# Electric Vehicle Range Estimation Using Regression Techniques

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Data Collection and Preprocessing

_{i}and y

_{i}denote the individual data points, while $\overline{x}$ and $\overline{y}$ denote their mean values.

#### 2.2. Regression Techniques

#### 2.2.1. Linear Regression

**θ**and

**x**denote the model’s parameter vector and instance’s feature vector, respectively. The normal equation used to solve for

**θ**is given by [27]:

#### 2.2.2. Support Vector Machine

_{1},y

_{1}), (x

_{2},y

_{2}), …, (x

_{n},y

_{n})} is expressed as [28,29]:

_{i}and b are the weight vector and a constant, respectively, and are found by first defining the following optimization problem. Also, the function $\mathit{\varphi}\left({x}_{i}\right)$ denotes the mapping (can be non-linear for generality) in the feature space. This optimization problem ensures that the function above, f(x), is as flat as possible [28,30].

#### 2.2.3. Model Training

#### 2.2.4. Model Evaluation

_{i}denote the model predicted and actual values, respectively, and m is the total number of observations/data points.

## 3. Results and Discussion

^{2}) error) were also calculated and are presented in Section S7. Similar to the trend observed in the RMSE model evaluations, SVM regression outperforms other regression methods in MAE and MAPE evaluations (Table S2). The R

^{2}error is a measure of the portion of variability in the dependent variable predicted from the independent variable, and when its value is close to 1, it indicates a good fit between the model and the data [37,38]. The R

^{2}value was almost 0.9 (Table S2), suggesting that the models can predict the variability of EV range from the independent variables.

## 4. Conclusions

## Supplementary Materials

^{2}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**A plot, along with the lines of best fit and Pearson correlation coefficients between (

**A**) EPA and WLTP ranges and (

**B**) EPA and NEDC ranges. All units are in km. Furthermore, the bootstrapped linear regression parameters for each iteration are presented for (

**C**) EPA and WLTP ranges and (

**D**) EPA and NEDC ranges.

**Figure 4.**Plots of independent variables against EPA range, where the independent variables are (

**A**) model year, (

**B**) battery capacity (in KWh), (

**C**) number of battery cells in an EV, (

**D**) number of battery modules, (

**E**) EV battery pack voltage, (

**F**) EV top speed (in km/h), (

**G**) EV acceleration from 0 to 100 km/h (in s), (

**H**) EV curb weight (in kg), and (

**I**) gross vehicle weight rating (in kg).

**Figure 5.**Scatter plot of independent variables, (

**A**) EV model year, (

**B**) battery capacity (in KWh), (

**C**) top speed, (

**D**) acceleration from 0 to 100 km/h (in s), and (

**E**) EV curb weight (in kg), with EPA range, with scatter points colored differently based on EV body style.

**Figure 6.**Histograms and boxplots of (

**A**) EV body style, (

**B**) battery cooling mechanism, and (

**C**) type of lithium-ion battery used. The histograms plot the frequency (referred to as the count) of data points against the qualitative independent variables. Boxplots display the average and quartiles of the EPA range against the qualitative independent variables.

Variables | Correlations |
---|---|

Battery Capacity (kWh) | 0.903860 |

Top Speed (mph) | 0.794916 |

Curb Weight (lb) | 0.700247 |

Number of Battery Cells | 0.689241 |

GVWR (lb) | 0.660293 |

Model Year | 0.262226 |

Voltage (V) | 0.187742 |

Number of Battery Modules | 0.041696 |

Acceleration from 0 to 100 km/h (s) | −0.839825 |

Model | Parameters |
---|---|

Normal Linear Regression | - |

Ridge Regression | α = 1 |

Lasso Regression | α = 0.1 |

Elastic Net | α = 0.1 |

r = 0.5 | |

SVM Regression | ε = 0.1 |

C = 1 |

Model | RMSE |
---|---|

Normal Linear Regression | 33.200 |

Ridge Regression | 33.540 |

Lasso Regression | 33.084 |

Elastic Net | 37.423 |

SVM Regression | 31.428 |

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**MDPI and ACS Style**

Ahmed, M.; Mao, Z.; Zheng, Y.; Chen, T.; Chen, Z.
Electric Vehicle Range Estimation Using Regression Techniques. *World Electr. Veh. J.* **2022**, *13*, 105.
https://doi.org/10.3390/wevj13060105

**AMA Style**

Ahmed M, Mao Z, Zheng Y, Chen T, Chen Z.
Electric Vehicle Range Estimation Using Regression Techniques. *World Electric Vehicle Journal*. 2022; 13(6):105.
https://doi.org/10.3390/wevj13060105

**Chicago/Turabian Style**

Ahmed, Moin, Zhiyu Mao, Yun Zheng, Tao Chen, and Zhongwei Chen.
2022. "Electric Vehicle Range Estimation Using Regression Techniques" *World Electric Vehicle Journal* 13, no. 6: 105.
https://doi.org/10.3390/wevj13060105