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Research Papers

Residual Analysis of Autoregressive Models of Terrain Topology

[+] Author and Article Information
Shannon Wagner, John B. Ferris

Vehicle Terrain Performance Laboratory, Virginia Tech Department of Mechanical Engineering, Blacksburg, VA24061

J. Dyn. Sys., Meas., Control 134(3), 031003 (Mar 27, 2012) (6 pages) doi:10.1115/1.4005502 History: Received August 10, 2010; Revised March 10, 2011; Published March 27, 2012; Online March 27, 2012

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to parsimoniously characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar topological characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model and a residual process provide the mathematical framework to describe this process. A statistical test is developed to determine if the residual process is independent and identically distributed (IID) and, therefore, stationary. A reference joint probability distribution of the residuals is constructed based on the assumption that the data are realizations of an IID stochastic process. The distribution of the residuals is then compared to this reference distribution via the Kolmogorov–Smirnov “goodness of fit” test to determine whether the IID assumption is valid. If the residual process is IID, a single probability distribution can be used to generate residuals and synthetic terrain of any desired length. This modeling method and statistical test are applied to a set of U.S. highway profile data and show that the residual process can be assumed to be IID in virtually all of these cases of nondeformable terrain surfaces.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Terrain profile from a U.S. highway

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Figure 2

Set of residuals for the AR model

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Figure 3

Transition matrix for the set of residuals

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Figure 4

Sample joint probability matrix

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Figure 5

Reference joint PMF

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Figure 6

Reference joint PMF with a circular region of interest

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Figure 7

Residual transitions with a circular region of interest

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Figure 8

CPFs from the reference joint PMF and the set of residual values

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Figure 9

Graphical representation of the Kolmogorov-Smirnov test

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Figure 10

Distribution of the Kolmogorov-Smirnov test statistic for U.S. highways

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