# The Vertical Force Estimation Algorithm Based on Smart Tire Technology

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of the Tire Finite Element Model

#### 2.1. Element Type

#### 2.2. Material Model and Sensor Positioning

## 3. Verification of the Tire Finite Element Model

#### 3.1. Statics Experiment Verification

- (a)
- Set tire inflation pressure; the inflation pressure range is 0.181 MPa to 0.281 MPa.
- (b)
- Adjust camber angle to 0° through the attitude sensor and the test bench controller.
- (c)
- Control the tire to move toward the bottom plate until the tire tread lightly touches the bottom plate, at this moment the pressure exerted by the tire on the road surface is 0 N.
- (d)
- Record the distance from the center of the rim to the bottom plate at this moment.
- (e)
- Use the controller to control the tire to move down, and simultaneously record the distance between the tire and the ground and the radial reaction force of the four-dimensional force sensor at the center of the rim.
- (f)
- Draw the radial stiffness curve.

#### 3.2. Dynamic Experiments Validation

## 4. Simulation Results and Discussion

#### 4.1. The Influence of Different Inflation Pressures on the Contact Patch

#### 4.2. The Influence of Different Loads on the Contact Patch

#### 4.3. The Effect of Different Speeds on the Contact Patch

#### 4.4. The Effects of Different Wear Amounts on the Contact Patch

## 5. Vertical Force Prediction

#### 5.1. Determination of Input Characteristic Parameters

#### 5.2. Estimation of the Length of the Longitudinal Contact Patch Length

#### 5.3. Vertical Force Calculation Algorithm Based on GA-BP Neural Network Algorithm

- (1)
- BP neural network

- (a)
- The forward propagation of the data flow, from the input layer through the hidden layer, finally reaches the output layer;
- (b)
- The back-propagation of the error, from the output layer to the hidden layer and finally to the input layer, constantly adjusts the weights and thresholds of each layer, when the error of the network output is reduced to the accuracy set according to a certain rule or reaches the set number of learning times stop.

^{−5}. In order to avoid the outcome where the result cannot be obtained due to the long-term calculation failure during the training process, the upper limit of the number of model iterations is set to 10,000 times. At the same time, in order to prevent overfitting by affecting the accuracy of the predicted data, the maximum number of verifications of the neural network is set to 6. The training result is easily affected by the learning rate of the neural network. If the learning rate is too large or too small, it will cause the neural network to “oscillate” or reduce the convergence speed, its value is usually between 0.01 and 0.2. So, the learning rate is set to 0.1 in this paper. Finally, the parameters of the BP neural network model are shown in Table 3.

- (2)
- Genetic Algorithm (GA)

- (1)
- Calculation of fitness function

- (2)
- Select operation

- (3)
- Crossover operation

#### 5.4. Analysis of the Estimation of Tire Vertical Force Results

## 6. Conclusions

- (1)
- The effects of different inflation pressure, speed, load and wear amount on the length of the longitudinal contact patch and the radial displacement at the virtual acceleration sensor are analyzed. The simulation results show that the length of the longitudinal contact patch decreases with the increase of inflation pressure and wear amount and increases with the increase of speed and load. The peak value of the radial displacement wave decreases with the increase of tire pressure and increases with the increase of load, but it is independent of the amount of tread wear and speed.
- (2)
- It was found that the radial acceleration signal of the virtual triaxial acceleration sensor has the highest correlation with the longitudinal length of the tire contact patch. The calculation method of the longitudinal contact patch length built with this signal has high prediction accuracy and good robustness. The mean absolute error is 0.64 mm.
- (3)
- According to the different input characteristic parameters, three vertical force prediction models based on GA-BP neural network algorithm are established. The inputs of Model 1 are inflation pressure, speed and length of longitudinal contact patch; Model 2 considers the influence of tread wear on the basis of Model 1, and its input features are inflation pressure, speed, length of longitudinal contact patch and tread wear. The input quantities of Model 3 are the peak value of radial displacement and inflation pressure. The mean absolute error, mean absolute error percentage and computation time of the three forecasting models were compared. The prediction results show that the three evaluation indicators of the Prediction Model 3 are all optimal, which are more suitable for practical engineering applications, and can further improve vehicle safety, handling stability, fuel economy and ride comfort.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**205/55/R16 finite element model: (

