# Research on Electric Vehicle Braking Intention Recognition Based on Sample Entropy and Probabilistic Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Sample Entropy Extraction for Braking Signals

#### 2.1. Brake Signal Processing

_{k}and ω

_{k}.

^{−6}.

#### 2.2. Sample Entropy Extraction

- (1)
- Construct a sequence of vectors of dimension m, ${\mathrm{X}}_{\mathrm{m}}\left(1\right),......,{\mathrm{X}}_{\mathrm{m}}(\mathrm{N}-\mathrm{m}+1)$. where, ${\mathrm{X}}_{\mathrm{m}}(\mathrm{i})=\left\{\mathrm{x}(\mathrm{i}),\mathrm{x}(\mathrm{i}+1),...,\mathrm{x}(\mathrm{i}+\mathrm{m}-1)\right\},1\le \mathrm{i}\le \mathrm{N}-\mathrm{m}+1$.
- (2)
- Take the absolute value of the maximum difference between the corresponding elements of ${\mathrm{X}}_{\mathrm{m}}(\mathrm{i})$ and ${\mathrm{X}}_{\mathrm{m}}(\mathrm{j})$ as the distance between the two vectors.$$\mathrm{d}\left[{\mathrm{X}}_{\mathrm{m}}\left(\mathrm{i}\right),{\mathrm{X}}_{\mathrm{m}}\left(\mathrm{j}\right)\right]=\underset{\mathrm{k}=0,...,\mathrm{m}-1}{\mathrm{max}}\left(\left|\mathrm{x}(\mathrm{i}+\mathrm{k})-\mathrm{x}(\mathrm{j}+\mathrm{k})\right|\right)$$
- (3)
- Define ${B}_{i}$ as the number of $j$($1\le j\le N-m,j\ne i$) for which the distance between ${X}_{m}\left(i\right)$ and ${X}_{m}\left(j\right)$ is less than or equal to r. When $1\le i\le N-m$, it can be expressed as:$${B}_{i}^{m}\left(r\right)=\frac{1}{N-m-1}{B}_{i}$$
- (4)
- Define ${\mathrm{B}}^{(\mathrm{m})}(\mathrm{r})$ as:$${B}^{m}(r)=\frac{1}{N-m}\sum _{i=1}^{N-m}{B}_{i}^{m}\left(r\right)$$
- (5)
- Increase the dimension to m + 1 and count the number of ${\mathrm{X}}_{\mathrm{m}+1}\left(\mathrm{i}\right)$ and ${\mathrm{X}}_{\mathrm{m}+1}\left(\mathrm{j}\right)$($1\le \mathrm{j}\le \mathrm{N}-\mathrm{m},\mathrm{j}\ne \mathrm{i}$) whose distances are less than or equal to r. Denote the definition of ${\mathrm{A}}_{\mathrm{i}}$ as: Define ${\mathrm{A}}_{\mathrm{i}}$ as the number of ${X}_{m+1}\left(i\right)$ with distances less than or equal to r from ${X}_{m+1}\left(j\right)$($1\le j\le N-m,j\ne i)$ in m + 1 dimensions$${A}_{i}^{m}(r)=\frac{1}{N-m-1}{A}_{i}$$
- (6)
- Define ${\mathrm{A}}^{\mathrm{m}}(\mathrm{r})$ as:$${\mathrm{A}}^{\mathrm{m}}\left(\mathrm{r}\right)=\frac{1}{\mathrm{N}-\mathrm{m}}\sum _{\mathrm{i}=1}^{\mathrm{N}-\mathrm{m}}{\mathrm{A}}_{\mathrm{i}}^{\mathrm{m}}\left(\mathrm{r}\right)$$

