A Review on Fractal Analysis and its Applications in Structural Engineering

Abstract

Fractals refer to rough or fragmented geometric shape in which each sub-section is a reduced-size copy of the whole. Its potential to describe the complex and irregular phenomena leads to wider applicability, and its enormous unexplored potential in the field of structural engineering is to be attended by the research community. This paper first presents a brief theoretical background of the most popular algorithms, such as the box-counting method, Multifractal Detrended Fluctuation Analysis (MFDFA), and Multifractal Detrended Cross-Correlation Analysis (MFDCCA). This paper further presents a comprehensive review of the potential of fractals and multifractals in four specific domains, such as crack identification, pore structure analysis and chloride resistance, and structural damage detection. The review of literature further reveals that 2 dimensional and multi-dimensional extension of fractal theory can be effectively coupled with image analysis for micro-level examination of pore structures, which opens the scope for abundant applications in research in the field of structural materials. The applications of MFDFA and cross-correlation analysis structural health monitoring are very recent research contributions in the field, and they are in the infant stage of applications. The review of research works performed in this study shows that the complete potential of fractals in the structural engineering field is not yet explored by the researchers.