# Identification of Tire Model Parameters with Artificial Neural Networks
## 2 Artificial Neural Networks (ANNs)  
The ANNs can be defined as processing algorithms that infer patterns and relationships between known input and output data, provided sufficient information is given to the system to learn. An ANN is set up mimicking the neural structure of the human brain, where hundreds of thousands of \"simple\" processor units (neurons) work together by interconnections among them (synapses) to allow learning. In this way, in one type of ANN, the network topology is composed of simple nodes that are organized in layers. The first layer usually has as many nodes as input parameters. The last layer is set up with as many nodes as output parameters (Figure 1). Between these two layers there exist some hidden layers, each of them comprised of a given number of nodes. Nodes from two consecutive layers are usually fully connected between them. Each connection is given a weighting factor that is used to modify the information traveling through it. These connections allow passing information from one node to others connected to it. When the information is passed from left to right, it is called a \"feed forward\" connection. Nodes between consecutive layers can develop connections among them passing in this way information from one node to the other. Nodes sum up all the weighted information from their input connections in the previous layer and transmit the result to the output connections in the following layers. To start the training process, after proper randomizing of the weights, the input layer of the ANN gets the input information from the algorithm and passes it on to the following layers. Each node receiving information acts on it and modifies it according to its activation configuration (normally a sigmoid, or similar function). In this way, the information travels through the ANN from the input nodes to the output ones. The training algorithm compares this result to the known solution of the provided training data. If the solution is not ok, then a so-called \"backpropagation\" algorithm modifies the weights of the connections according to the size of the error difference. Once the weights of all the connections have been updated, all the process is repeated until the answer given by the output layer is satisfactory (or a given stop flag is activated). This procedure is called \"supervised learning\", because one knows in advance the correct answer and, if the algorithm fails to obtain it, the ANN weights are corrected in order to get a better solution. Once the ANN has learned from the training data, it can provide solutions for unknown data. Therefore, the ANN is trained with the so-called \"training data\", and its performance is usually measured by getting an answer from unknown \"test data\". If the learning of the ANN has been successful, the answer to the \"test data\" will be satisfactory. Figure 1: Example of an ANN (3-5-2). ANNs have already been used in a countless number of applications where analytical solutions do not exist or are very costly to obtain. There are many types of ANN. The configuration of the connections of ANNs is very dependent on the type of problem under study [21; 22; 23]. In order to build an efficient ANN, it is necessary to determine its type, topology and learning rule. In this case, it is desired to know the optimum tire parameters related to the known test data of a particular tire. The input data will be the known test data for certain slips. In this paper, the input data to the network will be the longitudinal force measurements corresponding to slips ranging from -75% to 75%, discretized in steps of 2% for the slip. This gives us 76 entries to the network. These inputs are of a continuous character since the measured longitudinal force can have any continuous real value. The output of the ANN are the parameters of the chosen tire model. In this case, it has been decided to work with the well-known Magic Formula [1], which is a semi-empirical tire model, and is the most used in the work related to tire models.