# A Novel Online State of Health Estimation Method for Electric Vehicle Pouch Cells Using Magnetic Field Imaging and Convolution Neural Networks

^{*}

## Abstract

**:**

## 1. Introduction

^{TM}, developed a revolutionary battery management solution that uses wireless communications protocols to send data on the state of individual battery cells throughout the battery pack. According to [15], the BMS chipset combines near-field communication technology with a single antenna to monitor and analyse data directly on individual battery cells using machine learning algorithms, and wirelessly transmit these data to the central BMS.

- A novel SoH estimation approach based on current density images (CDIs) is proposed. This method uses the convolutional neural network (CNN) algorithm to classify and characterise a collection of captured CDIs, from a highly accurate Newman model of the NMC graphite cells of the battery pack and calculates the accurate SoH based on the cell parameters.
- Fast, online readings using an Arduino board connected to a 4 × 8 array of magnetic sensors were carried out for capturing the current density distributions across the positive electrode of a Li-ion pouch cell.
- As a part of a condition monitoring system (CMS), a Python-based user interface with an embedded inference model was designed to monitor the remaining SoH of the selected cells, based on the recorded current density images.

## 2. Magnetic Field Monitoring in LiBs

#### 2.1. Preliminaries of the DFN Model

#### 2.2. Sources of Magnetic Fields Produced by a LiB Cell

## 3. Characterisation of Current Density Images Using Deep Learning

## 4. Experimental Validation and Discussion of Results

#### 4.1. Experimental Test-Bench and Model Validation

#### 4.2. The Effect of Fast-Charging and High Ambient Temperature on CDIs

#### 4.3. Classification of CDIs and CNN Training Accuracy

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of an EV battery pack. In each module, key parameters, including the magnetic field, are measured for each cell, and the generated data are then fed to the BMS.

**Figure 3.**The designed CNN architecture for SoH estimation. The captured CDI from a Li-ion cell is fed into the input layer of the neural network and the final output is the percentage of SoH, presenting the state of health in the corresponding cell.

**Figure 4.**This step diagram shows the process of how a CNN model is trained to characterise the CDIs for the SoH estimation.

**Figure 5.**Nissan leaf pouch cell connected to the Neware BTS4000 battery cycler, with magnetic sensor array module placed on top of the cell.

**Figure 6.**Comparison of charging/discharging cycle curves in the experiment and the DFN model of the cell.

**Figure 7.**CDIs from the positive electrode at room temperature (293.15 [K]). (

**a**,

**b**) A fresh cell was charged with C-rates of 6C and 5C, respectively. (

**c**,

**d**) An aged cell was charged with C-rates of 6C and 5C, respectively.

**Figure 8.**The effect of high ambient temperature on current density distribution during fast charging scenarios for fresh and aged cells.

**Figure 10.**Error distributions on the validation set for different values of SoH and the corresponding CDIs.

**Figure 14.**User Interface (UI) design for the condition monitoring system (CMS)—Cell ID is identified, as well as the related SoH% and SoH estimation graph.

**Table 1.**A summary of the main studied SoH estimation methods, including their categories, benefits, drawbacks, and errors%.

Estimation Category | Approach | Benefits | Drawbacks | SoH Error% |
---|---|---|---|---|

Experimental methods | Measuring internal resistance and internal impedance [10,12] | + Easy implementation + Widely used in automotive profiles | - Operating off-line - Possibility of error accumulation - High time consumption | <3% |

Experimental methods | Electrochemical Impedance Spectroscopy (EIS) [13] | + Low time consumption + Very good accuracy | - Required hardware is complex and costly | <2% |

Model-based methods (Adaptive filtering) [16,17] | Kalman filter-based method [18] Robust estimation method [21,22] | + Operating onboard + Low time consumption + High accuracy | - Accuracy depends on parameters of battery - High computational cost | <2% |

Model-based methods | Least square-based method [19] | + Operating onboard + Widely used in automotive profiles | - High computational complexity | <5% |

Machine Learning methods [23,24] | Convolutional Neural Network(CNN) method [22,28,29] | + Operating Online + Effectively capturing LiB’s non-linear characteristics | - Requires large dataset to train the network - The precision of the method is conditional * | <1.5% |

Li-ion concentration | Solid phase (${c}_{s}$) | $\frac{\partial {c}_{s}}{\partial t}=\frac{{D}_{s}}{{r}^{2}}\frac{\partial}{\partial r}\left(\right)open="("\; close=")">{r}^{2}\frac{\partial {c}_{s}}{\partial r}$ | (1a) |

Electrolyte phase (${c}_{e}$) | ${\epsilon}_{e}\frac{\partial {c}_{e}}{\partial t}=\frac{\partial}{\partial x}\left(\right)open="("\; close=")">{\epsilon}_{e}^{p}{D}_{e}\frac{\partial {c}_{e}}{\partial x}$ | (1b) | |

