Maximum tire/road friction coefficient prediction based on vehicle vertical accelerations using wavelet transform and neural network

Abstract

The maximum tire/road friction coefficient (TRFC) is the maximum potential for the generation of tire forces, and it is a crucial factor in the performance of vehicle dynamics control systems. This paper aims at developing a maximum TRFC prediction algorithm using a multi-layer perceptron neural network (NN). The NN is trained to predict the TRFC from input features extracted from vertical accelerations caused by road characteristics. Two sets of experiments have been performed to collect the training and target dataset. To produce the input training data, the authors drove the test vehicle on selected test roads and measured the vertical acceleration. Wavelet transform is used to extract features from the vertical accelerations, and the four most salient features have been selected. On the other hand, the target, ground-truth data are produced by measuring the TRFC through hard braking maneuvers on the test roads. The contribution of this study is in developing a TRFC estimation algorithm given four features that are extracted from the vehicle vertical acceleration. The developed algorithm enables TRFC estimation in constant-speed driving conditions. Statistical significance tests revealed that the trained NN predicts the ground-truth data with accuracies above 88%. More specifically, it was shown that there is a strong positive relationship between actual and predicted TRFC with correlation coefficients of ${R}_{\mathrm{train }}=0\text{.}889$, ${R}_{\mathrm{validation }}=\text{0.}859$, and ${R}_{\mathrm{test }}=\text{0.}862$. A fivefold cross-validation was performed, and it was observed that the performance (mean squared error) for the train and test sets is, respectively, equal to 0.0363 and 0.0985.