Using 3D road texture measurements for tyre / road noise modelling

Bernhard Baumgartner 1 , Reinhard Wehr 2 , Andreas Fuchs 3 , Johannes Ruisz 4

AIT Austrian Institute of Technology GmbH Giefinggasse 4, 1210 Vienna, Austria

ABSTRACT When investigating the generation of rolling noise, profound knowledge of the tyre / road interaction is inevitable. Research projects addressing the road surface influence on the noise generation are commonly based on standardized road surface texture parameters e.g. mean profile depth or spectral analysis of surface profiles. Such quantities are calculated from line texture measurements or equally sized parts of 3D-road surface samples. AIT has recently developed a high-speed continuous 3D road surface texture scanner which provides heightened spatial information down to 60 µ m. This allows the determination of a multitude of additional parameters of road surface geometries. In this paper, statistical analyses of the variability of 3D texture parameters on real road sections, as well as basic statistical models to investigate correlations between texture parameters and coupled CPX measurements will be described.

1. INTRODUCTION

Road tra ffi c noise can be seen as main source of noise pollution in Europe [1]. One key aspect of the road noise generation is the emission of tyre / road noise, which is the dominant source in a wide speed range from ca. 40 to 130 km / h [2]. Sustainable tra ffi c noise reduction can therefore be achieved by optimizing the tyre / road contact, where di ff erences in noise emission of roughly 10 dB can be observed for varying road surfaces.

In order to understand the di ff erent noise generation mechanisms of the tyre / road interaction detailed information regarding the rolling noise obtained via the CPX method [3], as well as the texture of the road surface is of great interest. Line texture measurements only contain rudimentary information to describe the geometric properties of the contact zone for isotropic surfaces, e.g. asphalt conrete, EACC and SMA top layers. Considering anisotropic road surfaces, e.g. diamond grinding structures, three-dimensional texture measurement systems gain more importance. This method provides detailed quantitative information of parts of the road surface and allows subsequent application of physical or statistical modelling of the tyre / road interaction.

1 bernhard.baumgartner@ait.ac.at

2 reinhard.wehr@ait.ac.at

3 andreas.fuchs@ait.ac.at

4 johannes.ruisz@ait.ac.at

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

Figure 1: Example of a 3D texture patch with dimensions of ∼ 10 x 10 cm. The surface height is color-encoded (green to red). The texture can be divided in two triangles (blue line), where in each triangle the local maximum is determined (blue crosses) for an adapted MPD calculation.

2. 3D TEXTURE MEASUREMENTS

To further enhance the possibilities to study e ff ects in the tyre / road contact, AIT has recently developed a high-speed 3D road texture scanner which continuously records the road surface with a resolution of 60 µ m. This line-scan stereo vision system captures the texture as well as the depth of a scanned object and is mounted in front of the CPX measurement tyre, thus ensuring that the investigated surface texture can be interpreted as the input function of the tyre.

The system consists of two inclined line-scan cameras and an illumination module. The optical axes of the setup are verged to obtain an enhanced overlapping region of ca. 10 cm, which corresponds to a line length of 2048 pixels. Given the two images from these cameras that were taken from slightly shifted viewpoints (resp. angles), a 3D model can be estimated by determining pixel correspondences between the images [4,5].

2.1. Texture parameter calculations In contrast to line texture measurements, where various texture parameters are defined and standardized (see [6], the utilization of 3D textures is a relatively new field in road research. Therefore, no set of standard descriptors is commonly used for characterizing di ff erent road surfaces. While line texture parameters may be computed via a single line extraction of the 3D surface, the parameters can also be adapted in order to represent similar and comparable quantities. For instance, the mean profile depth (MPD) can be determined based on dividing the surface and identifying the local maxima in the surface segments (see Figure 1). Here, all pre-processing steps as performed in the determination of a line-texture based MPD (zero-phase bandpass corrections, outlier and missing value detections, etc.) need to be considered prior to obtaining a well-defined surface descriptor.

