Evolutionary algorithms application for improving the tire rolling resistance based on Wismer–Luth model

  • Sajjad DerafshpourEmail author
  • Aref Mardani
  • Morteza Valizadeh
Original Article


Soil and tire interaction is a complex process that involves the exchange of variable stresses along the contact area of soil and tire. Despite this complexity, the description of this process in the form of mathematical models has long been of interest to the researchers. The same complexity has led the wheels and soil interaction patterns to be constantly evolving and optimizing. This evolution has coincided with the scientific progress of mathematics, modeling and computer until today. Nowadays, optimizing and predicting a model based on input variables using machine learning techniques and conventional evolutionary algorithms play an important role in predicting the relationships between input and output. These methods can be far better than the conventional statistical techniques. The modeling and prediction of wheel rolling resistance on the soil have many parameters. Using new techniques such as genetic, BAT and PSO algorithms to optimize them seems to be suitable approaches. The aim of this research is to investigate and optimize the parameters of the Wismer–Luth model using the evolutionary algorithms. To improve the model, the variables of multi-pass, forward velocity and depth of the cone index, are also incorporated to the Wismer–Luth model, and the corresponding parameters are optimized with the BAT algorithm. Analysis of experimental data showed that the correlation of the output of the proposed model with the experimental data is 0.87 where it is 0.77 for the Wismer–Luth model. Furthermore, experimental results in this study showed that there is a significant relationship between rolling resistance and multi-pass effect, neglected in most models.


Evolutionary algorithms BAT Rolling resistance Wismer–Luth model Multi-pass Optimization 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Sajjad Derafshpour
    • 1
    Email author
  • Aref Mardani
    • 2
  • Morteza Valizadeh
    • 3
  1. 1.Department of Mechanical Engineering of Biosystems, Faculty of AgricultureUrmia UniversityUrmiaIran
  2. 2.Department of Mechanical Engineering of BiosystemsUrmia UniversityUrmiaIran
  3. 3.Department of Electrical EngineeringUrmia UniversityUrmiaIran

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