Research Papers

Developing Compact Models of Terrain Surfaces

[+] Author and Article Information
John B. Ferris

e-mail: jbferris@vt.edu
Virginia Polytechnic Institute and State University,
150 Slayton Avenue,
Danville, VA 24540

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 24, 2012; final manuscript received July 12, 2013; published online August 23, 2013. Assoc. Editor: Sean Brennan.

J. Dyn. Sys., Meas., Control 135(6), 061008 (Aug 23, 2013) (9 pages) Paper No: DS-12-1070; doi: 10.1115/1.4025016 History: Received February 24, 2012; Revised July 12, 2013

Terrain topology is the principal source of vertical excitation to the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle and tire models over a wide range of terrain types, but it is computationally impractical to simulate long distances of every terrain variation. This work seeks to study the terrain surface, rather than the terrain profile, to maximize the information available to the tire model (i.e., wheel path data), yet represent it in a compact form. A method to decompose the terrain surface as a combination of deterministic and stochastic components is presented. If some, or all, of the components of the terrain surface are considered to be stochastic, then the sequence can be modeled as a stochastic process. These stochastic representations of terrain surfaces can then be implemented in tire and vehicle models to predict chassis loads.

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Fig. 1

Creating a uniform grid (curved regular grid) in the horizontal plane

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Fig. 2

Defining the surface coordinate system (u, v, s) in a CRG format

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Fig. 3

Example of a discretized terrain surface in curved regular grid format

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Fig. 4

Original terrain profile measured with VTMS of longitudinally tined concrete located at MnRoad test facility

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Fig. 5

First two empirical basis vectors for a sample of U.S. Highway data, bl

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Fig. 6

First two analytic basis vectors for a sample of U.S. Highway data, pl

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Fig. 7

First two empirical components of terrain for a sample of U.S. Highway data, σi,l

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Fig. 8

First two analytic components of terrain, σi,l for a sample of U.S. Highway data

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Fig. 9

Comparing true surface to subsequent empirical truncated surfaces for a sample of U.S. Highway data

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Fig. 10

Partial autocorrelation of the second empirical component of terrain σi,2 for a sample of U.S. Highway data

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Fig. 11

Empirical bank angle component of terrain and AR synthesis of bank angle component of terrain

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Fig. 12

Comparing true surface to truncated surface with AR synthesized bank angle component of terrain




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