Next to the adapted calculation of common texture parameters, new sets of surface descriptors can be established. Examples of parameters specific for grinding textures are depicted in Figure 2. In the left subplot, the bars of the grinding structures were identified and marked with green frames. Additionally, fractures in the bars can be detected (green rectangles in the right subplot). Both algorithms are based on convolutions with customized kernels.

Using image processing techniques as well as artificial intelligence, a variety of parameters for the description of road surfaces can be established. These might be based on purely geometric features

Figure 2: Example of a diamond grinding texture. Using signal and image processing techniques, the bars of the grinding (green framed areas in the left Figure) as well as structural defects (marked with green squares in the right Figure) can be identified .

Figure 3: Example of the cavity volume between the road surface and a deformed tyre based on a hertzian contact model.

of the road surface, but further allow the application on calculations towards rubber deformation in the tyre / road contact. An example of such a descriptor is shown in Figure 3: the rubber deformation based on a hertzian contact model is utilized for the volume determination of the cavity between a tyre and a road surface with a grinding texture.

2.2. Parameter variations Texture parameters should be designed to describe the geometric properties of road surfaces with regard to their application. Features valuable for describing the impact of road surface textures on tyre / road noise emission may not be useful to characterize other quantities, e.g. rolling resistance or friction. Furthermore, their variation within and outside of surface groups and measurement sections, i.e. their sensitivity, is of importance to be suited as road surface descriptors.

In Figure 4, a density estimate for two surface parameters of four exemplary road sections is shown. The parameters describe the number of local maxima per square meter, i.e. a parameter comparable to the peak count of the surface, with respect to the gradient of the road surface texture in longitudinal direction. A clear distinction between the measurement sections with similar density distribution shapes for grinding sections is apparent. In contrast, SMA sections exhibit visibly deviating density distribution shapes. Di ff erent road surfaces therefore may not only be

Figure 4: Variation of texture parameters within two grinding and two SMA road sections. Each data point describes a texture value pair of the number of local maxima per square meter and the gradient of the road surface in longitudinal direction. Filled contours depict the density estimates of the parameter distributions for the two road surfaces.

distinguishable by their texture parameters, but also by their density distribution shapes within road sections of certain length. Density distribution of texture parameters may further be used as an indicator of the uniformity of the installation quality as well as the constancy during its lifetime, i.e. ageing e ff ects.

3. STATISTICAL MODELLING APPROACHES

As tyre / road noise emissions strongly depend on the road surface texture, a modelling of the correlations of the two quantities is of high interest for noise reduction at the source. Various aims and approaches may be followed (Figure 5): First, a physical model of the tyre can be created with the aim of determining the vibrational modes of the tyre and thereby inferring on the sound emissions of the tyre itself. Information on the tyre behaviour thus may be obtained allowing for a tyre design adapted to real road surfaces. Second, a statistical model without the consideration of the physical properties of the tyre / road system may be assembled.

The choice of the modelling approach is also dependent on the aim of the investigation. When targeting the prediction of sound emission based on di ff erent road surface textures and both model types be used for inference of the correlation of texture and tyre / road noise emission, the statistical model may in many cases outperform the physical one. Especially with the current emergence of artificial intelligence models, further developments may be expected in the recent future. Highly flexible neural networks may possess the ability to combine the di ff erent tyre / road noise generation mechanisms. This, however, comes at a cost: whereas basic models preserve a certain interpretability of the interrelations of texture and noise emission, complex models tend to evolve towards black boxes.

When basic statistical models are developed, an important question is the model formulation, out of which two crucial considerations are as follows: Depending on the range of the input parameters (texture) and the output (tyre / road noise), models based on statistical formulations may need to incorporate nonlinear interrelations. These can be selected for linear models (via a transformation of the predictors), or model-inherent as in regression trees or neural networks. Another factor a ff ecting the model formulation is the extent of the available data. Especially if multivariate and more complex nonlinear models shall be used, the measured dataset must be of su ffi cient size in order to be split up into test and training subsets.