**a**) semi-2D tire section finite element model; (

**b**) semi-3D tire finite element model; (

**c**) full 3D tire finite element model.

**Figure 10.**Curves of tire contact area and longitudinal contact length under different inflation pressures.

**Figure 11.**Contact pressure distribution of tire longitudinal contact patch under different inflation pressures.

**Figure 21.**Contact pressure distribution of tire longitudinal contact patch under different wear amounts.

**Figure 22.**Curves of tire contact area and longitudinal contact length under different wear amounts.

Inflation Pressure (MPa) | Simulation Value (N) | Test Value (N) | Absolute Error Percentage (%) |
---|---|---|---|

0.18 | 1006 | 993.3 | 1.27 |

0.20 | 1087 | 1091.7 | 0.43 |

0.22 | 1186 | 1182.3 | 0.31 |

0.24 | 1246 | 1224.8 | 1.73 |

0.26 | 1324 | 1280.5 | 3.4 |

0.28 | 1402 | 1353.3 | 3.6 |

Predictive Model | Input | Output |
---|---|---|

Predictive model 1 | Inflation pressure, speed, longitudinal contact patch length | Vertical force |

Predictive mode 2 | Inflation pressure, speed, longitudinal contact patch length, wear amount | |

Predictive mode 3 | Inflation pressure, radial displacement peak value |

Method | Parameter | The Number of Neurons in the Hidden Layer | Hidden Layer Activation Function | Output Layer Activation Function | Target Error | Iteration Upper Limit | Learning Rate |
---|---|---|---|---|---|---|---|

Model 1 | Value | 5 | $\mathrm{tan}\mathrm{si}g(\mathrm{n})$ | $\mathrm{purelin}$ | 4 × 10^{−5} | 10,000 | 0.1 |

Model 2 | 4 | ||||||

Model 3 | 9 |

Parameter Name | Parameter Value |
---|---|

Number of iterations | 200 |

Population size | 60 |

Crossover probability | 0.5 |

Mutation probability | 0.05 |

Predictive Model | Input | MAE(N) | MPAE (%) | Calculation Time |
---|---|---|---|---|

Model 1 | Inflation pressure, speed, longitudinal contact patch length | 75.73 | 3.9% | 0.031 |

Model 2 | Inflation pressure, speed, longitudinal contact patch length, wear amount | 64.60 | 3.3% | 0.033 |

Model 3 | Inflation pressure, radial displacement peak value | 47.55 | 2.2% | 0.021 |

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## Share and Cite

**MDPI and ACS Style**

Gu, T.; Li, B.; Quan, Z.; Bei, S.; Yin, G.; Guo, J.; Zhou, X.; Han, X.
The Vertical Force Estimation Algorithm Based on Smart Tire Technology. *World Electr. Veh. J.* **2022**, *13*, 104.
https://doi.org/10.3390/wevj13060104

**AMA Style**

Gu T, Li B, Quan Z, Bei S, Yin G, Guo J, Zhou X, Han X.
The Vertical Force Estimation Algorithm Based on Smart Tire Technology. *World Electric Vehicle Journal*. 2022; 13(6):104.
https://doi.org/10.3390/wevj13060104

**Chicago/Turabian Style**

Gu, Tianli, Bo Li, Zhenqiang Quan, Shaoyi Bei, Guodong Yin, Jinfei Guo, Xinye Zhou, and Xiao Han.
2022. "The Vertical Force Estimation Algorithm Based on Smart Tire Technology" *World Electric Vehicle Journal* 13, no. 6: 104.
https://doi.org/10.3390/wevj13060104