Determination of Magic Tyre Model Parameters

Oosten, J.J.M. van; Bakker, E.

doi:10.1080/00423110408969995

Cited by 5 publications

(8 citation statements)

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“…According to [22], in order to estimate the parameters of the magic formula tyre model, the research team of the TNO (the research organization at the Netherlands), used the so called quasi-Newton method [23] and [24], implemented by the E04FDF subroutine of the NAG (Numerical Analysis Group) [25], (see http://www.nag.co.uk/). This method is similar to the Gauss-Newton method, but its application is not specific for least-squares problems, but its application field is wider, actually it can be used to optimize any function.…”

Section: 4-quasi-newton Methodsmentioning

confidence: 99%

“…Several authors who have worked in nonlinear multivariate optimization in tyre models agree that when using Newton, Gauss-Newton, quasi-Newton and Nelder-Mead methods, the selection of an adequate initial point of the parameters' vector is an important issue for the quality of the final solution, and minor variations in this initial point can produce different final results, see for example [36], [37], [22] and [20].…”

Section: 7-genetic Algorithmsmentioning

confidence: 99%

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Nonlinear optimization of a new polynomial tyre model

et al. 2014

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Tyre behavior is strongly nonlinear. This article presents the validation of a new polynomial tyre model with real test data, analyzing the convergence properties during the optimization process to calculate the values of the parameters. A multivariate model with 13 parameters is shown, including normal load and camber angle. The article reviews the methods of getting polynomial approximations of the magic formula tyre model used to develop the new polynomial model, the numerical optimization methods who calculate the parameters of the model from real test data and it explains how the terms of the Jacobian matrix are modified when we impose constraints to the curve; this can be useful to improve the adjustment in some areas of the curve. The convergence properties are shown both for the magic formula tyre model and for this polynomial tyre model.The proposed model presents a fast convergence both in one and in 3 variables. This is an additional advantage to its excellent analytical properties, the model is very easy to compute and can be easily derived and integrated. It is very well adapted for real time computing.

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Section: 4-quasi-newton Methodsmentioning

confidence: 99%

Section: 7-genetic Algorithmsmentioning

confidence: 99%

Nonlinear optimization of a new polynomial tyre model

et al. 2014

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“…The objective function commonly used in the specialized literature to perform the adjustment includes only the vertical component of the error between the mathematical model and the data measured by means of OLS. 3,4 Theoretically, this would be correct if the measured values of the independent variable were accurate or with a negligible error.…”

Section: Parameter Identification In Tire Models: a Reviewmentioning

confidence: 99%

“…OLS fitting has been the most predominant method for parameter identification in tire applications. 3,4 The reason for this dominance is the ease of implementation and calculation of the cost function since it is always possible to calculate the vertical differences between the point and the function. Therefore, it is generally a good and safe choice.…”

Section: Parameter Identification In Tire Models: a Reviewmentioning

confidence: 99%

“…When it is assumed that the variable x is not perfectly known and that it can have measurement inaccuracies from the tests, the errors to be measured change and have two components ( Figure 1). The combination of both errors is calculated in equation (4) and is the orthogonal distance between the measured point and the point corresponding to the curve F in the real x position (with its corresponding measuring error)…”

Section: Cost Functionsmentioning

confidence: 99%

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Optimal parameter estimation in semi-empirical tire models

López¹,

Olazagoitia

Marzal

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part D:

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Semi-empirical tire models are mathematical models, the parameters of which are identified after a process of error reduction to fit experimental data obtained in the laboratory. In this process, the algorithms used for estimating the model parameters are usually based on nonlinear least-squares fitting methods, in which only vertical residuals between the model and the test points are considered. Although extensively utilized, this type of fitting implicitly considers that errors in the slip data (horizontal residuals) are either nonexistent or negligible, which is not true. This paper introduces a new methodology to the identification of semi-empirical tire model parameters based on weighed orthogonal residuals, which takes into account possible errors inherent in the test measurements of dependent and independent variables. The results show that the methodology offers a reliable parameter identification providing an even fitting for all the zones of the mathematical semi-empirical tire model.

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