10000 # of maxima per m?

physical statistical

inference prediction

nonlinear linear

global local

Figure 5: Di ff erent scopes of trye / road noise modelling

It must further be known, whether the model needs to perform on a global scale of texture parameters (e.g. for a wide group of road surfaces), or detailed information with low estimates of the model error for a small range of texture variations is of interest. Another aspect has to be kept in mind in this context: multiple noise generation mechanisms may appear in overlapping frequency ranges, whereas they will alternately dominate the overall noise emission in the frequency range. Therefore, models might perform well for a certain group of road surfaces, but fail for a di ff erent set due to missing / insu ffi cient texture input information.

3.1. Example of a statistical modelling process An example of a local statistical modelling is described in [7] where acoustic ageing e ff ects of SMA road surfaces were investigated (local modelling). Therein, ca. 25 km of combined CPX and 3D texture measurements on SMA road sections of di ff ering ages were performed. Considering the characteristics of SMA road surfaces, a multitude of texture parameters were implemented. These parameters were established to represent the varieties of the ageing SMA sections as well as remain descriptive in order to allow for easy interpretability of the interrelations of texture variations and acoustic ageing e ff ects (inference modelling). Variations in the road surface were of interest only, therefore a purely statistical approach was chosen and no tyre model was implemented for further analysis. Finally, both a linear model based on a prior principal component analysis as well as a highly nonlinear random forest regression model were computed.

During the modelling, numerous aspects were considered: To prevent overfitting, the number of features for the prediction were restricted based on the sample size. In order to test for outliers or leverage datapoints, the dataset was split into test and training data. Feature space as well as resulting CPX level range were narrow, linearity in the model structure therefore proved to be a viable assumption. Considering the out-of-bag performance as benchmark parameters, the final model qualities of the linear and the random forest regression model are comparable. Based on two 3D texture parameters, frequency-dependent performance, expressed as root mean squared error between 0.7 and 0 . 9 dB could be achieved.

4. CONCLUSIONS

With the developing field of 3D road texture measurements, new possibilities emerge in tyre / road noise modelling. In combination with statistical and physical modelling approaches as well as artificial intelligence potentials, new impulses can be expected in research towards reducing tyre / road

noise. When choosing a statistical modelling approach to investigate tyre / road noise generation mechanisms, certain aspects have to be considered during the process. Descriptive parameters that exhibit an adequate value range to allow for statistical modelling and designed with respect to the problem formulation need to be found. The choice of the model formulation needs to be adapted to the scope of each individual investigation. Finally, a balance of costs for the data acquisition process and the model sample size, keeping in mind the partition in test and training dataset, needs to be taken into account.

REFERENCES

[1] European Environment Agency. Environmental noise in Europe, 2020. Publications O ffi ce, 2020. [2] Ulf Sandberg and Jerzy Ejsmont. Tyre / road noise reference book . INFORMEX, Harg, SE-59040 Kisa, Sweden, 2002. [3] International Organization for Standardization. ISO 11819-2: Acoustics - Method for measuring the influence of road surfaces on tra ffi c noise - Part 2: Close-proximity method . Geneva, 2017. [4] Kristiáán Valentín, Reinhold Huber-Mörk, and Svorad Stolc. Binary descriptor-based dense line- scan stereo matching. Journal of Electronic Imaging , 26(1):1 – 12, 2017. [5] Richard Szeliski. Computer Vision . Springer London, 2011. [6] International Organization for Standardization. ISO 13473-1:2019: Characterization of pavement texture by use of surface profiles – Part 1: Determination of mean profile depth . Geneva, 2019. [7] Reinhard Wehr, Andreas Fuchs, and Simon Breuss. Statistical tyre / road noise modelling based on continuous 3d texture data. Acta Acustica , 5:52, 2021.