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分析了二维分形布朗运动的功率谱,得出其与路面不平度二维功率谱具有相似的特性,提出了利用分形布朗运动建立路面不平度的二维重构模型。运用分形布朗运动随机中点位移插值算法基本原理,通过求解分形参数即分形维数与路面方差,利用随机中点位移算法实现了二维路面不平度重构。对重构模型的功率谱与理论功率谱进行对比。结果表明,分形布朗模型建立的路面不平度模型的功率谱能够较好的逼近理论值。
The power spectrum of two-dimensional fractal Brownian motion is analyzed. It is found that the two-dimensional power spectrum has similar characteristics with the two-dimensional power spectrum of the unevenness of pavement. A two-dimensional reconstruction model of pavement roughness using fractal Brownian motion is proposed. By using the basic principle of the fractal-Brownian motion stochastic mid-point displacement interpolation algorithm, fractal parameters such as fractal dimension and road surface variance are calculated and the two-dimensional road surface roughness is reconstructed by stochastic mid-point displacement algorithm. The reconstructed model is compared with the theoretical power spectrum. The results show that the power spectrum of the road roughness model established by the fractal Brownian model can approximate the theoretical value well.