# Identification of Tire Model Parameters with Artificial Neural Networks
## 3 Methodology and Results
### Ann Validation vs. Real Test Data  
In the previous section, ANN predictions were validated through \"clean\" prefabricated data, unknown to the ANN. In this section, we want to take an additional step and analyze the response \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Error Range** & \(B\) **(\%)** & \(C\) **(\%)** & \(E\) **(\%)** & \(D^{*}\!Fz\) **(\%)** & \(f_{y}\) **(\%)** & \(f_{x}\) **(\%)** \\ \hline \(<\)5\% & 98.67 & 98.81 & 94.78 & 99.61 & 99.99 & 99.64 \\ \hline
5–10\% & 1.25 & 1.13 & 4.71 & 0.37 & 0.01 & 0.35 \\ \hline
10–15\% & 0.06 & 0.06 & 0.42 & 0.02 & 0 & 0.01 \\ \hline
15–20\% & 0.02 & 0.01 & 0.06 & 0 & 0 & 0 \\ \hline \(>\)20\% & 0 & 0 & 0.02 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range of values for MF model parameters. Figure 11: Example of _fx_ parameter and ANN error. of the same network when predicting the parameters of real curves obtained in bench tire tests (with different types of errors). The results obtained will serve to draw conclusions about the validity of this methodology against the real problem of identification of parameters of curves from tests (Steps 9 and 10, in Figure 2). For this purpose, 21 curves from tests measuring the longitudinal force for a 206/65 R15 tire have been used. The curves include seven different slip angles (\(-8^{\circ}\), \(-4^{\circ}\), \(-2^{\circ}\), \(0^{\circ}\), \(2^{\circ}\), \(4^{\circ}\) and \(8^{\circ}\)) in three different normal load (\(F_{z}\)) conditions (2, 3 and 4 kN) with a camber of 0. These curves, coming from real tests, have different types of unknown errors. To begin with, the measurement errors are present due to the limited accuracy of the measurement equipment, with their intrinsic uncertainty. On the other hand, it is necessary to take into account the application of slip in steps of 1% between measure and measure, whose uncertainty is not available. In addition, errors and uncertainties can be found regarding the initial condition of the tire or the wear the tire had due to the previous tests or to the roughness of the surface on which the tire runs. Additionally, even environmental variables such as ambient temperature, humidity or wet rolling surface can influence the result of bench acquisitions. The values of these curves are discretized in the same way as the synthetic curves created in the previous sections so that the ANN can use them directly as input data. In this way, the ANN can give a prediction (Step 9) of the appropriate parameters according to its previous training. As an example, Figure 12 shows the actual data (in dotted red circles) of one of those 21 real curves. The black-discontinued line represents the curve predicted by the ANN. It is important to be able to evaluate the effectiveness of the prediction of [PERSON]'s parameters by the ANN. For this reason, it is necessary to compare the results of the ANN with other methods. As seen in the state of the art in the introduction, the identification of parameters can be done through many methods (least squares adjustment, genetic algorithms, particle-swarm optimization, etc.). In this case, for the validation, one of the most effective methods has been used, which, although it is not the fastest in the identification of parameters, it is certainly robust: the least squares adjustment [20]. The method has been applied individually to each of the actual tire test curves. In this sense, in Figure 12, the optimal curve, obtained from a non-linear least squares fitting adjustment using the ANN parameters as starting parameters, is drawn in a blue line. It can be seen that the ANN curve (in black) is quite close to the test data and that the optimal curve (in blue), obtained from this through successive iterations, gets an even better fit to the test data (in red). In order to quantify the accuracy of the ANN prediction, a comparison has been made between the parameters obtained from the ANN and those obtained from the optimum curves after a subsequent non-linear curve fitting least squares optimization.