# Identification of Tire Model Parameters with Artificial Neural Networks
## 3 Methodology and Results
### Ann Selection, Training and Validation  
After the selection of the training data, we can move on to the second part of the methodology (Steps 5 to 8 in Figure 2), which focuses on the determination of the topology of the ANN (Step 5), its training (Step 6) and its verification (Step 7). In Step 5 topology of the ANN is selected. This topology has to assure full connection between nodes of consecutive layers in the ANN. The selected learning rule type is supervised. Connection weights between neurons are updated in sequential training iterations according to the output targets and the obtained outputs. For the hidden layers, different architectures may be valid and there is no general rule on how to obtain an optimum one as it depends on the complexity of the problem under study. Most of the literature suggests that from a theoretical point of view it is possible to approximate almost any function with one layer of ANN. If this is correct, it means that a single layer ANN with a sufficient number of hidden neurons can provide a good approximation for most problems. It also means that adding a second or third layer yields little benefit. Following these recommendations, the possibility of using an ANN with a single hidden layer was explored. Figure 6 shows that more nodes on the hidden layer reduce the training RMS Error. This is true for different training data sets sizes (e.g., 6.25k or 25k). However, the improvement is very small despite continuing to increase the number of nodes in the network. Therefore, for this problem, it does not seem appropriate to use a single hidden layer ANN. The identification of tire parameters is a highly non-linear problem. For this reason, a study was carried out in order to identify the best network topology that best suits this situation. Several network topologies were tested from one (1H) to five (5H) internal hidden layers with the same number of training curves (6.25k and 25k) running over 1000 iterations (epochs). The distribution of nodes within the network between successive hidden layers was done progressively so that the transition between the 76 inputs and the 6 outputs was \"smooth\". The distribution of nodes was as follows: 76-41-6 (1H), 76-50-25-6 (2H), 76-50-40-20-6 (3H), 76-60-45-30-15-6 (4H), 76-60-45-35-25-15-6 (5H). Figure 7 shows the results of the network training for each of these networks. The best training performance was obtained for a three hidden layer network with 25k training curves. Figure 6: ANN with one hidden layer. In the course of this research, other less progressive network topologies between input and output for 3H networks were tested, and the results were no better. For this reason, it was decided to use the 3H configuration (76-50-40-20-6) (Figure 8) as a sufficiently good network topology for the problem of the identification of tire parameters. Taking into account that the ANN has a weight to be determined for each connection and that the connections were configured only between adjacent layers, the number of weights to be learned by the ANN can be calculated (\(76\times 50+50\times 40+40\times 20+20\times 6=6720\) weights). Once the ANN configuration is defined and the training dataset is available, the training can start. Figure 9 shows the details of the activities that are executed in this Step 6. In this case, due to the massive input data chosen (100k curves) for the training, the time to complete it was in the range of a full week with an Intel i5 processor. It is important to emphasize that the objective is to have a tool that can give a precise estimate of the parameters of the tire curve from the inputs provided in a universal way (within the range of parameters defined in Table 1). For this reason, the training time of the ANN is not key, since it will be a one-time calculation. Once the network is trained (Step 8), the ANN can be used as an estimation tool that takes only a few milliseconds for the prediction. It is usually common to divide the number of available curves to train the network into two subsets.