Prediction of Tire-Snow Interaction Forces Using Metamodeling

High-fidelity finite element (FE) tire-snow interaction models have the advantage of better understanding the physics of the tire-snow system. They can be used to develop semi-analytical models for vehicle design as well as to design and interpret field test results. For off-terrain conditions, there is a high level of uncertainties inherent in the system. The FE models are computationally intensive even when uncertainties of the system are not taken into account. On the other hand, field tests of tire-snow interaction are very costly. In this paper, dynamic metamodels are established to interpret interaction forces from FE simulation and to predict those forces by using part of the FE data as training data and part as validation data. Two metamodels are built based upon the Krieging principle: one has principal component analysis (PCA) taken into account and the other does not. The comparisons of two metamodels show that the metamodel with PCA can capture better the transient oscillations of the system and more useful to predict transient response than the metamodel without PCA. The metamodel without PCA can filter the transient oscillations, and thus can provide mean responses that are more useful for quasi-steady force prediction than the one with PCA. Model cross-validation of the two metamodels demonstrates that prediction errors of both are approximately the same. The predictive capability of the established metamodels is also assessed which shows that metamoding employed to tire-snow interaction with judiciously chosen training data can significantly reduce required sample data with acceptable degree of estimation errors.