Determination of Magic Formula Tyre Model Parameters Using Homotopy Optimization Approach

Kaidi Zhang, Yupeng Duan, Xiaobo Yang, James Yang, Yunqing Zhang

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


Tyre behavior plays an important role in vehicle dynamics simulation. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately in the handling simulation. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is nontrivial task due to its nonlinear nature and the presence of a large number of coefficients. In this paper, the homotopy algorithm is applied to the parameter identification of Magic Formula tyre model. A morphing parameter is introduced to correct the optimization process; as a result, the solution is directed converging to the global optimal solution, avoiding the local convergence. The method uses different continuation methods to globally optimize the parameters, which ensures that the prediction of the Magic Formula model can be very close to the test data at all stages of the optimization process. The results show that, compared with the general deterministic optimization methods and intelligent search algorithms, the homotopy algorithm has better global optimization ability and rapid convergence, which is an effective method to identify the parameters of Magic Formula tyre model.

Original languageEnglish
JournalSAE Technical Papers
Issue numberApril
StatePublished - Apr 14 2020
EventSAE 2020 World Congress Experience, WCX 2020 - Detroit, United States
Duration: Apr 21 2020Apr 23 2020


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