Modelling roughness of road profiles on parallel tracks using roughness indicators

Abstract

The vertical road input is the most important load for durability assessments of vehicles. We focus on stochastic modelling of the parallel road profiles with the aim to find a simple but still accurate model for such bivariate records. A model is proposed that is locally Gaussian with randomly gamma distributed variances leading to a generalized Laplace distribution of the road profile. This Laplace model is paired with the ISO spectrum and is specified by only three parameters. Two of them can be estimated directly from a sequence of roughness indicators, such as IRI or ISO roughness coefficient. The third parameter needed to define the cross spectrum between the left and right road profiles is estimated from the sample correlation. Explicit approximations for the expected fatigue damage for the proposed Laplace-ISO model are developed and its usefulness is validated using measured road profiles.

Laplace distribution models for road topography and roughness

“…In (Bogsjö et al, 2012) it was shown that replacing Gaussian noise by Laplace noise √ R k X k produces a more accurate model of roughness. In this paper we summarize principles of Laplace distribution modelling that arise from work in (Åberg et al, 2009;Bogsjö et al, 2012) and its extensions and applications presented in (Johannesson & Rychlik, 2013, 2014Kvanström et al, 2013;Johannesson et al, 2015a;Kozubowski et al, 2013).…”

“…Clearly, two-tracks data are strongly correlated, particularly in the regions of high roughness of the roads. Here we give extensions of the Laplace models to multiple correlated signals to cover the case of road profiles along parallel tracks, see (Kozubowski et al, 2013;Johannesson et al, 2015a).…”

“…Simply speaking it is Gaussian processes where the variance is randomly changing. In the current paper we present Laplace modelling based on (Bogsjö et al, 2012;Johannesson & Rychlik, 2014) and its extensions and applications presented in (Johannesson & Rychlik, 2013;Kvanström et al, 2013;Johannesson et al, 2015a;Kozubowski et al, 2013).…”

“…road profiles along two parallel tracks and multi-dimensional loads. First a non-stationary Laplace model of road profiles along two parallel paths taken by left and right wheels of a vehicle are presented, following (Kozubowski et al, 2013;Johannesson et al, 2015a). Then a stationary multi-dimensional Laplace model is presented, as described in (Kvanström et al, 2013), with an example on cultivator loads.…”

“…Note that the (squared) coherence spectrum is |K LR (Ω)| 2 . Based on the spectral representation there are methods to simulate Gaussian and Laplace roads, see (Kozubowski et al, 2013;Johannesson et al, 2015a). The algorithm and Matlab code to simulate the signal is presented in Appendix A.3.…”