Extended self-similarity based multi-fractal detrended fluctuation analysis: A novel multi-fractal quantifying method

Nian, Da; Fu, Zuntao

doi:10.1016/j.cnsns.2018.07.034

Cited by 12 publications

(3 citation statements)

References 24 publications

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“…It should be inferred that relative humidity fluctuations with a strong AM index has strong nonlinear characteristics. In order to explore the nonlinear features in relative humidity, we quantify the multi-fractal strength of relative humidity anomalies over Northeast China, which is a nonlinear characteristic, by means of the ESS-MF-DFA method (Nian and Fu, 2019). The result shows a great consistency (spatial correlation coefficient over the whole region is 0.54, significant at 99% level for Student's t test) between the multi-fractal intensity and AM index.…”

Section: Discussionmentioning

confidence: 99%

Amplitude modulation of relative humidity by wind in Northeast China: the formation of variance annual cycle in relative humidity

Nian

Huang

2022

Clim Dyn

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Relative humidity has an important impact not only on climate change and ecosystems but also on human life. The intensity of high-frequency fluctuations in relative humidity over Northeast China shows a predominant seasonally dependent structure, which may be closely related to regional monsoon activities. However, the factors responsible for this phenomenon remain unknown. This study defines the Variance Annual Cycle (VAC) to describe this seasonally dependent intensity structure of high-frequency relative humidity fluctuations. Relative humidity VAC shows a high correlation with low-frequency oscillations of wind speed. We examine the instantaneous amplitude-phase correlation map and amplitude modulation (AM) index between relative humidity and wind speed. We find that the wind speed with a period around 140-420 days has a significant amplitude modulation effect on the relative humidity with a period around 2-90 days over most regions in Northeast China, which reveals that the low-frequency oscillations of wind speed amplitudemodulate on the high-frequency fluctuations of relative humidity. To explore the physical mechanism behind this modulation, we examine the monthly mean patterns of the atmospheric fields. The patterns indicate that this amplitude modulation is induced by the evolution and transition of East Asian winter monsoon and summer monsoon.

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Section: Discussionmentioning

confidence: 99%

Amplitude modulation of relative humidity by wind in Northeast China: the formation of variance annual cycle in relative humidity

Nian

Huang

2022

Clim Dyn

Self Cite

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“…Many packaging materials have MF feature, and the application and innovation of MF algorithm [ 35 ] have become one of the important choices to analyze the performance of such packaging materials. For the description of non-uniform structures with rich scale features, in the mass fractal region, the box counting dimension of MF spectrum is consistent with the scattering index of the X-ray spectrometer curve, and changes from short-range mass fractal area to the long-range mass fractal region [ 36 ].…”

Section: Basic Theory Of Fractalmentioning

confidence: 99%

Review about the Application of Fractal Theory in the Research of Packaging Materials

Duan

Mao

et al. 2021

Materials

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The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

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“…Subsequently, the detrended moving average has been applied to two nonlinear time series. Nian and Fu [36] incorporated the extended selfsimilarity to construct a novel MF-DFA method, whose performance was more excellent than traditional MF-DFA.…”

Section: Introductionmentioning

confidence: 99%

Modified MF-DFA Model Based on LSSVM Fitting

Wang,

Zhong,

Yue

et al. 2024

Fractal Fract

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This paper proposes a multifractal least squares support vector machine detrended fluctuation analysis (MF-LSSVM-DFA) model. The system is an extension of the traditional MF-DFA model. To address potential overfitting or underfitting caused by the fixed-order polynomial fitting in MF-DFA, LSSVM is employed as a superior alternative for fitting. This approach enhances model accuracy and adaptability, ensuring more reliable analysis results. We utilize the p model to construct a multiplicative cascade time series to evaluate the performance of MF-LSSVM-DFA, MF-DFA, and two other models that improve upon MF-DFA from recent studies. The results demonstrate that our proposed modified model yields generalized Hurst exponents h(q) and scaling exponents τ(q) that align more closely with the analytical solutions, indicating superior correction effectiveness. In addition, we explore the sensitivity of MF-LSSVM-DFA to the overlapping window size s. We find that the sensitivity of our proposed model is less than that of MF-DFA. We find that when s exceeds the limited range of the traditional MF-DFA, h(q) and τ(q) are closer than those obtained in MF-DFA when s is in a limited range. Meanwhile, we analyze the performances of the fitting of the two models and the results imply that MF-LSSVM-DFA achieves a better outstanding performance. In addition, we put the proposed MF-LSSVM-DFA into practice for applications in the medical field, and we found that MF-LSSVM-DFA improves the accuracy of ECG signal classification and the stability and robustness of the algorithm compared with MF-DFA. Finally, numerous image segmentation experiments are adopted to verify the effectiveness and robustness of our proposed method.

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Extended self-similarity based multi-fractal detrended fluctuation analysis: A novel multi-fractal quantifying method

Cited by 12 publications

References 24 publications

Amplitude modulation of relative humidity by wind in Northeast China: the formation of variance annual cycle in relative humidity

Amplitude modulation of relative humidity by wind in Northeast China: the formation of variance annual cycle in relative humidity

Review about the Application of Fractal Theory in the Research of Packaging Materials

Modified MF-DFA Model Based on LSSVM Fitting

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