A new linear parametrization for peak friction coefficient estimation in real time

The correct estimation of the friction coefficient in automotive applications is of paramount importance in the design of effective vehicle safety systems. In this article a new parametrization for estimating the peak friction coefficient, in the tire-road interface, is presented. The proposed parametrization is based on a feedforward neural network (FFNN), trained by the Extreme Learning Machine (ELM) method. Unlike traditional learning techniques for FFNN, typically based on backpropagation and inappropriate for real time implementation, the ELM provides a learning process based on random assignment in the weights between input and the hidden layer. With this approach, the network training becomes much faster, and the unknown parameters can be identified through simple and robust regression methods, such as the Recursive Least Squares. Simulation results, obtained with the CarSim program, demonstrate a good performance of the proposed parametrization; compared with previous methods described in the literature, the proposed method reduces the estimation errors using a model with a lower number of parameters.