## 3. SSA-PNN Brake Intention Recognition Algorithm

#### 3.1. PNN Brake Intention Recognition Model

#### 3.2. PNN Smoothing Factor Optimization

#### 3.3. SSA-PNN Braking Intent Recognition Process

## 4. Experimental Analysis

#### 4.1. Data Acquisition

#### 4.2. Validation Analysis

## 5. Conclusions

- (1)
- Through the analysis of the experimental results, the effectiveness of using the sample entropy of the braking signal as the recognition feature is verified. Compared with the time-domain features such as pedal position, speed, and speed change rate, the sample entropy can identify the braking intention more effectively.
- (2)
- Compared with traditional machine learning algorithms, the SSA-PNN braking intention recognition algorithm proposed in this paper has higher braking intention recognition accuracy and can effectively achieve the accurate determination of braking intention.
- (3)
- In this paper, the SSA-PNN recognition model featuring sample entropy is constructed through the study of brake intention feature parameters and the recognition model, which improves the accuracy of brake intention recognition. However, there are still some shortcomings in this paper. The method only focuses on the accuracy of recognition and ignores the consideration of real time. In addition, further research is needed on how to extract braking signal features more accurately and quickly to improve the accuracy of braking intentions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zhou, H.; Niu, Z. Recognition of Driver’s Braking Intention Based on Extreme Learning Machine. Automob. Technol.
**2021**, 11, 30–34. [Google Scholar] - Zhu, L.; Li, S.; Li, Y.; Wang, M.; Zhang, C.; Li, Y.; Yao, J.; Ji, H. Analysis of braking intention based on fNIRS in driving simulation experiments. IET Intell. Transp. Syst.
**2019**, 13, 1181–1189. [Google Scholar] [CrossRef] - Li, M.; Wang, W.; Liu, Z.; Qiu, M.; Qu, D. Driver behavior and intention recognition based on wavelet denoising and bayesian theory. Sustainability
**2022**, 14, 6901. [Google Scholar] [CrossRef] - Zheng, H. Braking intention recognition algorithm based on electronic braking system in commercial vehicles. Int. J. Heavy Veh. Syst.
**2019**, 26, 268–290. [Google Scholar] [CrossRef] - Liu, J.; Zhang, X. Relationship among braking pedal displacement, braking In-tensity and braking strength in regenerative braking process of electric Vehicle. Sci. Technol. Eng.
**2018**, 18, 317–325. [Google Scholar] - Tang, J.; Zuo, Y. Braking Intention Recognition Method Based on the Fuzzy Neural Network. Wirel. Commun. Mob. Comput.
**2022**, 2022, 2503311. [Google Scholar] [CrossRef] - Lei, Y.; Zhang, Y.; Fu, Y.; Liu, K. Research on adaptive gearshift decision method based on driving intention recognition. Adv. Mech. Eng.
**2018**, 10, 1–12. [Google Scholar] [CrossRef] - Wang, B.; Tang, X.; Wang, L.; Yang, S.; Ma, L. Braking intention identification method for electric vehicles based on EEMD and entropy theory. Automot. Eng.
**2018**, 40, 936–941. [Google Scholar] - Wang, S.; Zhao, X.; Yu, Q.; Yuan, T. Identification of driver braking intention based on long short-term memory (LSTM) network. IEEE Access
**2020**, 8, 180422–180432. [Google Scholar] [CrossRef] - Xing, Z. Driver’s intention recognition algorithm based on recessive Markoff model. J. Intell. Fuzzy Syst.
**2020**, 38, 1603–1614. [Google Scholar] [CrossRef] - Li, X.; Zhang, X. Recognition Method of Braking Intention of Electric Vehicles Based on ABC-SVM Algorithm. China Mech. Eng.
**2021**, 32, 2125. [Google Scholar] - Xin, G.; Guo, P. Research on key technologies of driving intention identification for commercial vehicle based on HMM-SVM. In Proceedings of the 2019 Chinese Automation Congress (CAC), Hangzhou, China, 22–24 November 2019; pp. 4941–4946. [Google Scholar]
- Zhao, X.; Wang, S.; Ma, J.; Yu, Q.; Gao, Q.; Yu, M. Identification of driver’s braking intention based on a hybrid model of GHMM and GGAP-RBFNN. Neural Comput. Appl.
**2019**, 31, 161–174. [Google Scholar] [CrossRef] - Xu, S.; Zhao, X.; Yang, N.; Bai, Z. Control strategy of braking energy recovery for range-extended electric commercial vehicles by considering braking intention recognition and electropneumatic braking compensation. Energy Technol.
**2020**, 8, 2000407. [Google Scholar] [CrossRef] - Li, H.; Xu, Y.; An, D.; Zhang, L. Application of a flat variational modal decomposition algorithm in fault diagnosis of rolling bearings. J. Low Freq. Noise Vib. Act. Control.
**2020**, 39, 335–351. [Google Scholar] [CrossRef] - Chen, S.; Peng, K.; Zhou, P. Review of signal decomposition theory and its applications in machine fault diagnosis. J. Mech. Eng.
**2020**, 56, 91–107. [Google Scholar] - Zhang, W.; Li, j.; Chen, W. A compound fault feature separation method of rolling bearings based on VMD optimized by the bat algorithm. J. Vib. Shock.
**2022**, 41, 133–141. [Google Scholar] [CrossRef] - Zhang, J.; Hou, G.; Wang, H.; Zhao, Y.; Huang, J. Operation feature extraction of flood discharge structure based on improved variational mode decomposition and variance dedication rate. J. Vib. Control.
**2020**, 26, 229–240. [Google Scholar] [CrossRef] - Meng, Z.; Wang, X.; Liu, J.; Fan, F. An adaptive spectrum segmentation-based optimized VMD method and its application in rolling bearing fault diagnosis. Meas. Sci. Technol.
**2022**, 33, 125107. [Google Scholar] [CrossRef] - Pang, C.; Jiang, Y.; Liao, C.; Wu, T.; Jing, W. Automatic recognition of natural earthquaks and artificial blasting based on the sample entropy of the Mel frequency cepstrum coefficient and support vector machine optimized by gray wolf optimization. China Earthq. Eng. J.
**2022**, 44, 1169–1175. [Google Scholar] [CrossRef] - Javaid, M.; Abbas, M.; Liu, J. Topological properties of four-layered neural networks. J. Artif. Intell. Soft Comput. Res.
**2019**, 9, 111–122. [Google Scholar] [CrossRef] - Sharkawy, A.N. Principle of neural network and its main types: Review. J. Adv. Appl. Comput. Math.
**2020**, 7, 8–19. [Google Scholar] [CrossRef] - Liu, B.; Cao, M. Application of Probabilistic Neural Network in Fault Diagnosis of Turbo-generator. Softw. Guide
**2019**, 18, 10. [Google Scholar] - Wang, C.; Tang, Z.; Wu, X.; Li, C.; Zhang, H. Semi-supervised Land Use Classification Based on Particle Swarm Optimization Probabilistic Neural Network. Trans. Chin. Soc. Agric. Mach.
**2022**, 53, 2. [Google Scholar] - Xue, J.; Shen, B. A novel swarm intelligence optimization approach: Sparrow search algorithm. Syst. Sci. Control Eng.
**2020**, 8, 22–34. [Google Scholar] [CrossRef] - Bai, W.; Jia, X.; Lv, T. Application of Improved Sparrow Search Algorithms in Three-dimensional Path Planning. Control Eng. China
**2022**, 29, 10. [Google Scholar] - Pan, H.; Guo, X.; Pei, X.; Pan, J.; Zhang, J. Research on Regenerative Braking Control Strategy of Distributed EV Based on Braking Intention; SAE Technical Paper; SAE International: Warrendale, PA, USA, 2018. [Google Scholar]
- He, K.; Jiang, L. Research on DC Electronic Load System Based on BP Neural Network PID Control. Acad. J. Eng. Technol. Sci.
**2022**, 5, 56–61. [Google Scholar] [CrossRef] - Wu, Y.; Tao, G. Application of a New Loss Function-Based Support Vector Machine Algorithm in Quality Control of Measurement Observation Data. Math. Probl. Eng.
**2022**, 2022, 7266719. [Google Scholar] [CrossRef] - Xu, L.; Hou, L.; Zhu, Z.; Li, Y.; Liu, J.; Lei, T.; Wu, X. Mid-term prediction of electrical energy consumption for crude oil pipelines using a hybrid algorithm of support vector machine and genetic algorithm. Energy
**2021**, 222, 119955. [Google Scholar] [CrossRef]

