Laplace distribution models for road topography and roughness

Gaussian models are frequently used for road elevations. However, these models are often only valid for short sections of the road. Here we present a comprehensive approach to describe various aspects of road surface/elevation by using extensions of Gaussian models arising from random gamma distributed variances. These random variances result in the Laplace distribution and thus we refer to the so defined models as Laplace models. The approach is shown to perform well in modelling road topography, road roughness and multi-valued responses of forces and bending moments containing transients. The different Laplace models are presented together with numerical examples and Matlab code for simulation.

[1]  A. Palmgren.  Die Lebensdauer von Kugellargern , 1924 .

[2]  Lu Sun,et al.  MODELING INDIRECT STATISTICS OF SURFACE ROUGHNESS , 2001 .

[3]  Reza Ghorbani,et al.  Drive cycle generation for stochastic optimization of energy management controller for hybrid vehicles , 2010, 2010 IEEE International Conference on Control Applications.

[4]  E. W. C. Wilkins,et al.  Cumulative damage in fatigue , 1956 .

[5]  P. S. Heyns,et al.  Reconstruction of road defects and road roughness classification using vehicle responses with artificial neural networks simulation , 2010 .

[6]  K. Bogsjö.  Coherence of road roughness in left and right wheel-path , 2008 .

[7]  Michael W Gillespie Thomas D Queiroz Cesar A.V Sayers,et al.  The International Road Roughness Experiment (IRRE) : establishing correlation and a calibration standard for measurements , 1986 .

[8]  Nima Shariati Fokalaei,et al.  AR(1) time series with autoregressive gamma variance for road topography modeling , 2016 .

[9]  Peter Múčka,et al.  NON-STANDARD LONGITUDINAL PROFILES OF ROADS AND INDICATORS FOR THEIR CHARACTERISATION , 2004 .

[10]  Peter Múčka,et al.  ROAD WAVINESS AND THE DYNAMIC TYRE FORCE , 2004 .

[11]  Klas Bogsjö,et al.  Road profile statistics relevant for vehicle fatigue , 2007 .

[12]  C. H. Sim.  First-order autoregressive models for gamma and exponential processes , 1990 .

[13]  Eugene J. O'Brien,et al.  The use of vehicle acceleration measurements to estimate road roughness , 2008 .

[14]  Igor Rychlik,et al.  Models for road surface roughness , 2012 .

[15]  Peter Múčka,et al.  Indicators of longitudinal unevenness of roads in the USA , 2008 .

[16]  I. Rychlik.  Note on modelling of fatigue damage rates for non‐Gaussian stresses , 2013 .

[17]  Klas Bogsjö.  Evaluation of stochastic models of parallel road tracks , 2007 .

[18]  Darrel Charles.  Derivation of Environment Descriptions and Test Severities from Measured Road Transportation Data , 2006 .

[19]  Igor Rychlik,et al.  Laplace Processes for Describing Road Profiles , 2013 .

[20]  Vincent Rouillard.  Decomposing pavement surface profiles into a Gaussian sequence , 2009 .

[21]  Vincent Rouillard.  Using predicted ride quality to characterise pavement roughness , 2004 .

[22]  Krzysztof Podgórski,et al.  Multivariate generalized Laplace distribution and related random fields , 2013, J. Multivar. Anal..

[23]  Oldřich Kropáč,et al.  Indicators of Longitudinal Road Unevenness and their Mutual Relationships , 2007 .

[24]  Igor Rychlik,et al.  WAFO - A Matlab Toolbox For Analysis of Random Waves And Loads , 2000 .

[25]  Peter Andren,et al.  Power spectral density approximations of longitudinal road profiles , 2006 .

[26]  Igor Rychlik,et al.  Modelling of road profiles using roughness indicators , 2014 .

[27]  Samuel Kotz,et al.  The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance , 2001 .

[28]  J. D. Robson,et al.  The description of road surface roughness , 1973 .

[29]  Igor Rychlik,et al.  Modelling roughness of road profiles on parallel tracks using roughness indicators , 2016 .

[30]  I. Rychlik,et al.  Fatigue damage assessment for a spectral model of non-Gaussian random loads, Åberk, S. Podgorski, K. Rychlik; I. , 2009 .

[31]  Igor Rychlik,et al.  Laplace moving average model for multi-axial responses in fatigue analysis of a cultivator , 2013 .

[32]  Masanobu Shinozuka,et al.  Simulation of Multivariate and Multidimensional Random Processes , 1971 .

[33]  Patrick Guerin,et al.  Simulation of Real-World Vehicle Missions Using a Stochastic Markov Model for Optimal Powertrain Sizing , 2012, IEEE Transactions on Vehicular Technology.

[34]  Krzysztof Podgórski,et al.  Skewed Laplace distributions II: divisibility properties and extensions to stochastic processes. , 2008 .