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

Abstract: 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 ±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.