# Car-Following Modeling Incorporating Driving Memory Based on Autoencoder and Long Short-Term Memory Neural Networks

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## Abstract

**:**

## 1. Introduction

- We developed a car-following model highlighting driving memory and its impact on driving behavior;
- It identified the significance of different parameters underlying the time-series data in historical driving memory for car-following modeling;
- This paper also investigated three prediction patterns including various driving memory information and span levels in car-following models to predict car-following behaviors.

## 2. Literature Review

#### 2.1. Mathematical CF Models

#### 2.2. Data-Driven CF Models

#### 2.3. CF Models Considering Historical Driving Memory

## 3. Data Description and Pre-Processing

- A fake collision (e.g., if the relative distance was too small) or incorrect location.
- Lane changing of the following vehicle during the first or last 1.5 s of an identified trajectory (i.e., this does not reflect CF regimes).
- Identified trajectory lasted less than 1.0 s.
- The leading or following vehicle was a truck or a motorcycle.

## 4. Method

#### 4.1. Extracting Features Using Autoencoder

_{1}and S

_{2}are the number of neurons in the input layer and the first hidden layer.

#### 4.2. Testing on NGSIM Datasets

#### 4.3. Car-Following Model Based on LSTM

#### 4.3.1. Long Short-Term Memory Neural Network in CF Models

_{t}denotes the input vectors containing the historical driving memory information. C

_{t}and h

_{t}denote the hidden state and output of the LSTM cell at time t. The sig and tanh in the figure indicate the standard sigmoid and hyperbolic tangent function transforming the input into ranges [0,1] and [−1,1], respectively. In the hidden layers, the information flow keeps being computed and updated, passing though the LSTM cells one by one until the final predictions are obtained.

#### 4.3.2. Model Setups for CF Modeling

_{i}is the observed value of record i.

## 5. Results

^{2}. The follower’s most severe braking capability ${d}_{n}$ was also 1.0 m/s

^{2}, while the follower’s maximum acceleration ${a}_{n}$ was 2.4 m/s

^{2}.

- The LSTM model can learn the driving memory information and describe car-following behaviors with high accuracy especially when using the prediction strategy of pattern 2, because of the LSTM’s unique structure and the incorporation of important temporal information. Figure 6c shows that when v, △v, t were used as inputs, the model did not perform as well in predicting the distance gap. The Gipps model showed acceptable performance in predicting the velocity gap but did not provide good indirect predictions of the distance gap, with estimates substantially lower than the observed value when v, △v, △x were used as inputs (see Figure 6b).
- The time gap parameter ranked highly in the autoencoder analysis, but did not lead to better results, because it is dependent on the velocity parameter. Taking both the time gap and velocity as inputs introduced redundant information and did not improve model performance. Therefore, the variable set of v, △v and △x is recommended instead.
- In most cases, the model showed the best performance with 2.0 s as the time window in pattern 2. Only when predicting the distance gap, the model with a 1.0 s time window and with v, △v, △x as inputs performed better. The optimal time window for predicting velocity and distance gaps needs to be further investigated. A larger time window may lead to better performance, but will also lead to increased computational requirements, increased training time, and (potentially) convergence difficulty during training.
- For pattern 3, the reaction time and the historical driving memory were both considered explicitly, reflecting real driving behaviors. Some key temporal information has been removed, so the predictions are of slightly lower accuracy than using pattern 2 but are still acceptable (see Figure 6c, where v, △v, t are used as inputs). The model showed increased prediction error with 1.0 s time window as a considerable amount of key information was lost. Therefore, incorporating reaction time and historical driving memory at the same time remains challenging for car-following modeling.
- Results show that the prediction accuracy of the proposed LSTM model with patterns 2 and 3 was higher than that of existing models (i.e., the Gipps model).

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**Three prediction patterns in car-following models. Generally, a model only predicts one of the three outcome variables.

**Figure 6.**Simulated and actual results of (

**a**) velocity and (

**b**) distance gap (Vehicle ID: 2072). Figure (

**c**) shows the distance gap of Vehicle ID: 241. P1 means pattern 1.

Symbols | Meaning | Upper Bound | Lower Bound | Unit |
---|---|---|---|---|

IPT | Instantaneous perception time | 18 | 0.3 | s |

$\overline{v}$ | The average velocity during the time window | 22 | 0 | m/s |

$\u25b3{v}_{min}$ | The minimum velocity difference during the time window (negative) | 0 | −6 | m/s |

$\u25b3{v}_{max}$ | The maximal velocity difference during the time window (positive) | 6 | $0$ | m/s |

$\u25b3{v}_{abs}$ | The maximal absolute value of all velocity difference values | 6 | 0 | m/s |

$\u25b3{x}_{min}$ | The minimum distance gap during the time window | 45 | 0.5 | $\mathrm{m}$ |

