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AR(1) time series with autoregressive gamma variance for road topography modeling

Johannesson, Pär; Podgorski, Krzysztof LU ; Rychlik, Igor and Shariati Fokalaei, Nima LU (2016) In Probabilistic Engineering Mechanics 43. p.106-116
Abstract
A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) process with randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal.

A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed.

The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressive process is fitted from the autocorrelation of the squared values of the model.

The shape parameter of the gamma distribution is... (More)
A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) process with randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal.

A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed.

The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressive process is fitted from the autocorrelation of the squared values of the model.

The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution.

Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method.

It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely Gaussian model. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
road roughness, road surface profile, generalized Laplace distribution, Non-Gaussian time series, gamma distributed variances, road topography, road hilliness
in
Probabilistic Engineering Mechanics
volume
43
pages
106 - 116
publisher
Elsevier
external identifiers
  • scopus:84954350405
  • wos:000370999000009
ISSN
0266-8920
DOI
10.1016/j.probengmech.2015.12.006
language
English
LU publication?
yes
id
33d52106-a191-4e22-9fa4-2cf23db71eb5 (old id 8727777)
date added to LUP
2016-02-19 16:15:36
date last changed
2017-05-21 03:06:57
@article{33d52106-a191-4e22-9fa4-2cf23db71eb5,
  abstract     = {A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) process with randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal.<br/><br>
A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed.<br/><br>
The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressive process is fitted from the autocorrelation of the squared values of the model.<br/><br>
The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution.<br/><br>
Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method.<br/><br>
It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely Gaussian model.},
  author       = {Johannesson, Pär and Podgorski, Krzysztof and Rychlik, Igor and Shariati Fokalaei, Nima},
  issn         = {0266-8920},
  keyword      = {road roughness,road surface profile,generalized Laplace distribution,Non-Gaussian time series,gamma distributed variances,road topography,road hilliness},
  language     = {eng},
  pages        = {106--116},
  publisher    = {Elsevier},
  series       = {Probabilistic Engineering Mechanics},
  title        = {AR(1) time series with autoregressive gamma variance for road topography modeling},
  url          = {http://dx.doi.org/10.1016/j.probengmech.2015.12.006},
  volume       = {43},
  year         = {2016},
}