# Efficient Anticipatory Longitudinal Control of Electric Vehicles through Machine Learning-Based Prediction of Vehicle Speeds

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emission [1]. Despite the concerted efforts towards powertrain concepts that can be powered with renewable energies such as battery electric vehicles or fuel cell electric vehicles, this leads to an immense demand of additional green energies for the operation of a new electric vehicle fleet. According to [2], electric vehicles in European cities have a share of about 11% in 2020, thus the majority of vehicles is still fuel based. Therefore, the simultaneous reduction of energy demand in this area has a significant influence on the efforts against climate change.

## 2. Related Work

## 3. Co-Simulation Environment

#### 3.1. Traffic Environment

#### 3.1.1. Microscopic Traffic Simulator

#### 3.1.2. Car-Following Modeling Approach

#### 3.1.3. Validation of the Car-Following Model

^{2}are taken into account. Figure 3 shows a comparison of the simulated driving profiles with the default model parameters of the EIDM and the optimized parameter set. The accelerations in the real driving data mostly stay below 2 m/s

^{2}and decrease towards a vehicle speed of 50 km/h, as this is the dominant vehicle speed limit in the city center. With the default model parameter set, the acceleration of the traffic vehicles tends to be too high compared to the real driving data of the company car, even though buses and trucks are also modeled in the simulation with lower maximum accelerations. A similar conclusion can be drawn for the decelerations which are significantly smaller in the real driving data set. Therefore, both the maximum acceleration ${a}_{\mathrm{max}}$ and desired deceleration $b$ are reduced across all vehicle types to yield a better agreement of real driving data and simulated data with respect to acceleration, as shown in Figure 3b. The mean speed of the driving profile for the default parameter set, on the other hand, is closer to the mean speed of the real driving data. However, there is a higher percentage of driving in areas with a reduced vehicle speed limit of 30 km/h in the simulation, hence the mean speed is generally expected to be lower.

^{2}is reduced, indicating a smaller number of emergency decelerations when using the optimized parameter set. The percentage of standstill states is similar for both parameter sets and close to the real driving data.

#### 3.1.4. Validation of the Macroscopic Traffic Flows

#### 3.2. Vehicle Model

## 4. Control Approach

## 5. Training and Analysis of the Prediction Model

#### 5.1. Model Definition

**f**,

**i**and

**o**denote the input, output and forget gate activation vectors, respectively,

**c**and

**h**the cell state and hidden state vectors, W, U and

**b**the weight matrices and bias vectors and f the nonlinear activation functions. The final hidden state ${h}_{n}^{\mathrm{LSTM}1}$ of the encoder is referred to as the encoder state which has encoded all the relevant temporal information of the input sequences in a fixed length vector. It is then used as input for every time step of the LSTM layer of the decoder (LSTM2). Additionally, the final hidden and cell states of the encoder are used as initial values for the hidden and cell state of the decoder to preserve the information encoded in the cell state. The hidden state sequence of the decoder is processed further in a subsequent fully-connected (dense) layer with a Rectified Linear Unit (ReLU) activation and mapped onto the two output sequences of leader and ego speed with a linear activation.

#### 5.2. Model Training Process

**b**is minimized. The Mean Absolute Error (MAE) over the prediction horizon and both outputs ${\widehat{v}}_{\mathrm{l}}$ and ${\widehat{v}}_{\mathrm{e}}$ is chosen as loss metric.

## 6. Simulative Experiments

#### 6.1. Simulative Case Study

_{p}in the presented simulation environment, a number of routes throughout the traffic net and different BEV with varying powertrain specifications are defined. In this study, 10 routes shown in Figure 11 with 6 different starting times are chosen which leads to a total amount of 217 driven km.

_{ref}with speed and headway control modes is derived from the architecture shown in Figure 6. As mentioned earlier, both controllers are equally parametrized for a high comparability. Three different vehicles are specified, i.e., three BEV with varying rated powers of the EM and varying transmissions, to assess the robustness of the results towards vehicles with different specifications. A transmission ratio of i = 7 combined with the EM characteristics results in a maximum possible vehicle speed of 160 km/h. Hence, the corresponding operating points in this city driving scenario are rather located in the lower EM speed range. A summary of the key vehicle parameters is given in Table 3. The parameters of the BEV-1 are loosely based on a VW ID.3 powertrain. By also analyzing the two-speed BEV, more insight into the effects of different operating points on the vehicle energy demand can be gained.

