Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation

Paun, Maria‐Alexandra; Paun, Vladimir‐Alexandru; Pãun, Viorel-Puiu

doi:10.3390/fractalfract6080458

Cited by 3 publications

(2 citation statements)

References 21 publications

(34 reference statements)

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“…When describing particular images (or surfaces) and signals, the fractal structure often plays a very effective role. For example, Huang and Lee [1] used fractal analysis to classify pathological prostate images; Lin et al [2] also adopted fractal analysis to classify solitary pulmonary nodules; He and Liu [3] screened dry coal online through fractal analysis and image processing; Yakovlev et al [4] also used fractal analysis to evaluate changes in a modified cement composite; Guo et al [5] characterized and classified tumor lesions of digital mammograms through fractal texture analysis; Crescenzo et al [6] adopted FBM to predict temperature fluctuation; Paun et al [7] used fractal analysis to evaluate micro fractographies; and Hu et al [8] combined FBM and particle swarm optimization to propose a stock prediction model.…”

Section: Introductionmentioning

confidence: 99%

Deep-Learning Estimators for the Hurst Exponent of Two-Dimensional Fractional Brownian Motion

Chang

2024

Fractal Fract

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The fractal dimension (D) is a very useful indicator for recognizing images. The fractal dimension increases as the pattern of an image becomes rougher. Therefore, images are frequently described as certain models of fractal geometry. Among the models, two-dimensional fractional Brownian motion (2D FBM) is commonly used because it has specific physical meaning and only contains the finite-valued parameter (a real value from 0 to 1) of the Hurst exponent (H). More usefully, H and D possess the relation of D = 3 − H. The accuracy of the maximum likelihood estimator (MLE) is the best among estimators, but its efficiency is appreciably low. Lately, an efficient MLE for the Hurst exponent was produced to greatly improve its efficiency, but it still incurs much higher computational costs. Therefore, in the paper, we put forward a deep-learning estimator through classification models. The trained deep-learning models for images of 2D FBM not only incur smaller computational costs but also provide smaller mean-squared errors than the efficient MLE, except for size 32 × 32 × 1. In particular, the computational times of the efficient MLE are up to 129, 3090, and 156248 times those of our proposed simple model for sizes 32 × 32 × 1, 64 × 64 × 1, and 128 × 128 × 1.

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Section: Introductionmentioning

confidence: 99%

Deep-Learning Estimators for the Hurst Exponent of Two-Dimensional Fractional Brownian Motion

Chang

2024

Fractal Fract

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“…Utilizing the phase space-embedding technique to reconstruct the attractor and to compute the autocorrelation dimension, the fracture surface of the Zircaloy-4 samples was investigated. The fractal analysis method manages to highlight damage complications, and provides a description of the morphological parameters of various fractures by calculating the fractal dimension and lacunarity [7].…”

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confidence: 99%

Special Issue: Nonlinear Dynamics in Complex Systems via Fractals and Fractional Calculus

Pãun

2023

Fractal Fract

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Fractal-Based Evaluation of the Spatial Relationship Between Conditioning Factors and the Distribution of Landslides (a Case Study in Tinh Tuc, Cao Bang Province, Vietnam)

Van Duong,

Fomenko,

Nguyen

2023

Progress in Landslide Research and Technology

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This paper presents the assessment results of the spatial relationship between past landslides and four landslide factors in Tinh Tuc town, Cao Bang province, Vietnam, including distance to roads, distance to faults, distance to drainage, and distance to geological boundaries. The fractal dimension values were determined using fractal analyses on three sets of raw data, including the number of landslides, landslide density, and landslide relative density. Using a combination of the frequency ratio (FR) method and the fractal method, landslide susceptibility maps were produced to determine which raw data set more properly analyzes the role of factors in the development of the landslide process. Assessment results using the receiver operating characteristic (ROC) method indicate that the fractal analysis of the raw data sets successfully determines the spatial relationship between conditioning factors and landslides in the study area. In addition, relationship analyses using datasets based on landslide density provide more optimal outcomes. The authors also suggest integrating the fractal method with other quantitative assessment methods to improve the accuracy of landslide prediction in Vietnam and worldwide.

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Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation

Cited by 3 publications

References 21 publications

Deep-Learning Estimators for the Hurst Exponent of Two-Dimensional Fractional Brownian Motion

Deep-Learning Estimators for the Hurst Exponent of Two-Dimensional Fractional Brownian Motion

Special Issue: Nonlinear Dynamics in Complex Systems via Fractals and Fractional Calculus

Fractal-Based Evaluation of the Spatial Relationship Between Conditioning Factors and the Distribution of Landslides (a Case Study in Tinh Tuc, Cao Bang Province, Vietnam)

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