The Patterns of the Power Spectral Density Distribution of Fractal and Multifractal Processes

Akhmetkhanov, R. S.

doi:10.3103/s1052618818030020

Cited by 6 publications

(2 citation statements)

References 3 publications

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“…In a number of studies, fractal theory has been used to determine the characteristics of various signals (time series), and good results have been obtained. In article [29], using the example of diagnostic data of a centrifugal pump rolling bearing, the characteristic differences between the spectral power densities of monofractal and multifractal dynamic processes are considered. In [30], the electromagnetic radiation signals of sandstone samples were analyzed by the method of multifractal analysis to detect moisture.…”

Section: Introductionmentioning

confidence: 99%

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Zagretdinov,

Ziganshin,

Izmailova

et al. 2024

Fractal Fract

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In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.

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Section: Introductionmentioning

confidence: 99%

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Zagretdinov,

Ziganshin,

Izmailova

et al. 2024

Fractal Fract

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show abstract

“…The normally used method to extract the fractal feature of packaging materials is to employ the material micromorphology in the preparation process, surface, or fracture morphology of packaging material, and the test data in the property change process of packaging material (e.g., acoustic emission (AE) signal [ 18 ]) to carry out image gray processing and noise reduction processing, respectively. Common methods for calculating fractal dimension include the box counting method [ 19 ], correlation dimension method [ 20 ], Hurst index method [ 21 ], slit island method [ 22 ], yard stick method [ 23 ], area-perimeter method [ 24 ], Sierpiński carpet method [ 25 ], semi-variance method [ 26 ], and power spectral density [ 27 ] (PSD) method. The main methods to obtain object image are scanning electron microscope [ 28 ] (SEM), transmission electron microscope [ 29 ] (TEM), atomic force microscope [ 30 ] (AFM), and other imaging techniques.…”

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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The application of fractal theory to diagnostics of composite materials by acoustic methods

Akhmetkhanov¹

2020

MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2020): Proceeding of the 14th International Conference O

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The Patterns of the Power Spectral Density Distribution of Fractal and Multifractal Processes

Cited by 6 publications

References 3 publications

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

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

The application of fractal theory to diagnostics of composite materials by acoustic methods

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