$\u25b3{x}_{max}$ | The maximal distance gap during the time window | 45 | 0.5 | $\mathrm{m}$ |

$\u25b3\overline{x}$ | The average distance gap during the time window | 45 | 0.5 | $\mathrm{m}$ |

${\mathrm{t}}_{min}$ | The minimum time gap during the time window | 5 | 0.2 | s |

${\mathrm{t}}_{max}$ | The maximal time gap during the time window | 5 | 0.2 | s |

$\overline{t}$ | The average time gap during the time window | 5 | 0.2 | s |

Parameters | Value | Parameters | Value |
---|---|---|---|

Learning rate | 0.009 | Loss function | See Equation (4) |

Epochs | 25 | Optimizer | Adam |

Batch size | 40 | Number of hidden layers | 7 |

Activation function | tanh | Sparsity penalty (α) | 0.002 |

Parameter | Model Run 1 | Model Run 2 | Model Run 3 | Average Activation |
---|---|---|---|---|

$\overline{v}$ | 1.743 | 1.182 | 1.334 | 1.420 |

$\u25b3{v}_{abs}$ | 1.491 | 1.147 | 1.087 | 1.242 |

$\u25b3{v}_{min}$ | 1.434 | 1.149 | 1.115 | 1.233 |

$\u25b3{v}_{max}$ | 1.365 | 1.162 | 1.051 | 1.193 |

$\overline{t}$ | 1.361 | 1.065 | 1.088 | 1.171 |

IPT | 1.295 | 1.134 | 1.032 | 1.154 |

${\mathrm{t}}_{max}$ | 1.151 | 1.14 | 0.858 | 1.050 |

${\mathrm{t}}_{min}$ | 0.979 | 1.152 | 0.759 | 0.963 |

$\u25b3{x}_{max}$ | 0.998 | 1.055 | 0.79 | 0.948 |

$\u25b3{x}_{min}$ | 0.715 | 0.751 | 0.571 | 0.679 |

$\u25b3\overline{x}$ | 0.255 | 0.446 | 0.278 | 0.326 |

Parameters | Value | Parameters | Value |
---|---|---|---|

Learning rate | 0.002 | Loss function | RMSE |

Epoch | 2 | Optimizer | Adam |

Number of LSTM cells | 60 | Batch size | ≥587 |

Activation function | ReLU * | Time steps | 20/10 |

Number of LSTM layers | 4 | Dropout rate | 0.2 |

**Table 5.**Performance comparison of models with different input variables and patterns for training the LSTM.

Pattern | Window Length (s) * | Input Variables | Output Variables | |||
---|---|---|---|---|---|---|

Velocity | Distance Gap | |||||

MSE | MAPE (%) | MSE | MAPE (%) | |||

1 | 0.1 | $v\u25b3v\u25b3x$ | 2.494 | 24.396 | − | − |

2 | 2.0 | $v\u25b3v\u25b3x$ | 0.264 | 6.951 | 3.285 | 16.555 |

2 | 2.0 | $v\u25b3vt$ | 0.589 | 9.689 | 4.855 | 17.192 |

2 | 1.0 | $v\u25b3v\u25b3x$ | 0.367 | 9.045 | 1.705 | 11.467 |

2 | 1.0 | $v\u25b3vt$ | 1.227 | 16.474 | 2.795 | 14.044 |

3 | 1.0 | $v\u25b3v\u25b3x$ | 0.986 | 12.942 | 3.065 | 15.076 |

3 | 1.0 | $v\u25b3vt$ | 2.353 | 22.163 | 12.543 | 31.612 |

3 | 1.5 | $v\u25b3v\u25b3x$ | 0.624 | 10.364 | 4.178 | 16.762 |

3 | 1.5 | $v\u25b3vt$ | 2.148 | 18.337 | 4.954 | 20.771 |

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**MDPI and ACS Style**

Fan, P.; Guo, J.; Zhao, H.; Wijnands, J.S.; Wang, Y.
Car-Following Modeling Incorporating Driving Memory Based on Autoencoder and Long Short-Term Memory Neural Networks. *Sustainability* **2019**, *11*, 6755.
https://doi.org/10.3390/su11236755

**AMA Style**

Fan P, Guo J, Zhao H, Wijnands JS, Wang Y.
Car-Following Modeling Incorporating Driving Memory Based on Autoencoder and Long Short-Term Memory Neural Networks. *Sustainability*. 2019; 11(23):6755.
https://doi.org/10.3390/su11236755

**Chicago/Turabian Style**

Fan, Pengcheng, Jingqiu Guo, Haifeng Zhao, Jasper S. Wijnands, and Yibing Wang.
2019. "Car-Following Modeling Incorporating Driving Memory Based on Autoencoder and Long Short-Term Memory Neural Networks" *Sustainability* 11, no. 23: 6755.
https://doi.org/10.3390/su11236755