Journal of Zhejiang University-SCIENCE A

, Volume 7, Supplement 2, pp 287–292 | Cite as

Fractal modelling of off-road terrain oriented to vehicle virtual test

  • Wang Qian-ting 
  • Guo Jian 
  • Chen Yi-zhi 


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 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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. [doi:10.1006/gmip.1996.0035]CrossRefGoogle Scholar
  2. 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. [doi:10.1016/j.jterra.2005.05.005]CrossRefGoogle Scholar
  3. Sun, L., 2001. Computer simulation and field measurement of dynamic pavement loading. Mathematics and Computers in Simulation, 56(3):297–313. [doi:10.1016/S0378-4754(01)00297-X]MathSciNetCrossRefMATHGoogle Scholar
  4. Luo, X.F., 2005. Knowledge acquisition based on the global concept of fuzzy cognitive maps. Lecture Notes in Computer Science, 3795:579–584.CrossRefGoogle Scholar
  5. Mandelbrot, B.B., 1982. The Fractal Geometry of Nature. Freeman, San Francisco.MATHGoogle Scholar
  6. Pentland, A.P., 1984. Fractal-based description of natural scenes. IEEE Trans. on Pattern Analysis and Machine Intelligence, 6(6):661–674.CrossRefGoogle Scholar
  7. 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. [doi:10.1504/IJVD.2004.005356]CrossRefGoogle Scholar
  8. 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. [doi:10.1061/(ASCE)0733-947X(2005)131:3(239)]CrossRefGoogle Scholar
  9. Uys, P.E., Els, P.S., Thoresson, M.J., 2006. Criteria for handling measurement. Journal of Terramechanics, 43(1):43–67. [doi:10.1016/j.jterra.2004.08.005]CrossRefGoogle Scholar

Copyright information

© Zhejiang University 2006

Authors and Affiliations

  • Wang Qian-ting 
    • 1
  • Guo Jian 
    • 2
  • Chen Yi-zhi 
    • 3
  1. 1.School of Mechanical and Energy EngineeringZhejiang UniversityHangzhouChina
  2. 2.Department of Civil EngineeringZhejiang UniversityHangzhouChina
  3. 3.College of Statistics & Computing ScienceZhejiang Gongshang UniversityHangzhouChina

Personalised recommendations