# Lane-Change Risk When the Subject Vehicle Is Faster Than the Following Vehicle: A Case Study on the Lane-Changing Warning Model Considering Different Driving Styles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and −2.7 m/s

^{2}. Fu et al. [16] analyzed the characteristics of drivers’ behaviors in performing and canceling lane changing based on the data collected from a real road test. The researchers identified the drivers’ subjective judgement for risk assessment and established lane-changing warning rules between the SV and surrounding vehicles in different speed ranges. Mar et al. [17] proposed a crash avoidance system to optimize the processing time of lane changes based on cascading fuzzy reasoning and determined appropriate lane-changing rules by analyzing the relative distance and relative speed between the SV and FVs under multiple conditions. Kim et al. [18] proposed an adaptive cruise control and crash avoidance system to improve driving comfort and lane-changing safety and determined the longitudinal and lateral control strategy of autonomous vehicles in a mixed traffic environment by analyzing severe braking maneuvers and lane-changing trajectories.

## 2. Methods

#### 2.1. Participants and Test Routes

#### 2.2. Apparatus

#### 2.3. Extraction of Lane-Changing Events

## 3. Driving Style Classification in Lane-Changing Situations

#### 3.1. Clustering Model Establishment

#### 3.1.1. K-Means Algorithm

#### 3.1.2. Gaussian Mixture Model with the Inputs of K-Means Algorithm

- Initialize centroids by first shuffling all data points and randomly selecting k data points as the cluster centers.
- Compute the sum of the squared distance between each data point and k centroids and assign each data point to the possible cluster based on the principle of the minimum distance.
- Update k centroids by iterating until there is no change to the centroids.
- Compute the proportion and the mean vector of the data points in each cluster determined by the k-means algorithm.
- Take the clustering result of the k-means algorithm as the initial input parameters of the GMM (i.e., mean vector and weight of a cluster and covariance matrix of clusters).
- Run the improved GMM algorithm to obtain the optimized clustering result.

#### 3.2. Lane-Changing Safety Indicator Selection

_{subject_vehicle}− V

_{following_vehicle}, so the relative speed analyzed in this section is negative. The average time gap and the TTC in various relative speed ranges and different speed ranges in the process of lane changes from the 50 drivers were calculated, as shown in Figure 8.

#### 3.3. Clustering Results and Verification

## 4. Lane-Changing Warning Model Considering Different Driving Styles

#### 4.1. Lane-Changing Safety Distance Model

- (1)
- Ensure that the SV is always in front of the FV during lane changes

_{R}is the longitudinal distance between the SV and the FV at the starting point of lane changes, D

_{S}is the longitudinal distance when the SV completely enters the adjacent lane, D

_{F}is the longitudinal distance of the FV, D

_{W}is the width of the SV, and θ is the angle between the front of the SV and the boundary line of the adjacent lane.

_{R},0}. That is to say, if the FV cannot keep up with the SV during the entire lane-changing process, the minimum distance between these two vehicles at the starting point of lane changes can be set to be zero.

- (2)
- Ensure a safety distance between the SV and the FV after entering the adjacent lane

_{0}is the relative distance between the SV and the FV after entering the adjacent lane. B

_{S}is the travelling distance of the SV, and B

_{F}is the travelling distance of the FV. To avoid possible collisions between two vehicles after entering the adjacent lane, the following conditions should be met:

#### 4.2. Lane-Changing Warning Model

^{2}, that is, most drivers do not have obvious acceleration or deceleration operations during lane changes, as shown in Figure 14. Based on this, the minimum safety distance model described in Section 4.1 is then simplified, and it is assumed that the SV and the FV maintain a constant speed during lane changes. That is to say, the acceleration values of the SV and the FV are set to be zero.

#### 4.3. Recognition Results of Lane-Changing Warning Model

^{2}is used as the hazard perception threshold, and the lane-changing data are classified into the hazardous area [42,43]; data with slight braking (−0.5 < a

_{F}≤ −0.15 m/s

^{2}) is classified into the potential conflict area [44]; and data with an acceleration value above −0.15 m/s

^{2}is considered as safe lane-changing data and is classified into the safety area. The distribution of the acceleration of the FV when the SV starts to change lanes is shown in Figure 15 and Figure 16.

## 5. Conclusions

- For different speed ranges of the SV, the time to collision was relatively stable under high relative speed conditions (<−15 km/h), while the time gap was stable under low relative speed conditions (≥−15 km/h).
- A significant difference existed in the lane-changing durations for the three types of drivers, and the peak frequencies of the lane-changing duration for aggressive drivers, calm drivers, and conservative drivers were 3–4 s, 4–5 s, and 5–6 s, respectively.
- The overall recognition accuracy of the lane-changing warning model considering driving styles was 81%, and the overall recognition accuracy of the model for aggressive drivers was relatively higher at 84% when compared with the other two types of drivers.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distributions of the ages and driving experiences of the 50 drivers. (

**a**) Age distribution (

**b**) Driving experience distribution.

**Figure 9.**Contour map (

**left**) and surface diagram (

**right**) of the GMM model based on the k-means clustering results.

**Figure 14.**Distributions of the FV (

**left**) and the SV (

**right**) acceleration values during lane changes.

**Figure 17.**Recognition results of the lane-changing warning model in different speed ranges. (

**a**) v

_{S.}≤ 70 km/h. (

**b**) 70 < v

_{S.}≤ 90 km/h. (

**c**) 90 < v

_{S.}≤ 110 km/h. (

**d**) v

_{S.}> 110 km/h.