#### 6.2. Results

_{p}and C

_{ref}. Generally, C

_{p}operates 44% of the time in the anticipatory control mode and 30% in efficient speed mode and only switches into safe speed mode when the headway to the leader is too small. In the first section of the route, several stops at junctions that occur with the reference control C

_{ref}can be avoided by first tracking a set speed below the lane speed limit of 50 km/h and then switching into anticipatory control to track the predicted mean speed of the leader’s trajectory. The trip time up to a driving distance of 1500 m is nearly identical, although the accelerations with C

_{p}overall are considerably lower. On this single exemplary route, the BEV-1 with C

_{p}has a significantly lower consumption of 12.77 kWh/km in comparison to 15.59 kWh/km with C

_{ref}. This reduction is mainly caused by the less frequent braking, lowering the overall breaking losses. Even though the BEV are able to recuperate some of the kinetic energy when braking, a significant percentage of the energy is lost during the conversion of energy in the electric machine.

_{p}and C

_{ref}. The results are shown in Figure 14 for both the rush hour and the off-peak period traffic models of BEV-1. In general, C

_{p}achieves a reduction in the energy consumption across all routes and traffic models of 3.3–23.2% while lowering the mean speed up to 20.5%. However, there are several routes, for instance, R9 during rush hour or R3 during the off-peak period, in which using C

_{p}results in a significant reduction in energy consumption while sustaining the same mean speed. Regarding the jerk, the more anticipatory driving with C

_{p}reduces the RMS of jerk across all routes up to 28.2%.

_{p}leads to a mean reduction in the energy consumption of 6.7%.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Co-simulation environment consisting of an ego vehicle simulation and a microscopic traffic simulation.

**Figure 2.**The modeled area of the city center of Darmstadt, Germany is shown in (

**a**). The integrated elevation profile is shown in (

**b**).

**Figure 3.**Aggregated driving profile of the simulated traffic fleet for (

**a**) default model parameters and (

**b**) optimized model parameters. The mean vehicle speeds of the simulated fleet and the measured driving data and the 90% and 10% quantiles of acceleration as a function of vehicle speed are highlighted.

**Figure 4.**Cumulative traffic flows at several junctions displayed in (

**a**) in the simulation and from measurement data. The traffic flows are shown during (

**b**) rush hour and during (

**c**) off-peak period. The error bars denote the standard deviations of the traffic flow measurements over the weekdays of one week.

**Figure 5.**Overview of the control architecture and the vehicle model which is based on the generic powertrain model shown on the bottom and the simplified lower level control.

**Figure 8.**Workflow of the two-stage model selection process. At the first stage, the main neural network parameters are determined and at the second stage, the best set of features is determined through a backwards elimination feature wrapper method. Both stages use k-fold validation for the training and validation data set.

**Figure 9.**Results of the model selection process. In (

**a**), the training and validation losses for the selected net size are displayed. The model assessment metrics as a function of net size are shown in (

**b**) and the results of the feature wrapping subprocess are shown in (

**c**).

**Figure 10.**Comparison of the prediction errors of ego and leader speed ${v}_{\mathrm{e}}$ and ${v}_{\mathrm{l}}$ on the test data for the models with V2X features, without V2X features and a naive model with a constant acceleration assumption.

**Figure 14.**Reductions of performance indicators with the proposed control C

_{p}compared to the reference C

_{ref}for BEV-1. The results are shown for (

**a**) the rush hour and (

**b**) the off-peak period.

**Table 1.**Comparison of the EIDM model parameters and statistical assessment metrics of the resulting driving profiles. The parameters in the default SUMO parametrization are scalar values while the optimized parameters are drawn from normal distributions with given means and standard deviations.

