Katz Fractal Dimension of Geoelectric Field during Severe Geomagnetic Storms

Gil, Agnieszka; Glavan, Vasile; Wawrzaszek, Anna; Modzelewska, Renata; Tomasik, Łukasz

doi:10.3390/e23111531

Cited by 7 publications

(7 citation statements)

References 82 publications

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“…In this work, basing on the review of literature and continuing our previous studies [32,45], we initially compared a few methods: the Katz algorithm [11], which revealed discriminating power [32,38], its modifications [46,47], Higuchi method [12], Structure Function scaling [18,[48][49][50], and Detrended Fluctuation Analysis [15,51].…”

Section: Fractal Methods Selectionmentioning

confidence: 99%

“…Gil et al [32] considered geomagnetic field components and modelled geoelectric field for the Belsk mid-latitude station during the full solar magnetic cycle of 1996-2019. Katz fractal dimension technique was applied in moving windows of 60 min and a significant increase in roughness (Katz dimension) of the analysed characteristics during severe geomagnetic storms was revealed.…”

Section: Introductionmentioning

confidence: 99%

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Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

Wawrzaszek

Modzelewska

Krasińska

et al. 2022

Entropy

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We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

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Section: Fractal Methods Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

Wawrzaszek

Modzelewska

Krasińska

et al. 2022

Entropy

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“…For this reason, and its easy implementation [ 38 ], the use of the Katz fractal dimension is proposed in this work. This index has been used in different applications, such as the detection of faults on induction motors [ 38 ], the study of the geoelectric field of the earth during severe geomagnetic storms [ 39 ], and speech emotion classification [ 40 ].…”

Section: Materials and Methodsmentioning

confidence: 99%

Supervised Machine-Learning Methodology for Industrial Robot Positional Health Using Artificial Neural Networks, Discrete Wavelet Transform, and Nonlinear Indicators

Galan-Uribe

Amezquita-Sanchez

Morales-Velazquez

2023

Sensors

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Robotic systems are a fundamental part of modern industrial development. In this regard, they are required for long periods, in repetitive processes that must comply with strict tolerance ranges. Hence, the positional accuracy of the robots is critical, since degradation of this can represent a considerable loss of resources. In recent years, prognosis and health management (PHM) methodologies, based on machine and deep learning, have been applied to robots, in order to diagnose and detect faults and identify the degradation of robot positional accuracy, using external measurement systems, such as lasers and cameras; however, their implementation is complex in industrial environments. In this respect, this paper proposes a method based on discrete wavelet transform, nonlinear indices, principal component analysis, and artificial neural networks, in order to detect a positional deviation in robot joints, by analyzing the currents of the actuators. The results show that the proposed methodology allows classification of the robot positional degradation with an accuracy of 100%, using its current signals. The early detection of robot positional degradation, allows the implementation of PHM strategies on time, and prevents losses in manufacturing processes.

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“…However, this method cannot catch the sudden changes happen in the irregular time-series datasets [71]. To explore the complexity of scale-free time-series data, a variety of different nonlinear techniques such as Higuchi algorithm, power spectrum analysis, and Katz algorithm have been highlighted in different areas [72][73][74][75][76][77]. To approximate the complexity index of Drought Monitor Categories database, we utilize the Higuchi Algorithm [72].…”

Section: Higuchi Fractal Dimension Algorithmmentioning

confidence: 99%

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

Azizi,

Azizi

2024

EURASIP J. Adv. Signal Process.

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Drought is characterized by a moisture deficit that can adversely impact the environment, economy, and society. In North America, like many regions worldwide, predicting the timing of drought events is challenging. However, our novel study in climate research explores whether the Drought Monitor database exhibits fractal characteristics, represented by a single scaling exponent. This database categorizes drought areas by intensity, ranging from D0 (abnormally dry) to D4 (exceptional drought). Through vibration analysis using power spectral densities (PSD), we investigate the presence of power-law scaling in various statistical moments across different scales within the database. Our multi-fractal analysis estimates the multi-fractal spectrum for each category, and the Higuchi algorithm assesses the fractal complexity, revealing that D4 follows a multi-fractal pattern with a wide range of exponents, while D0 to D3 exhibit a mono-fractal nature with a narrower range of exponents.

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Katz Fractal Dimension of Geoelectric Field during Severe Geomagnetic Storms

Cited by 7 publications

References 82 publications

Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

Supervised Machine-Learning Methodology for Industrial Robot Positional Health Using Artificial Neural Networks, Discrete Wavelet Transform, and Nonlinear Indicators

Classification of drought severity in contiguous USA during the past 21 years using fractal geometry

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