Surface Profile Evaluation by Fractal Dimension and Statistic Tools Using Matlab

Abstract

A lot of natural structures in industry applications can be hardly described by conventional methods – mostly statistic tools, because they are complex and irregular. A relatively new approach is the application of the fractal geometry that is successfully used in science, but an application in industry is sporadic and experimental only. However, the fractal geometry can be used as a useful tool for an explicit, objective and automatic description of production process data (laboratory, off-line and potential on-line). The article is intended on application of the fractal geometry with combination of statistic tool for a quantification of metal surface changes of relatively new materials: iron aluminides in comparison with currently used chrome-nickel steels in contact with a glass melt. The software Matlab was used for the generation and classification of dividing lines (a surface profile or a surface roughness evaluation) and for evaluation of results. Basic statistic and roughness parameters were used. The obtained data in a digital form can be described by the fractal geometry, which expressing the complexity degree of structured data (ideally) by means of a single number, the fractal dimension. The dimension can be estimated by many different methods. A compass method is one of them and the method is based on the measurement of the dividing line by different size of a ruler.