Surface evaluation by estimation of fractal dimension and statistical tools

Area of Science:

• Materials Science
• Data Analysis
• Fractal Geometry

Background:

• Structured and complex data are prevalent in R&D and industrial settings.
• Existing methodologies for data complexity analysis have limitations.
• Surface roughness analysis is crucial for understanding material properties and performance.

Purpose of the Study:

• To develop and apply a novel methodology for describing structured data complexity.
• To analyze surface roughness data using fractal dimension and statistical tools.
• To evaluate the effectiveness of the methodology on a large dataset and compare parameters.

Main Methods:

• Developed a methodology integrating fractal dimension with statistical tools.
• Applied the methodology to analyze data from surface roughness testers.
• Evaluated a large collection of structured surface samples with diverse properties.
• Compared standard and non-standard roughness parameters and assessed sensitivity to directionality.

Main Results:

• The methodology successfully analyzes complex data in various forms (sequences, 2D images).
• Identified optimal parameters for comprehensive surface analysis.
• Demonstrated the methodology's sensitivity to sample directionality.
• Validated the application of fractal geometry for complex surface analysis.

Conclusions:

• The developed methodology provides a robust approach for analyzing structured data complexity.
• Fractal dimension combined with statistical tools offers advanced capabilities for surface analysis.
• The findings have implications for improving data analysis in research and industrial practices.