**Figure 2.**Brake pedal output signal and decomposition results. (

**a**) brake pedal output signals; (

**b**) deceleration brake signal; (

**c**) parking brake signal; (

**d**) emergency brake signal.

**Figure 3.**Sample entropy of the IMF component of the braking signals.(

**a**) deceleration brake signal sample entropy; (

**b**) parking brake signal sample entropy; (

**c**) emergency braking signal sample entropy.

**Figure 7.**Recognition results of different algorithms. (

**a**) Random Forest; (

**b**) BP; (

**c**) SVM; (

**d**) PNN; (

**e**) GA-PNN; (

**f**) SSA-PNN.

Feature | Identification Accuracy | ||
---|---|---|---|

Train (%) | Test (%) | Kappa for Testing | |

Brake pedal position | 90.83 | 90.00 | 0.8387 |

Brake pedal position variation rate | 87.75 | 86.67 | 0.7996 |

Brake pedal speed variation rate | 81.67 | 83.33 | 0.7463 |

Sample Entropy | 94.16 | 93.33 | 0.8982 |

Algorithm | Parametric | |||
---|---|---|---|---|

PNN | RBF neuron expansion coefficient: | 0.01 | ||

Random forest | Minimum number of leaves | 50 | Number of decision trees: | 50 |

SSA | Number of sparrow groups | 20 | Iterations | 50 |

GA | Hereditary algebras: | 50 | Population size: | 5 |

SVM | RBF parameters | 0.01 | Penalty factor | 10 |

BP | Training error: 1 × 10^{−6} Learning rate: 0.01 Iterations: 13 |

Brake Intention Recognition Algorithm | Identification Accuracy | ||
---|---|---|---|

Train (%) | Test (%) | Kappa for Testing | |

Random forest | 79.04 | 77.84 | 0.6725 |

BP | 84.71 | 84.44 | 0.7666 |

SVM | 86.67 | 88.89 | 0.8352 |

PNN | 92.38 | 93.33 | 0.9011 |

GA-PNN | 96.19 | 95.56 | 0.9334 |

SSA-PNN | 97.14 | 97.78 | 0.9667 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wen, J.; Zhang, H.; Li, Z.; Fang, X.
Research on Electric Vehicle Braking Intention Recognition Based on Sample Entropy and Probabilistic Neural Network. *World Electr. Veh. J.* **2023**, *14*, 264.
https://doi.org/10.3390/wevj14090264

**AMA Style**

Wen J, Zhang H, Li Z, Fang X.
Research on Electric Vehicle Braking Intention Recognition Based on Sample Entropy and Probabilistic Neural Network. *World Electric Vehicle Journal*. 2023; 14(9):264.
https://doi.org/10.3390/wevj14090264

**Chicago/Turabian Style**

Wen, Jianping, Haodong Zhang, Zhensheng Li, and Xiurong Fang.
2023. "Research on Electric Vehicle Braking Intention Recognition Based on Sample Entropy and Probabilistic Neural Network" *World Electric Vehicle Journal* 14, no. 9: 264.
https://doi.org/10.3390/wevj14090264