# Survey on Modelling and Techniques for Friction Estimation in Automotive Brakes
## 2 Techniques for the Estimation of BLCF in Automotive Disc Brakes
### Neural Networks for BLCF Estimation
The neural network must be learned and trained on a set of experimental data defining the relationships among the friction material behaviour and different formulations, environmental conditions and operating conditions (Figure 9). In other words, before the direct application of the network, it is required to teach analytical relations between input and output values to the neural network in order to get results with the possible lowest error. It is necessary to take into consideration that the number of training data pairs has a significant influence on the network's generalization capability. One of the most common approaches for the training of a network is based on the backpropagation method, whose basic principle is to reduce the square error between the expected and measured output of the network by modifying the weight vector. Hence, the squared error between the expected and the predicted output is differentiated against the weights in order to define in which direction the latter must be updated in order to reduce the error. \[\frac{\partial E}{\partial w_{ij}}=\frac{\partial\Big{[}\frac{1}{2}\big{(} \overline{y}-y\big{)}^{2}\Big{]}}{\partial w_{ij}} \tag{7}\]  
In Equation (7), \(\overline{y}\) represents the target output and \(y\) is the actual output of the network (also corresponding to Equation (5)) particularized in the last layer. After the training procedure is completed, two additional steps must be performed for the achievement of good network performances, namely validation and testing. A validation dataset is used to monitor the quality of the neural network model training and to indicate when to terminate the training process. A test dataset is used to examine the final quality of the developed neural model and to evaluate its generalization and prediction capabilities. Hence, the neural network can be seen as a parallel distributed processor that is intrinsically prone to store experiential knowledge and to apply the latter for future decisions. In [61] a neural model is proposed to predict the BLCF by using as input parameters the brake pad composition, the manufacturing process conditions and the brake operating conditions. In [62] another approach is proposed that in addition to the temperature, speed and load dependence of the BLCF also considers the role of hysteresis phenomenon by including the sliding acceleration influence. Moreover, the authors of [62] envisage applying the neural networks to generate 3D maps of the BLCF for the implementation of advanced control algorithms in the electronic units such as for brake enhancing. In [63] a neural network is used for predicting the tribological properties of frictional materials, in particular BLCF and wear rate. The author of [64] puts forth a prediction of the mean value of the BLCF for non-asbestos brake linings with different compositions. In [65], the artificial neural network has been used for modelling and prediction of BLCF by considering several influencing factors such as the friction material composition, manufacturing parameters and the brakes' operating conditions. Further studies concern the employment of dynamic neural networks to sift out the influences of the disc brake operation conditions (applied pressure, speed and brake interface temperature) and material characteristics of a friction couple against the generated braking torque [60; 66]. In summary, the approach based on neural network is purely black box, therefore it is not able to describe the actual phenomenology of the tribological contact. Despite this, it can be used to look for an analytical formulation that considers all the functional relationships between the variables and the BLCF. There is still a problem affecting the neural network and linked to the extrapolation procedure: how does the neural network behave when it is fed with a combination of input not provided during the learning procedure?