# Identification of Typical Sub-Health State of Traction Battery Based on a Data-Driven Approach

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## Abstract

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## 1. Introduction

## 2. Voltage Data Analysis

#### 2.1. Data Introduction and Preprocessing

#### 2.2. Types of Sub-Health Status

## 3. Identification of Sub-Health Status

#### 3.1. Identification Algorithm of Sub-Health State Type

#### 3.1.1. ICC

#### 3.1.2. Z-Score

#### 3.1.3. Differential Area Method

#### 3.2. Identification of Sub-Health Status Type I

#### 3.2.1. ICC Calculation of Sub-Health State Type

#### 3.2.2. Threshold Calculation of Sub-Health State Type I

_{j,diff}and V

_{diff}are both higher. Using a threshold of 0.75 as the criterion to determine the sub-health state does not match the actual characteristics of the battery voltage data. Therefore, this paper uses vehicle operation data under different working conditions to determine the threshold value. Figure 5 shows a box diagram of the ICCs of vehicles under different working conditions. We divided the one-month operation data of 72 vehicles at fixed time intervals and calculated the ICC value of each section of data. The figure shows that the lower limit of the box diagram of the 72 vehicles is distributed above 0.7.

#### 3.3. Identification of Sub-Health State Type II

#### 3.3.1. Z-Score Calculation for Sub-Health Type II

#### 3.3.2. Calculation of Sub-Health Type II by Differential Area Method

#### 3.3.3. Threshold of Sub-Health State Type II Based on the 3δ Rule

## 4. Method Verification

#### 4.1. Verification Methods for Sub-Health State Type I

#### 4.2. Verification Methods for Sub-Health State Type II

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Nomenclature variable | |

${V}_{j,diff}$ | The difference in voltage of a single cell at adjacent time points in the j-th column |

${\overline{V}}_{diff}$ | Difference between the average values of cell pack voltage at adjacent time points |

$M{S}_{er}$ | Mean square error of the error term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$M{S}_{bl}$ | The mean square error of the block term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$S{S}_{er}$ | Sum of squares of deviation from mean of the error term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$S{S}_{\mathit{bl}}$ | Sum of squares of deviation from mean of the block term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$S{S}_{tr}$ | Sum of squares of deviation from mean of the treatment term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

${v}_{\mathit{bl}}$ | The degree of freedom of the block term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

${v}_{\mathit{er}}$ | The degree of freedom of the error term between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$k$ | The number of treatment groups between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$b$ | The number of blocks between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$\mathrm{C}$ | Correction coefficient between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

$N$ | Total number of data points between ${V}_{j,diff}$ and ${\overline{V}}_{diff}$ |

${Z}_{i,j}$ | The i-th time point and the j-th Z-score of single battery voltage |

${x}_{i,j}$ | The i-th time point and the j-th single battery voltage |

${\mu}_{j}$ | The i-th time point average value of battery pack voltage |

${\sigma}_{j}$ | The i-th time point standard deviation of battery pack voltage |

