# Toward Synthetic Data Generation to Enhance Skidding Detection in Winter Conditions

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Vehicle Models Commonly Used

#### 2.2. Neural Network Structures

## 3. Results

#### 3.1. Simulated Vehicle Dynamics

#### 3.2. Real Vehicle Dynamics

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | Artificial neuaral network |

CAN | Controller area network |

GNSS | Global navigation satellite system |

GoG | Center of Gravity |

MEMS | Micro-electro-mechanical systems |

TDNN | Time-delayed neural network |

NAR | nonlinear auto-regressive |

NARX | nonlinear auto-regressive network with exogenous inputs |

SNR | Signal to noise ration |

OBD2 | On-board diagnostic 2 |

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**Figure 3.**Generic tire longitudinal slip ratio vs. longitudinal force for different normal tire force cases.

**Figure 4.**Generic tire lateral side slip angle vs. lateral force for different normal tire force cases.

Rank | Dynamics Variable | Description | Unit |
---|---|---|---|

1–4 | ${a}_{{y}_{whee{l}_{i}}}$ | Wheel y-axis Acceleration | [m/s${}^{2}$] |

5 | ${a}_{z}$ | Vehicle Acceleration z-axis | [m/s${}^{2}$] |

6 | ${v}_{x}$ | Vehicle Velocity x-axis | [m/s] |

7 | ${\theta}_{sw}$ | Steering Wheel angle | [-] |

8 | ${a}_{y}$ | Vehicle Acceleration y-axis | [m/s${}^{2}$] |

9 | $\dot{{\omega}_{x}}$ | Vehicle Angular Accelerations x-axis | [s${}^{-2}$] |

10 | ${\omega}_{y}$ | Vehicle Angular Velocities y-axis | [s${}^{-1}$] |

11 | ${\omega}_{z}$ | Vehicle Angular Velocities z-axis | [s${}^{-1}$] |

12 | $\dot{{\omega}_{z}}$ | Vehicle Angular Accelerations z-axis | [s${}^{-2}$] |

13 | $\dot{{\omega}_{y}}$ | Vehicle Angular Accelerations y-axis | [s${}^{-2}$] |

14 | ${\dot{a}}_{whee{l}_{y}}$ | Wheel y-axis Jerk | [m/s${}^{3}$] |

15 | ${a}_{x}$ | Vehicle Acceleration x-axis | [m/s${}^{2}$] |

16 | ${\dot{a}}_{y}$ | Vehicle Jerk y-axis | [m/s${}^{3}$] |

17 | ${\omega}_{x}$ | Vehicle Angular Velocity x-axis | [s${}^{-1}$] |

Dynamics Variable | Description | Unit |
---|---|---|

${\theta}_{sw}$ | Steering Wheel angle | [-] |

${\tau}_{MT}$ | Motor Load | [%] |

${v}_{x}$ | Vehicle Velocity x-axis | [m/s] |

${a}_{i}$ | Vehicle Acceleration | [m/s${}^{2}$] |

${\dot{a}}_{i}$ | Vehicle Jerk | [m/s${}^{3}$] |

${\omega}_{i}$ | Vehicle Angular Velocities | [s${}^{-1}$] |

$\dot{{\omega}_{i}}$ | Vehicle Angular Accelerations | [s${}^{-2}$] |

$\ddot{{\omega}_{i}}$ | Vehicle Angular Jerk | [s${}^{-3}$] |

${\omega}_{wheel}$ | Wheel Angular Velocity | [s${}^{-1}$] |

${v}_{whee{l}_{y}}$ | Wheel Velocity (calculated using effective radius) | [m/s] |

