Abstract: Accurate road roughness model is the key to the simulation research on vehicle dynamic performance. Based on the Weierstrass-Mandelbrot(W-M) function and the definitions of power spectral density(PSD) and coherence function，the analytic coherence relation of the phase angles in the components of fractal model for the left and right wheels is derived. The 2D road roughness fractal models which considers on the phase angle coherence and the Cholesky decomposition of PSD matrix of road roughness are established, respectively，by combining with W-M fractal function and the Cholesky decomposition of PSD matrix of road roughness with different wheelmarks.Theoretical research shows that the road simulation method based on W-M fractal function is equivalent to the harmonic superposition method for γ→1.The fractal model based on the Cholesky decomposition of PSD matrix of road roughness is a universal model，and the fractal model based on the coherence of phase angle is a special case of the above model. Simulated results show that the auto-PSDs of the two models are in good agreement with the corresponding reference PSD，and the accuracy and credibility of the two models are verified consequently for γ→1.

Key words: roadroughness, fractal, powerspectraldensity, phaseangle, coherencefunction, Choleskydecomposition