consumption signals of four different Operating Systems, namely, Raspberry Pi OS Lite, Raspberry Pi OS Desktop, DietPi, and UbuntuCore, all running on a Raspberry Pi 3B are studied. From the energy consumption time series, three distinct scaling regimes (small, medium, and large) are identified, each characterized by specific scaling features. The analysis reveals complex behaviors in the energy consumption signals, including fractality, multifractality, and non-scaling behaviors, which vary across both operating systems and scaling regimes. Later, using Empirical Mode Decomposition, consistent scaling patterns are observed across all regimes despite variations in the original signals. The multifractal analysis shows that high-frequency intrinsic mode functions (IMFs) shift from persistence to antipersistence, while low-frequency IMFs exhibit non-stationary, highly persistent behaviors. Additionally, the degree of multifractality varies more at smaller scales but increases at larger scales, stabilizing before decaying in the residual. Overall, the results demonstrate that multifractal analysis provides a precise method for capturing complex energy consumption patterns across different operating systems, offering deeper insights into the hardware-software energy consumption relationship.