Subscripts | |

diff | Difference |

er | Error |

bl | Block |

tr | Treatment |

Acronyms | |

ICC | Interclass correlation coefficient |

EVs | Electric vehicles |

BMS | Battery management system |

C | Capacity |

## References

- Zhang, S.; Xiong, R.; Gao, J. Battery durability and longevity based power management for plug-in hybrid electric vehicle with hybrid energy storage system. Appl. Energy
**2016**, 179, 316–328. [Google Scholar] [CrossRef] - Merkle, L.; Pthig, M.; Schmid, F. Estimate e-Golf Battery State Using Diagnostic Data and a Digital Twin. Batteries
**2021**, 7, 15. [Google Scholar] [CrossRef] - Pearre, N.S.; Kempton, W.; Guensler, L.R.; Elango, V.V. Electric vehicles: How much range is required for a day’s driving. Transp. Res. Part C Emerg. Technol.
**2011**, 19, 1171–1184. [Google Scholar] [CrossRef] - Li, X.; Zhao, J.; Duan, J.; Panchal, S.; Yuan, J.; Fraser, R.; Fowler, M.; Chen, M. Simulation of cooling plate effect on a battery module with different channel arrangement. J. Energy Storage
**2022**, 49, 104113. [Google Scholar] [CrossRef] - Chen, Z.; Li, X.; Shen, J.; Yan, W.; Xiao, R. A Novel State of Charge Estimation Algorithm for Lithium-ion Battery Packs of Electric Vehicles. Energies
**2016**, 9, 710. [Google Scholar] [CrossRef] - Dubarry, M.; Vuillaume, N.; Liaw, B.Y. From single cell model to battery pack simulation for Li-ion batteries. J. Power Sources
**2009**, 18, 500–507. [Google Scholar] [CrossRef] - Li, X.; Zhang, X.; Zhou, Y. Power battery fault diagnosis system based on fuzzy neural network. Chin. J. Power Sources
**2019**, 43, 1391–1394. [Google Scholar] - Baronti, F.; Roncella, R.; Saletti, R. Performance comparison of active balancing techniques for lithium-ion batteries. J. Power Sources
**2014**, 267, 603–609. [Google Scholar] [CrossRef] [Green Version] - Rafael, C.; Frederic, H.; Peter, B. Methodology for Determining Time-Dependent Lead Battery Failure Rates from Field Data. Batteries
**2021**, 7, 39. [Google Scholar] [CrossRef] - Wu, C.; Zhu, C.; Ge, Y.; Zhao, Y. A review on fault mechanism and diagnosis approach for Li-ion batteries. J. Nanomater.
**2015**, 2015, 8. [Google Scholar] [CrossRef] [Green Version] - Tran, M.-K.; Panchal, S.; Khang, T.D.; Panchal, K.; Fraser, R.; Fowler, M. Concept Review of a Cloud-Based Smart Battery Management System for Lithium-Ion Batteries: Feasibility, Logistics, and Functionality. Batteries
**2022**, 8, 19. [Google Scholar] [CrossRef] - Zhao, R.; Liu, J.; Gu, J. Simulation and experimental study on lithiumion battery short circuit. Appl. Energy
**2016**, 173, 29–39. [Google Scholar] [CrossRef] - Dey, S.; Biron, Z.A.; Tatipamula, S.; Das, N.; Mohon, S.; Ayalew, B.; Pisu, P. On-board Thermal Fault Diagnosis of Lithium-ion Batteries for Hybrid Electric Vehicle Application. IFAC Pap.
**2015**, 2015, 389–394. [Google Scholar] [CrossRef] - Yao, L.; Xiao, Y.; Gong, X.; Hou, J.; Chen, X. A novel intelligent method for fault diagnosis of electric vehicle battery system based on wavelet neural network. J. Power Sources
**2020**, 453, 227870. [Google Scholar] [CrossRef] - Chen, Z.; Xiong, R.; Tian, J.; Shang, X.; Liu, J. Model-based fault diagnosis approach on external short circuit of lithium-ion battery used in electric vehicles. Appl. Energy
**2016**, 184, 365–374. [Google Scholar] [CrossRef] - Dey, S.; Biron, Z.A.; Tatipamula, S.; Das, N.; Mohon, S.; Ayalew, B.; Pisu, P. Model-based real-time thermal fault diagnosis of Lithium-ion batteries. Control. Eng. Pract.
**2016**, 56, 37–48. [Google Scholar] [CrossRef] [Green Version] - Han, B.; Wang, D.; Li, S. Research on battery connection reliability based on DC internal resistance. Chin. J. Power Sources
**2017**, 41, 981–983. [Google Scholar] - Xia, B.; Chen, Z.; Mi, C.; Robert, B. External short circuit fault diagnosis for lithium-ion batteries. In Proceedings of the Transportation Electrification Conference and Expo (ITEC), Dearborn, MI, USA, 15–18 June 2014; pp. 1–6. [Google Scholar] [CrossRef]
- Chen, W.; Chen, W.-T.; Saif, M.; Li, M.-F.; Wu, H. Simultaneous fault isolation and estimation of lithium-ion batteries via synthesized design of luenberger and learning observers. IEEE Trans. Control. Syst. Technol.
