Laplace Models for Describing Road Profiles

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Laplace Models for Describing Road Profiles

Johannesson, Pär / Rychlik, Igor

Gaussian models are frequently used for modelling environmental loads, e.g. sea elevation, wind loads and road profiles. However, the Gaussian model is often only valid for short sections of the load. Here we will study road profiles, which is the longitudinal road elevation along a road track. The profile for short sections of roads, say 100 m, is well modelled by a Gaussian process, whereas longer sections of roads, say 10 km, typically contain shorter sections with high irregularity. The variability between sections is higher than what can be explained by the stationary Gaussian model. This phenomenon can be captured by a Laplace process, which can be seen as a Gaussian process with randomly varying variance. Laplace models for both a single track and for two parallel tracks will be treated. Further, an approximation of the expected damage can be computed from the parameters of the Laplace process. We will give examples of modelling road profiles using Laplace models. Especially, it will be demonstrated how to reconstruct a road profile based on sparse road roughness measurements, such as a sequence of IRI (International Roughness Index) for 100 metre road sections.