# Investigating Micro-Driving Behavior of Combined Horizontal and Vertical Curves Using an RF Model and SHAP Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Geometric Design and Safety

#### 2.2. Combined Curves’ Geometric Design and Micro-Driving Behaviors

## 3. Data Preparation

#### 3.1. Geometric Data

#### 3.2. Micro-Driving Behavior Data Collection

^{2}to +6.5 m/s

^{2}.

## 4. Micro-Driving Behavior

#### 4.1. Speed Change Behavior

#### 4.2. Lane Departure Behavior

#### 4.3. Micro-Behavior Comparison of Four Combined Curves

## 5. Shapley Explanation for the Relationship between Micro-Behavior and Geometric Design

#### 5.1. Methodology

#### 5.1.1. Random Forest

#### 5.1.2. SHAP

#### 5.2. RF-SHAP Analysis of Mirco-Behavior on Combined Curves

#### 5.2.1. Speed Change Behavior on Downslope and Sag Curve

- (1)
- Downslope Curve

- (2)
- Sag Curve

#### 5.2.2. Lane Departure Behavior on Downslope, Upslope, and Crest Curves

- (1)
- Downslope Curve

- (2)
- Upslope Curve

- (3)
- Crest Curve

## 6. Discussion

- Selecting key safety evaluation measures.

- Ranking of geometric design parameters of combined curves.

- Optimizing design based on safety evaluation measures.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**IDCF and ADCF categorization diagrams: (

**a**) IDCF departure occurs during vehicle left turn; (

**b**) IDCF departure occurs during vehicle right turn; (

**c**) ADCF departure occurs during vehicle left turn; (

**d**) ADCF departure occurs during vehicle right turn.

**Figure 12.**The SHAP values for the geometric design parameters of IDCF lane departure behavior on downslope curve.

**Figure 13.**The SHAP values for the geometric design parameters of ADCF lane departure behavior in downslope curve.

**Figure 14.**The SHAP values for the geometric design parameters of IDCF lane departure behavior on upslope curve.

**Figure 15.**The SHAP values for the geometric design parameters of ADCF lane departure behavior on upslope curve.

**Figure 16.**The SHAP values for the geometric design parameters of IDCF lane departure behavior on crest curve.

**Figure 17.**The SHAP values for the geometric design parameters of ADCF lane departure behavior on crest curve.

Continuous Variable | |||||
---|---|---|---|---|---|

Variables | Description | Mean | S.D. | Min | Max |

${G}_{mean}(\%)$ | Mean slope of combined curve | −2.23 | 2.39 | −5.25 | 5.25 |

$\u2206G$ | Slope differential of maximum and minimum slope | 2.86 | 1.93 | 0.00 | 8.10 |

$L\left(m\right)$ | Length of combined curve | 413.97 | 135.35 | 222.51 | 790.76 |

${L}_{cc}\left(m\right)$ | Length of circular curve | 211.13 | 122.64 | 35.00 | 490.76 |

${L}_{at}\left(m\right)$ | Length of approach transition | 101.10 | 25.30 | 0.00 | 160.00 |

${L}_{dt}\left(m\right)$ | Length of departure transition | 101.74 | 25.08 | 0.00 | 155.00 |

$R\left(m\right)$ | Radius of combined curve | 821.56 | 447.23 | 400.00 | 2500.00 |

Variables | Description | Mean | S.D. | Min | Max |
---|---|---|---|---|---|

${\u2206C}_{p}$ ^{1} | The preceding curvature change | 0.00079 | 0.00048 | 0.00004 | 0.0020 |

${\u2206G}_{p}$ ^{2} | The slope change of the preceding section | 3.45 | 3.57 | 0.00 | 12.00 |

${\u2206C}_{f}$ ^{3} | The following curvature change | 0.00079 | 0.0005 | 0.00005 | 0.0024 |

${\u2206G}_{f}$ ^{4} | The slope change of the following section | 1.93226 | 1.93277 | 0.00 | 9.00 |

^{1}The difference in curvature between the preceding segment of the combined curve and the current combined curve.

^{2}The difference in slope between the preceding segment of the combined curve and the current combined curve.

^{3}The difference in curvature between the following segment of the combined curve and the current combined curve.

^{4}The difference in slope between the following segment of the combined curve and the current combined curve.

Curve | Minimum Value | Maximum Value | S.D. | 7.5th Percentile Value | 92.5th Percentile Value |
---|---|---|---|---|---|

Downslope | −39.96 | 42.30 | 11.98 | −15.17 | 17.94 |

Upslope | −41.88 | 29.57 | 9.71 | −14.49 | 12.80 |

Sag | −32.32 | 40.24 | 13.53 | −17.83 | 19.91 |

Crest | −35.03 | 42.53 | 11.12 | −17.48 | 12.59 |

Type | Mean (m) | Max (m) | Min (m) | S.D (m) | |
---|---|---|---|---|---|

IDCF lane departure | Maximum lateral departure | 0.81 | 1.10 | 0.01 | 0.29 |

Departure persistence distance | 72.75 | 500 | 5 | 70.48 | |

ADCF lane departure | Maximum lateral departure | 0.36 | 1.52 | 0.00 | 0.35 |

Departure persistence distance | 60.64 | 410 | 5 | 61.93 |

Road Type | Speed Change | Lane Departure |
---|---|---|

Upslope curve | 4.436 | 19.753 |

Downslope curve | 15.884 | 41.114 |

Crest curve | 8.435 | 12.482 |

Sag curve | 5.111 | 2.203 |

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**MDPI and ACS Style**

Wang, X.; Wei, X.; Wang, X.
Investigating Micro-Driving Behavior of Combined Horizontal and Vertical Curves Using an RF Model and SHAP Analysis. *Appl. Sci.* **2024**, *14*, 2369.
https://doi.org/10.3390/app14062369

**AMA Style**

Wang X, Wei X, Wang X.
Investigating Micro-Driving Behavior of Combined Horizontal and Vertical Curves Using an RF Model and SHAP Analysis. *Applied Sciences*. 2024; 14(6):2369.
https://doi.org/10.3390/app14062369

**Chicago/Turabian Style**

Wang, Xiaomeng, Xuanzong Wei, and Xuesong Wang.
2024. "Investigating Micro-Driving Behavior of Combined Horizontal and Vertical Curves Using an RF Model and SHAP Analysis" *Applied Sciences* 14, no. 6: 2369.
https://doi.org/10.3390/app14062369