${a}_{{y}_{whee{l}_{i}}}$ | Wheel y-axis Acceleration | [m/s${}^{2}$] |

${\dot{a}}_{{y}_{whee{l}_{i}}}$ | Wheel y-axis Jerk | [m/s${}^{3}$] |

Rank | Dynamics Variable | Description | Unit |
---|---|---|---|

1 | $\dot{{\omega}_{x}}$ | Vehicle Angular Accelerations x-axis | [s${}^{-2}$] |

2–5 | ${a}_{{y}_{whee{l}_{i}}}$ | Wheel y-axis Acceleration | [m/s${}^{2}$] |

6 | ${v}_{x}$ | Vehicle Velocity x-axis | [m/s] |

7 | ${\theta}_{sw}$ | Steering Wheel angle | [-] |

8 | ${a}_{y}$ | Vehicle Acceleration y-axis | [m/s${}^{2}$] |

9 | ${a}_{z}$ | Vehicle Acceleration z-axis | [m/s${}^{2}$] |

10 | ${\omega}_{y}$ | Vehicle Angular Velocities y-axis | [s${}^{-1}$] |

11 | ${\omega}_{z}$ | Vehicle Angular Velocities z-axis | [s${}^{-1}$] |

12 | $\dot{{\omega}_{z}}$ | Vehicle Angular Accelerations z-axis | [s${}^{-2}$] |

13 | $\dot{{\omega}_{y}}$ | Vehicle Angular Accelerations y-axis | [s${}^{-2}$] |

14 | ${\omega}_{x}$ | Vehicle Angular Velocity x-axis | [s${}^{-1}$] |

15 | ${a}_{x}$ | Vehicle Acceleration x-axis | [m/s${}^{2}$] |

16 | ${\dot{a}}_{whee{l}_{y}}$ | Wheel y-axis Jerk | [m/s${}^{3}$] |

17 | ${\dot{a}}_{y}$ | Vehicle Jerk y-axis | [m/s${}^{3}$] |

Rank | Dynamics Variable | Description | Unit |
---|---|---|---|

1–4 | ${a}_{{y}_{whee{l}_{i}}}$ | Wheel y-axis Acceleration | [m/s${}^{2}$] |

5 | ${a}_{z}$ | Vehicle Acceleration z-axis | [m/s${}^{2}$] |

6 | ${v}_{x}$ | Vehicle Velocity x-axis | [m/s] |

7 | ${\theta}_{sw}$ | Steering Wheel angle | [-] |

8 | ${a}_{y}$ | Vehicle Acceleration y-axis | [m/s${}^{2}$] |

9 | $\dot{{\omega}_{x}}$ | Vehicle Angular Accelerations x-axis | [s${}^{-2}$] |

10 | ${\omega}_{y}$ | Vehicle Angular Velocities y-axis | [s${}^{-1}$] |

11 | ${\omega}_{z}$ | Vehicle Angular Velocities z-axis | [s${}^{-1}$] |

12 | $\dot{{\omega}_{z}}$ | Vehicle Angular Accelerations z-axis | [s${}^{-2}$] |

13 | $\dot{{\omega}_{y}}$ | Vehicle Angular Accelerations y-axis | [s${}^{-2}$] |

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## Share and Cite

**MDPI and ACS Style**

McKenzie, B.; Kelouwani, S.; Gaudreau, M.-A.
Toward Synthetic Data Generation to Enhance Skidding Detection in Winter Conditions. *World Electr. Veh. J.* **2022**, *13*, 231.
https://doi.org/10.3390/wevj13120231

**AMA Style**

McKenzie B, Kelouwani S, Gaudreau M-A.
Toward Synthetic Data Generation to Enhance Skidding Detection in Winter Conditions. *World Electric Vehicle Journal*. 2022; 13(12):231.
https://doi.org/10.3390/wevj13120231

**Chicago/Turabian Style**

McKenzie, Bryan, Sousso Kelouwani, and Marc-André Gaudreau.
2022. "Toward Synthetic Data Generation to Enhance Skidding Detection in Winter Conditions" *World Electric Vehicle Journal* 13, no. 12: 231.
https://doi.org/10.3390/wevj13120231