Abstract
Accurate modeling of tire characteristics is one of the most challenging tasks. Many mathematical models can be used to fit measured data. Identification of the parameters of these models usually relies on least squares optimization techniques. Different researchers have shown that the proper selection of an initial set of parameters is key to obtain a successful fitting. Besides, the mathematical process to identify the right parameters is, in some cases, quite time-consuming and not adequate for fast computing. This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. In this case, the Pacejka’s “Magic Formula” has been chosen for the identification due to its complex mathematical form which, in principle, could result in a more difficult learning than other formulations. The proposed methodology is based on the creation of a sufficiently large training dataset, without errors, by randomly choosing the MF parameters within a range compatible with reality. The results obtained in this paper suggest that the use of ANN to directly identify parameters in tire models for real test data is possible without the need of complicated cost functions, iterative fitting or initial iteration point definition. The errors in the identification are normally very low for every parameter and the fitting problem time is reduced to a few milliseconds for any new given data set, which makes this methodology very appropriate to be used in applications where the computing time needs to be reduced to a minimum.
Highlights
The identification of parameters in tire models has been addressed through different techniques.It is common practice in the literature to consider the cost function that takes into account only the vertical component of the error between measured data and the mathematical model, assuming indirectly that the independent variable is well known or, at least, that its contribution to the total error is negligible.Historically, the most used methodology to identify tire model parameters has been the OrdinaryLeast Squares on the Pacejka’s Magic Formula (MF) model [1]
The results obtained in this paper suggest that the use of Artificial Neural Networks (ANN) to directly identify parameters in tire models for real test data is possible without the need of complicated cost functions, iterative fitting or initial iteration point definition
In order to answer this question, the work has been proposed according to the methodology shown in Figure 2, which is divided into three large blocks: (1) creation of curves to train the ANN; (2) determination of the topology of the ANN and its training; and (3) validation of the ANN against real test bench data
Summary
The identification of parameters in tire models has been addressed through different techniques. Unlike previous ANN works, limited training data (due to data from only one, or a limited set of tires) is not a problem, since the methodology provides means to create as much training data as is necessary to ensure good network training Based on this information, the ANN topology is selected and its performance is evaluated. 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. 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 selection of the chosen ANN topology is detailed as part of the working methodology
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