Four Parameter Inverse Characterization of Fractal Surfaces

Motivated by the need to determine the mechanical, electrical and thermal properties of contact surfaces between deformable materials that conduct electricity and heat, we are presenting here a method for characterizing certain topological characteristics of rough surfaces. The inverse identification of a set of parameters associated with the parametric representation of any rough surface based on profilometric data is described in contrast with the standard one parameter approaches. The description of the surface topography parametrization is first given in terms of a function that enables the generation of synthetic data. Objective functions are created based on both the profilometric evaluations of the parametric representation of the surface as well as its power spectrum. A statistical Monte Carlo based optimization method is implemented for determining the characteristic parameters needed for further analysis that leads to the determination of other physical properties of the surface. Numerical application of the method validates the efficiency and the accuracy of the proposed approach.