基于分形插值的三维路面重构与分析

Reconstruction and analysis of 3D road based on 3D fractal interpolation

原始精细的路面谱是研究车辆与路面耦合的重要基础,对车辆的通过性和噪声、振动及不平顺性NVH(noise,vibration and harshness)分析有重要的应用价值。为了构建与原始路面相同或相近的路面谱,利用非接触式激光路面不平度仪测量沥青路面、水泥路面、比利时路面和砂石路面的三维路面不平度;基于分形理论,采用迭代函数法重构这四种路面谱;结合路面不平度的统计特性评价指标和分形维数对四种路面的原始谱和重构谱进行评价。研究结果表明:重构前、后路面谱的平均值、标准差、峰度系数以及分形维数变化范围在±5%以内,除水泥路面的偏态系数变化范围均在±9%以内,重构路面谱与原始谱具有一致性;重构路面谱保持了原始路面的结构特性,并具有路面的细微结构。

The interaction between tire and pavement guarantees ground driving force which is used to drive a car forward, so it is a significant foundation to study the interactional principle between them. In addition, studying the coupling-principle of tire and pavement can be conducive to address the NVH （Noise, Vibration and Harshness） issues caused by the roughness and unevenness of pavement, while an accurate pavement model is essential to the simulation study of tire and pavement coupling, because the precise pavement model can provide realistic data for a simulation process. This paper was trying to establish a precise pavement model based on fractal theory and limited sparse roughness data. By using a laser profiler with a sampling interval of 5mm and a sampling precision of 1mm, the sparse roughness data of Bituminous pavement, Concrete pavement, Sand-gravel pavement, and Belgium＇s pavement were obtained in Wageningen University, which is located in Netherlands, and the sampled data were preserved to be a digital elevation matrix in the Matlab workspace. Based on the 3D fractal interpolation method theory, iterated function system was used to reconstruct four types of the road. The 3D figures that display the striking surfaces of the road were plotted by utilizing the original and interpolated digital elevation matrix in the Matlab. Besides, the statistical indexes of material surface roughness （i.e. Arithmetic Mean, Standard Deviation, Deviation Coefficient, and Coefficient of Kurtosis） and fractal dimensions were introduced to evaluate original data and interpolated data, Arithmetic Mean;Standard Deviation is the parameters to reflect the situation of fluctuation; Deviation Coefficient is utilized to describe the distributional level of dents and peaks while coefficient of Kurtosis is to embody a degree of road sharpness, and fractal dimension was computed by utilizing a method of box-counting; ultimately, results were concluded by comparing with the variation of evaluated index. The results show that average value and standard deviation can, to some extent, be used to reflect general fluctuation of pavement, and deviation coefficient and coefficient of kurtosis can be utilized to evaluate fine roughness of pavement, the varied ranges of three indexes, i.e. average value, standard deviation and coefficient of kurtosis, before and after reconstructed were less than ＆#177;5%, while the ranges of the deviation coefficients were less than ±9% except Sand-gravel pavement with 22.7%, which represented that the basic structures of four kinds of pavements were sustained well after interpolated. In addition, the variations of fractal dimensions between original data and interpolated data were within the range of ±5%, which mean that the complexity of pavement before and after interpolated were sustained well. In summary, the 3D figures plotted by data collecting by the laser profiler could sustain a basic structure of pavement, but could not represent a fine structure, whereas the 3D figure plotted by interpolated data was not only able to hold the basic structure, but reflect their exquisite and plump fine structure.