**Figure 18.**Recognition results in different speed ranges for aggressive drivers. (

**a**) vs. ≤70 km/h. (

**b**) 70< vs. ≤90 km/h. (

**c**) 90< vs. ≤110 km/h. (

**d**) vs. >110 km/h.

Driving Styles | Driver #s | Average Time Gap (s) | Average TTC_Min (s) |
---|---|---|---|

Aggressive | 6, 7, 16, 17, 20, 22, 23, 26, 28, 40, 43, 50 | 1.36 | 4.21 |

Calm | 3, 4, 5, 9, 12, 14, 18, 21, 30, 32, 34, 35, 39, 41, 44, 45, 46, 47 | 1.55 | 5.84 |

Conservative | 2, 8, 15, 24, 25, 37 | 1.83 | 7.62 |

Speed Ranges (km/h) | Lane-Changing Safety Distance Model |
---|---|

${v}_{S}$ ≤ 70 | $\mathrm{DSS}=\{\begin{array}{c}-5.9\Delta v+10\Delta v0\\ -0.6\Delta v+10\Delta v\ge 0\end{array}$ |

$70{v}_{S}$ ≤ 90 | $\mathrm{DSS}=\{\begin{array}{c}-5.7\Delta v+13.17\Delta v0\\ -0.6\Delta v+13.17\Delta v\ge 0\end{array}$ |

$90{v}_{S}$ ≤ 110 | $\mathrm{DSS}=\{\begin{array}{c}-5.5\Delta v+16.5\Delta v0\\ -0.6\Delta v+16.5\Delta v\ge 0\end{array}$ |

${v}_{S}$ > 110 | $\mathrm{DSS}=\{\begin{array}{c}-5.3\Delta v+19.33\Delta v0\\ -0.6\Delta v+19.33\Delta v\ge 0\end{array}$ |

Speed Ranges (km/h) | Lane-Changing Warning Model |
---|---|

${v}_{S}$ ≤ 70 | $\mathrm{DWS}=\{\begin{array}{cc}-T\Delta v\hfill & \hfill \Delta v<-15\\ -5.9\Delta v+10\hfill & \hfill -15\le \Delta v0\\ -0.6\Delta v+10\hfill & \hfill \Delta v\ge 0\end{array}$ |

$70{v}_{S}$ ≤ 90 | $\mathrm{DWS}=\{\begin{array}{cc}-T\Delta v\hfill & \hfill \Delta v<-15\\ -5.7\Delta v+13.17\hfill & \hfill -15\le \Delta v0\\ -0.6\Delta v+13.17\hfill & \hfill \Delta v\ge 0\end{array}$ |

$90{v}_{S}$ ≤ 110 | $\mathrm{DWS}=\{\begin{array}{cc}-T\Delta v\hfill & \hfill \Delta v<-15\\ -5.5\Delta v+16.5\hfill & \hfill -15\le \Delta v0\\ -0.6\Delta v+16.5\hfill & \hfill \Delta v\ge 0\end{array}$ |

${v}_{S}$ > 110 | $\mathrm{DWS}=\{\begin{array}{cc}-T\Delta v\hfill & \hfill \Delta v<-15\\ -5.3\Delta v+19.33\hfill & \hfill -15\le \Delta v0\\ -0.6\Delta v+19.33\hfill & \hfill \Delta v\ge 0\end{array}$ |

(a) v_{S} ≤ 70 km/h | ||

Warning Area | Safety Zone | |

Hazardous data | 83 | 21 |

Potential conflict/Safe data | 26 | 309 |

(b) 70 km/h < v ≤ 90 km/h | ||

Warning Area | Safety Zone | |

Hazardous data | 96 | 28 |

Potential conflict/Safe data | 25 | 277 |

(c) 90 km/h < v ≤ 110 km/h | ||

Warning Area | Safety Zone | |

Hazardous data | 80 | 24 |

Potential conflict/Safe data | 11 | 225 |

(d) v > 110 km/h | ||

Warning Area | Safety Zone | |

Hazardous data | 24 | 6 |

Potential conflict/Safe data | 11 | 45 |

Warning Area | Safety Zone | |
---|---|---|

Hazardous data | 243 | 69 |

Potential conflict/Safe data | 57 | 692 |

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**MDPI and ACS Style**

Liu, T.; Wang, C.; Fu, R.; Ma, Y.; Liu, Z.; Liu, T.
Lane-Change Risk When the Subject Vehicle Is Faster Than the Following Vehicle: A Case Study on the Lane-Changing Warning Model Considering Different Driving Styles. *Sustainability* **2022**, *14*, 9938.
https://doi.org/10.3390/su14169938

**AMA Style**

Liu T, Wang C, Fu R, Ma Y, Liu Z, Liu T.
Lane-Change Risk When the Subject Vehicle Is Faster Than the Following Vehicle: A Case Study on the Lane-Changing Warning Model Considering Different Driving Styles. *Sustainability*. 2022; 14(16):9938.
https://doi.org/10.3390/su14169938

**Chicago/Turabian Style**

Liu, Tong, Chang Wang, Rui Fu, Yong Ma, Zhuofan Liu, and Tangzhi Liu.
2022. "Lane-Change Risk When the Subject Vehicle Is Faster Than the Following Vehicle: A Case Study on the Lane-Changing Warning Model Considering Different Driving Styles" *Sustainability* 14, no. 16: 9938.
https://doi.org/10.3390/su14169938