Boundary condition for Li-ion concentration | Solid phase | ${\left(\right)}_{\frac{\partial {c}_{s}}{\partial r}}r=0=\frac{{j}_{\mathrm{Li}}}{{a}_{s}F}$ | (2a) |

Electrolyte phase | ${\left(\right)}_{\frac{\partial {c}_{e}}{\partial x}}x=0=0$ | (2b) | |

Exchange current density | ${i}_{0}={k}_{0}{c}_{e}^{{\alpha}_{a}}{\left(\right)}^{{c}_{s,max}}{\alpha}_{a}$ | (3a) | |

Measurable terminal voltage | $V\left(t\right)={\varphi}_{s}(L,t)-{\varphi}_{s}(0,t)-\frac{{R}_{f}}{{A}_{\mathrm{surf}\phantom{\rule{4.pt}{0ex}}}}{i}_{\mathrm{app}}\left(t\right)$ | (3b) |

Symbol | Description | Value |
---|---|---|

${A}_{surf}$ | Area of electrode plate | 6.264 [cm${}^{2}$] |

${\alpha}_{a}$ | Anodic transfer coefficient | 0.5 [1] |

${\alpha}_{c}$ | Anodic transfer coefficient | 0.5 [1] |

${a}_{s}$ | The specific inter-facial surface area | $3{\epsilon}_{s}/{R}_{s}$ |

${c}_{s,ma{x}_{pos}}$ | Maximum solid-phase concentration in positive electrode | 49,000 [mol/m${}^{3}$] |

${c}_{s,ma{x}_{neg}}$ | Maximum solid-phase concentration in negative electrode | 31,507 [mol/m${}^{3}$] |

${c}_{s,e}$ | Solid-phase concentration at the solid–electrolyte interface | ${c}_{s,e}(x,t)={c}_{s}\left(\right)open="("\; close=")">{R}_{s},x,t$ |

${\delta}_{p}$ | Positive electrode thickness | 60 [$\mathsf{\mu}$m] |

${\delta}_{sep}$ | Separator thickness | 30 [$\mathsf{\mu}$m] |

${\delta}_{n}$ | Negative electrode thickness | 60 [$\mathsf{\mu}$m] |

${D}_{s}$ | Li-ion diffusion coefficient in the solid phase | $5\times {10}^{-13}$ [m${}^{2}$/s] |

${D}_{e}$ | Li-ion diffusion coefficient in the electrolyte | $7.5\times {10}^{-11}$ [m${}^{2}$/s] |

${\u03f5}_{s,pos}$ | Volume fraction of active particles in positive electrode | 0.35 |

${\u03f5}_{s,neg}$ | Volume fraction of active particles in negative electrode | 0.68 |

${\u03f5}_{e}$ | Electrolyte volume fraction | 0.65 |

${i}_{app}$ | Applied current through the cell | (variable) |

${K}_{{0}_{pos}}$ | Kinetic rate constant in positive electrode | $1.38\times {10}^{-5}$ |

F | Faraday’s constant | $9.65\times {10}^{4}$ [C/mol] |

${K}_{{0}_{neg}}$ | Kinetic rate constant in negative electrode | $0.64\times {10}^{-5}$ |

L | Cell thickness | 160 [$\mathsf{\mu}$m] |

p | Bruggeman porosity exponent | 1.5 |

${R}_{f}$ | Film resistance | $2\times {10}^{-3}$ [$\Omega \xb7{\mathrm{m}}^{2}$] |

${R}_{s,pos}$${t}_{+}^{0}$ | Transport number | 0.363 |

x | Position across the cell | (variable) |

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**MDPI and ACS Style**

Javadipour, M.; Wickramanayake, T.; Alavi, S.A.; Mehran, K.
A Novel Online State of Health Estimation Method for Electric Vehicle Pouch Cells Using Magnetic Field Imaging and Convolution Neural Networks. *Electrochem* **2022**, *3*, 769-788.
https://doi.org/10.3390/electrochem3040051

**AMA Style**

Javadipour M, Wickramanayake T, Alavi SA, Mehran K.
A Novel Online State of Health Estimation Method for Electric Vehicle Pouch Cells Using Magnetic Field Imaging and Convolution Neural Networks. *Electrochem*. 2022; 3(4):769-788.
https://doi.org/10.3390/electrochem3040051

**Chicago/Turabian Style**

Javadipour, Mehrnaz, Toshan Wickramanayake, Seyed Amir Alavi, and Kamyar Mehran.
2022. "A Novel Online State of Health Estimation Method for Electric Vehicle Pouch Cells Using Magnetic Field Imaging and Convolution Neural Networks" *Electrochem* 3, no. 4: 769-788.
https://doi.org/10.3390/electrochem3040051