Model Parameters | Default | Optimized | Driving Data | |
---|---|---|---|---|

a_{max} | Passenger car | 2.6 m/s^{2} | 1.5 ± 0.8 m/s^{2} | - |

Bus | 1.2 m/s^{2} | 1.1 ± 0.5 m/s^{2} | ||

Truck | 1.3 m/s^{2} | 1.1 ± 0.5 m/s^{2} | ||

b | Passenger car | 4.5 m/s^{2} | 1.0 ± 0.6 m/s^{2} | - |

Bus | 4 m/s^{2} | 0.8 ± 0.4 m/s^{2} | ||

Truck | 4 m/s^{2} | 0.8 ± 0.4 m/s^{2} | ||

h | 1 s | 0.8 ± 0.1 s | - | |

k_{v} | 1 | 1 ± 0.1 | - | |

Assessment metrics | ||||

Mean speed | 17.7 km/h | 16.8 km/h | 19.1 km/h | |

Percentage standstill | 36.7% | 35.5% | 35.2% | |

Percentage acceleration below 3 m/s^{2} | 1.560% | 0.070% | 0.096% | |

MSE 90% acceleration quantile curve | 0.324 | 0.094 | - | |

MSE 10% acceleration quantile curve | 0.768 | 0.139 | - |

Sensor-Based Features | V2V-Based Features | V2I-Based Features |
---|---|---|

Speed ego vehicle | Mean speed on lane | Phase TLS |

Speed leading vehicle | Local traffic density | Distance to TLS |

Relative speed | Indicator light leading vehicle | Duration until next TLS phase switch |

Distance to leader | Vehicle string length at TLS | Upcoming speed limit |

Acceleration ego vehicle | Distance to oncoming vehicles | Distance to upcoming speed limit |

Acceleration leading vehicle | Leading vehicle type | Number of lanes |

Relative acceleration | Number of links at next junction | |

Lane speed limit | Distance to next junction | |

Indicator light ego vehicle |

Parameter | BEV-1 | BEV-2 | BEV-3 |
---|---|---|---|

EM Power | 150 kW | 100 kW | 200 kW |

Number of speeds | 1 | 2 | 2 |

Transmission ratios | 7 | (14, 7) | (10, 5) |

Vehicle mass m | 1800 kg | ||

Drag coefficient c_{w}A | 0.66 m^{2} | ||

Rolling resistance coefficient c_{r} | 0.0075 | ||

Lower level control lag $\tau $ | 0.5 s |

Vehicle | Traffic Model | Performance Indicators | |||||
---|---|---|---|---|---|---|---|

Consumption [kWh/100km] | Mean Speed [km/h] | RMS Jerk [m/s ^{3}] | |||||

C_{p} | C_{ref} | C_{p} | C_{ref} | C_{p} | C_{ref} | ||

BEV-1 | Rush hour | 13.84 | 15.10 | 22.31 | 24.90 | 0.36 | 0.46 |

Off-peak | 13.11 | 14.28 | 27.99 | 30.58 | 0.40 | 0.47 | |

BEV-2 | Rush hour | 11.16 | 11.94 | 22.31 | 24.90 | 0.36 | 0.46 |

Off-peak | 10.96 | 11.65 | 27.99 | 30.58 | 0.40 | 0.47 | |

BEV-3 | Rush hour | 13.43 | 14.24 | 22.31 | 24.90 | 0.36 | 0.46 |

Off-peak | 12.93 | 13.68 | 27.99 | 30.58 | 0.40 | 0.47 |

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**MDPI and ACS Style**

Eichenlaub, T.; Heckelmann, P.; Rinderknecht, S.
Efficient Anticipatory Longitudinal Control of Electric Vehicles through Machine Learning-Based Prediction of Vehicle Speeds. *Vehicles* **2023**, *5*, 1-23.
https://doi.org/10.3390/vehicles5010001

**AMA Style**

Eichenlaub T, Heckelmann P, Rinderknecht S.
Efficient Anticipatory Longitudinal Control of Electric Vehicles through Machine Learning-Based Prediction of Vehicle Speeds. *Vehicles*. 2023; 5(1):1-23.
https://doi.org/10.3390/vehicles5010001

**Chicago/Turabian Style**

Eichenlaub, Tobias, Paul Heckelmann, and Stephan Rinderknecht.
2023. "Efficient Anticipatory Longitudinal Control of Electric Vehicles through Machine Learning-Based Prediction of Vehicle Speeds" *Vehicles* 5, no. 1: 1-23.
https://doi.org/10.3390/vehicles5010001