**2014**, 22, 290–298. [Google Scholar] [CrossRef] - Xu, J.; Liang, D.; Wei, G.; Zhu, C. Series battery pack’s contact resistance fault diagnosis analysis. Trans. China Electrotech. Soc.
**2017**, 32, 106–112. [Google Scholar] [CrossRef] - Sidhu, A.; Izadian, A.; Anwar, S. Adaptive Nonlinear Model-Based Fault Diagnosis of Li-ion Batteries. IEEE Trans. Ind. Electron.
**2014**, 62, 1002–1011. [Google Scholar] [CrossRef] [Green Version] - Liu, Z.; He, H. Model-based Sensor Fault Diagnosis of a Lithium-ion Battery in Electric Vehicles. Energies
**2015**, 6, 6509–6527. [Google Scholar] [CrossRef] - Dey, S.; Mohon, S.; Pisu, P.; Ayalew, B. Sensor fault detection, isolation, and estimation in lithium-ion batteries. IEEE Trans. Control. Syst. Technol.
**2016**, 24, 2141–2149. [Google Scholar] [CrossRef] - Tran, M.-K.; Cunanan, C.; Panchal, S.; Fraser, R.; Fowler, M. Investigation of Individual Cells Replacement Concept in Lithium-Ion Battery Packs with Analysis on Economic Feasibility and Pack Design Requirements. Processes
**2021**, 9, 2263. [Google Scholar] [CrossRef] - Chen, Z.; Zheng, C.; Lin, T.; Yang, Q. Multifault Diagnosis of Li-Ion Battery Pack Based on Hybrid System. IEEE Trans. Transp. Electrif.
**2022**, 8, 1769–1784. [Google Scholar] [CrossRef] - Hu, J.; He, H.; Wei, Z.; Li, Y. Disturbance-immune and aging-robust internal short circuit diagnostic for lithium-ion battery. IEEE Trans. Ind. Electron.
**2021**, 69, 1988–1999. [Google Scholar] [CrossRef] - Hong, J.; Wang, Z.; Yao, Y. Fault prognosis of battery system based on accurate voltage abnormity prognosis using long short-term memory neural networks. Appl. Energy
**2019**, 5, 113381. [Google Scholar] [CrossRef] - Yang, R.; Xiong, R.; He, H.; Chen, Z. A fractional-order model-based battery external short circuit fault diagnosis approach for all-climate electric vehicles application. J. Clean. Prod.
**2018**, 187, 950–959. [Google Scholar] [CrossRef] - Gao, Z.; Cheng, C.S.; Woo, W.L.; Jia, J.; Wei, D.T.W. Genetic algorithm based back-propagation neural network approach for fault diagnosis in lithium-ion battery system. In Proceedings of the 6th International Conference on Power Electronics Systems and Applications, Hong Kong, China, 15–17 December 2015. [Google Scholar] [CrossRef]
- Xia, F.; Ma, X.; Luo, Z.; Zhang, H.; Sun, P. Application of improved D-S evidence theory in fault diagnosis of lithium batteries in electric vehicles. CAAI Trans. Intell. Syst.
**2017**, 12, 526–537. [Google Scholar] [CrossRef] - Li, X.; Wang, Z. A novel fault diagnosis method for lithium-Ion battery packs of electric vehicles. Measurement
**2018**, 10, 402–411. [Google Scholar] [CrossRef] - Xue, Q.; Li, G.; Zhang, Y.; Shen, S.; Chen, Z.; Liu, Y. Fault diagnosis and abnormality detection of lithium-ion battery packs based on statistical distribution. J. Power Sources
**2021**, 482, 228964. [Google Scholar] [CrossRef] - Zou, D.; Chen, H.; Li, X.; Lu, Y.; Huang, P. Consistency evaluation method of lithium battery pack based on cloud charging data. Power Grid Technol.
**2022**, 2022, 308. [Google Scholar] [CrossRef] - Dai, H.F.; Wang, N.; Wei, X.Z.; Sun, Z.C.; Wang, J.Y. A review of the research on monomer inconsistency of automotive power lithium-ion batteries. Automot. Eng.
**2014**, 36, 181–188. [Google Scholar] [CrossRef] - Kumro, F.G.; Smith, F.M.; Yallop, M.J.; Ciernia, L.A.; Lucy, M.C. Estimates of intra- and interclass correlation coefficients for rump touches and the number of steps during estrus in postpartum cows. J. Dairy Sci
**2020**, 104, 2318–2333. [Google Scholar] [CrossRef] - Zidan, M.; Thomas, R.L.; Slovis, T.L. What you need to know aboutstatistics, part II: Reliability of diagnostic and screening tests. Pediatr. Radiol.
**2015**, 45, 317–328. [Google Scholar] [CrossRef] [PubMed] - Post, M.W. What to do with “Moderate” reliability and validity coefficients? Arch. Phys. Med. Rehabil.
**2016**, 97, 1051–1052. [Google Scholar] [CrossRef] [PubMed] [Green Version]

Vehicle Type | Pure Electric Vehicle |
---|---|

Curb weight (kg) | 2420 |

Energy consumption per hundred kilometers (kwh/100) | 20.5 |

Maximum speed (km/h) | 155 |

Rated total energy of battery (kwh) | 82 |

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**MDPI and ACS Style**

Wang, C.; Yu, C.; Guo, W.; Wang, Z.; Tan, J.
Identification of Typical Sub-Health State of Traction Battery Based on a Data-Driven Approach. *Batteries* **2022**, *8*, 65.
https://doi.org/10.3390/batteries8070065

**AMA Style**

Wang C, Yu C, Guo W, Wang Z, Tan J.
Identification of Typical Sub-Health State of Traction Battery Based on a Data-Driven Approach. *Batteries*. 2022; 8(7):65.
https://doi.org/10.3390/batteries8070065

**Chicago/Turabian Style**

Wang, Cheng, Chengyang Yu, Weiwei Guo, Zhenpo Wang, and Jiyuan Tan.
2022. "Identification of Typical Sub-Health State of Traction Battery Based on a Data-Driven Approach" *Batteries* 8, no. 7: 65.
https://doi.org/10.3390/batteries8070065