AR(1) time series with autoregressive gamma variance for road topography modeling
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8727777
- author
- Johannesson, Pär ; Podgorski, Krzysztof LU ; Rychlik, Igor and Shariati Fokalaei, Nima LU
- organization
- publishing date
- 2016
- 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
- 2016-04-01 10:09:00
- date last changed
- 2022-02-02 06:50:58
@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}}, keywords = {{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}}, doi = {{10.1016/j.probengmech.2015.12.006}}, volume = {{43}}, year = {{2016}}, }