Journal of Zhejiang University SCIENCE A
2006 Vol. 7 Suppl. II p. 287-292ISSN 1009-3095(Print), 1862-1775(Online)
Fractal modelling of off-road terrain oriented to vehicle virtual test
Wang Qian-Ting†1, Guo Jian2, Chen Yi-Zhi3
(1School of Mechanical and Energy Engineering, Zhejiang University, Hangzhou 310027, China)
(2Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China)
(3College of Statistics & Computing Science, Zhejiang Gongshang University, Hangzhou 310035, China)
Received Mar. 3, 2006 revision accepted June 2, 2006
Abstract: In order to reconstruct typical off-road terrain surface for vehicle performance virtual test, a terrain generation method with controllable roughness was proposed based on fractal dimension. Transverse profile sampling and unevenness characteristics of typical off-road terrain were discussed according to the choices of appropriate wavelength and sampling interval. Since the off-road terrain in virtual environment is self-similar, the method of calculating the discrete fractal Gauss noise and its auto-correlation function were analyzed. The terrain surface fractal dimension was estimated by determining the Hurst coefficient. As typical off-road terrain is rugged terrain, the method of reconstructing it using fractal modelling is presented. The steps include calculating statistical variations in the absolute value of the difference in elevation between two points, plotting the points in log-log space, identifying linear segments and estimating fractal dimension from the linear segments slope. The constructed surface includes information on potholes, bumps, trend and unevenness of terrain, and can be used as the excitation of vehicle performance virtual test.
Key words: Off-road terrain, Transverse profile of terrain, Terrain surface reconstruction, Fractal dimension
doi:10.1631/jzus.2006.AS0287 CLC number: U467.3
 Arakawa, K., Krotkov, E., 1996. Fractal modelling of natural terrain: analysis and surface reconstruction with range data. Graphical Models and Image Processing, 58(5):413-436.
 Fukami, K., Ueno, M., Hashiguchi, K., Okayasu, T., 2006. Mathematical models for soil displacement under a rigid wheel. Journal of Terramechanics, 43(3):287-301.
 Sun, L., 2001. Computer simulation and field measurement of dynamic pavement loading. Mathematics and Computers in Simulation, 56(3):297-313.
 Luo, X.F., 2005. Knowledge acquisition based on the global concept of fuzzy cognitive maps. Lecture Notes in Computer Science, 3795:579-584.
 Mandelbrot, B.B., 1982. The Fractal Geometry of Nature. Freeman, San Francisco.
 Pentland, A.P., 1984. Fractal-based description of natural scenes. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(6):661-674.
 Schmeitz, A.J.C., Jansen, S.T.H., Pacejka, H.B., Davis, J.C., Kota, N.N., Liang, C.G., Lodewijks, G., 2004. Application of a semi-empirical dynamic tyre model for rolling over arbitary road profiles. International Journal of Vehicle Design, 36(2/3):194-215.
 Siddharthan, R.V., Sebaaly, P.E., El-Desouky, M., Strand, D., Huft, D., 2005. Heavy off-road vehicle tire-pavement interactions and response. Journal of Transportation Engineering, 131(3):239-247.
 Uys, P.E., Els, P.S., Thoresson, M.J., 2006. Criteria for handling measurement. Journal of Terramechanics, 43(1):43-67.