On the use of non-Gaussian models for statistical description of road micro-surface profiles

When analysing vehicle-road interaction, probability density function (PDF) of random micro-surface is required. Since the asperity tops are polished by tyres stronger than the valley bottoms, the surface height profiles become asymmetrical. As a result, the PDFs of micro-surface signals are often different from the Gaussian model and one needs a non-Gaussian PDF model operating with skewness and kurtosis. Previous solutions by the Pearson and Johnson distributions do not lend themselves for further implementation in analytical form. To overcome this difficulty, a non-Gaussian PDF can be constructed from a few Gaussian sections with different mean values and standard deviations. To use such a piecewise-Gaussian model for analytical derivations, it is simply necessary to apply the classic Gaussian equation several times. An example of skewed PDF of micro-surface of an asphaltic concrete highway measured by a laser scanning system was adequately approximated by the tetra-Gaussian model consisting of four Gaussian sections.