不确定系统的多信号多重分形去趋势波动分析——在单片机软件程序能耗中的应用

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Juan Carlos de la Torre, Pablo Pavón-Domínguez, Bernabé Dorronsoro, Pedro L. Galindo, Patricia Ruiz
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引用次数: 0

摘要

不确定系统是那些观察到一些可变性的系统,这意味着对系统的不同观察将产生不同的测量结果。研究这样的系统需要在多个测量中使用统计方法,这可以克服不确定性,前提是单个测量不能代表系统的行为。在这种情况下,现有的多重分形去趋势波动分析(MFDFA)方法无法给出可靠的结论。这项工作提出了多信号MFDFA (MS-MFDFA),这是一种使用MFDFA算法精确表征不确定系统的新方法,它可以通过同时考虑大量信号来克服系统的不确定性。作为一个案例研究,我们考虑表征软件(Sw)消费的问题。问题的困难主要来自软件和硬件(硬件)之间交互的复杂性,以及消耗测量的高度不确定性,这受到并发软件服务、硬件和外部因素(如环境温度)的影响。我们应用MS-MFDFA来生成软件消费配置文件的签名,而不考虑执行时间、消费级别和不确定性。多个消耗信号(或时间序列)从不同的Sw运行中构建,在运行Sw时获得每个瞬时输入电流的高频采样。还提出了八个软件程序的基准分析。此外,一个功能齐全的应用程序自动执行MS-MFDFA分析已经免费提供。结果表明,所提出的方法是一种适用于不确定系统中大量时间序列多重分形分析的近似方法。此外,多重分形特性分析表明,该方法能够区分所研究的8个Sw程序,显示多重分形行为存在的时间尺度范围的差异。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers
Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a single measurement is not representative of the system’s behavior. In such cases, the current multifractal detrended fluctuation analysis (MFDFA) method cannot offer confident conclusions. This work presents multi-signal MFDFA (MS-MFDFA), a novel methodology for accurately characterizing uncertain systems using the MFDFA algorithm, which enables overcoming the uncertainty of the system by simultaneously considering a large set of signals. As a case study, we consider the problem of characterizing software (Sw) consumption. The difficulty of the problem mainly comes from the complexity of the interactions between Sw and hardware (Hw), as well as from the high uncertainty level of the consumption measurements, which are affected by concurrent Sw services, the Hw, and external factors such as ambient temperature. We apply MS-MFDFA to generate a signature of the Sw consumption profile, regardless of the execution time, the consumption levels, and uncertainty. Multiple consumption signals (or time series) are built from different Sw runs, obtaining a high frequency sampling of the instant input current for each of them while running the Sw. A benchmark of eight Sw programs for analysis is also proposed. Moreover, a fully functional application to automatically perform MS-MFDFA analysis has been made freely available. The results showed that the proposed methodology is a suitable approximation for the multifractal analysis of a large number of time series obtained from uncertain systems. Moreover, analysis of the multifractal properties showed that this approach was able to differentiate between the eight Sw programs studied, showing differences in the temporal scaling range where multifractal behavior is found.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
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