Statistical artefacts in the determination of the fractal dimension by the slit island method

Maxence Bigerelle (1) , Alain Iost (2)

1 Roberval - Roberval
2 LMPGM - Laboratoire de Métallurgie Physique et Génie des Matériaux

This paper comments upon some statistical aspects of the slit island method which is widely used to calculate the fractal dimension of fractured surfaces or of materials’ features like grain geometry. If a noise is introduced when measuring areas and perimeters of the islands (experimental errors), it is shown that errors are made in the calculation of the fractal dimension and more than a false analytical relation between a physical process parameter and the fractal dimension can be found. Moreover, positive or negative correlation with the same physical process parameter can be obtained whether the regression is performed by plotting the variation of the noisy area versus the noisy perimeter of the considered islands or vice versa. Monte-Carlo simulations confirm the analytical relations obtained under statistical considerations.

Mots clés: Artefact measurement; Statistics; Slit island method; Monte-Carlo simulation; Fractal dimension

Domaines: Matériaux; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Méthodologie [stat.ME]

Maxence Bigerelle, Alain Iost. Statistical artefacts in the determination of the fractal dimension by the slit island method. Engineering Fracture Mechanics, 2004, 71 (7-8), pp.1081-1105. ⟨10.1016/S0013-7944(03)00136-X⟩. ⟨hal-01320673⟩