## 6 Surface Characteristics Assessment
### Interaction Between Surface Texture, Runway Friction and Aircraft Skid Resistance
The Persson model can also be combined with numerical analysis to calculate the stresses in the contact area and increase the reliability of the model [167]. In some of the more recent studies [114; 131; 162], artificial neural networks were used for friction prediction. An artificial neural network is a good tool for friction analysis, and \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Model** & \(\mathbf{R^{2}}\) & **Friction Assessment** & **Texture Assessment** & **Reference** \\ \hline
6 & \(FN=42719\)\(MPD^{2}-1508.8\)\(MPD\) & 0.10 to & Locked-wheel trailer & & & \\  & \(+43.5\) & 0.73 & (speed higher than & Mean profile depth & [160] \\
7 & Linear correlation models for different & 0.56 to & 45 mph) & & \\  & testing speeds and testing devices & 0.79 & Grip Tester & Mean profile depth & [161] \\
8 & Artificial neural network model & 0.88 & Grip Tester & Laser profilometry (macro-textural parameters) & [162] \\  & & & British Pendulum & Macrotexture and & \\
9 & \(Y_{Fr}=\beta_{0}+\beta_{macro}\) & \(\times X_{macro}\) & 0.43 to & Number, Grip & microtexture \\  & \(+\beta_{micro}\times X_{micro}\) & 0.82 & Number, Dynamic & parameters, obtained & \\  & \(+\sum_{i=1}^{4}\beta_{i}X_{type\ i}\) & & Friction Test & by profilometry & \\  & & & Texture parameters, & & \\
10 & \(\mu=\varphi+\sum\limits_{1}^{8}k_{i}\mu_{i}\) & 0.78 & Grip Tester & obtained by 3D & [164] \\
11 & Rubber friction theoretical model [22] & 0.60 & British Pendulum & & \\  & with modified data from 3D scanning & & Number & 3D scanning data & [165] \\
12 & \(S_{MI}=BPN\times 0.0102+0.846\) & 0.84 & British Pendulum & Microtexture index & \\  & \(PTV_{predicted}=\) & \(-837.43+96.26\)\(S_{d_{i},MIC}\) & Number & 3D & \\
13 & & \(-852.14\)\(S_{k,MIC}\) & 0.82 & British Pendulum & Texture parameters, & \\  & \(+10.41\)\(S_{mr2,MIC}\) & & Number & 3D & \\  & \(+4.92\)\(S_{pc,MAC}\) & & & & \\
14 & Artificial neural network model & 0.77 to & Dynamic Friction & 3D scanning data & [131] \\  & & 0.95 & Tester & & \\  & & & Sideway-Force & & \\
15 & Artificial neural network model & 0.85 & Coefficient Routine & Sand patch test and & \\  & & & Investigation & 3D scanning & \\  & & & Machine (SCRIM) & & \\  & & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \end{tabular}
\end{table} 
Table 8: _Cont._it shows a high correlation between predicted and measured values. However, one of the drawbacks of neural network models is that they work as a 'black box', since the calculation process is not presented for analysis. This creates a risk, since the result is based mostly on the training process and not on fundamental dependencies [168]. In addition to the studies presented in Table 8, there are also other studies of texture influence on friction, but they were not included due to their lack of numerical analysis of data or lack of experimental data. For example, one study investigated the texture skewness parameter [169], which was developed in early research [170,171]. This was found to be well correlated to the friction coefficient of the pavement. However, the calculation method for the friction estimation was not provided. In another study, the influence of texture on different parts of the runway on braking performance was studied [172]. It was concluded that macrotexture affects braking performance in touch-down zones more than microtexture. In a similar study [173], a correlation between macrotexture and measured friction was observed. However, the correlation was low due to lack of microtexture measurements. Finally, a correlation between texture parameters and friction was obtained based on the analysis of different parameters on sections of the Belgian road network [174]. However, the results contradict all other findings (Table 8), which cannot be explained by any theoretical model.