# Design Optimisation of Metastructure Configuration for Lithium-Ion Battery Protection Using Machine Learning Methodology

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## Abstract

**:**

## 1. Introduction

## 2. Geometry and Numerical Model

#### 2.1. Bi-Stable Design

#### 2.2. Result Validation

## 3. Metastructure Configurations Modelling and Machine Learning Optimisation

#### 3.1. Data Sampling Process

#### 3.1.1. Geometry Definition

#### 3.1.2. Material Definition

#### 3.1.3. Sampling Process

#### 3.2. Data Pre-Processing

#### 3.3. ANN Architecture Model

#### 3.4. ANN Model Accuracy

#### 3.5. Decision of Optimised Model

## 4. Battery System Analysis with Optimised Protection Configuration

#### 4.1. Decision of Optimised Model

#### 4.2. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**3D bi-stable baseline configuration with an impactor (

**left**), and its crushing result (

**right**).

**Figure 17.**Cell configuration 1 (

**upper left**), cell configuration 2 (

**upper right**), cell configuration 3 (

**lower left**), cell configuration 4 (

**lower right**).

**Figure 21.**Numerical simulation result of the most optimised battery protector system configuration using concentrated impactor.

**Figure 22.**Numerical simulation result of the optimised cell structure for quasi-static loading using rigid plane impactor from data training process.

Parameters | Value (mm) |
---|---|

$t$ | 0.9 |

$h$ | 6 |

$L/2$ | 15 |

$w=H2=H4$ | 2.5 |

$wm$ | 5 |

$H1$ | 9.5 |

$H3$ | 8.6 |

$l$ | 40 |

$Htot=H3+H1+h+t$ | 25 |

Predictor Variable | Output | |||
---|---|---|---|---|

Continuous (Numerical) Variable | Categorical (Discrete) Variable | |||

Inner cell spacing | 9.5–11.2 $\mathrm{m}\mathrm{m}$ | Cross section shape | Bi-stable, Star, DUH | Specific Energy Absorption (SEA) |

Vertical stack units | $1,2,3$ | |||

Material thickness | 1–3 $\mathrm{m}\mathrm{m}$ | Material Type | SS304 [26], Al6061-T6 [27,28,29], ST37 [26] |

Cross-Section Shape | Geometrical Limitations |
---|---|

Bi-stable | ${h}^{\prime}=h\to 9.5\mathrm{m}\mathrm{m}\le {h}^{\prime}\le 11.2\mathrm{m}\mathrm{m}$ |

Star-shaped | ${h}^{\prime}=0.834h\to 7.92\mathrm{m}\mathrm{m}\le {h}^{\prime}\le 9.34\mathrm{m}\mathrm{m}$ |

DUH (Double-U Honeycomb) | ${h}^{\prime}=2h\to 19\mathrm{m}\mathrm{m}\le {h}^{\prime}\le 22.4\mathrm{m}\mathrm{m}$ |

Category | Variable | SS304 | Al 6061-T6 | ST37 | Unit |
---|---|---|---|---|---|

Mechanical Property | $\mathrm{Density}(\rho $) | 8000 | 2700 | 7330 | $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ |

Young’s Modulus (E) | 200 | 68.9 | 200 | $\mathrm{G}\mathrm{P}\mathrm{a}$ | |

$\mathrm{Yield}\mathrm{strength}(\sigma $) | 290 | 276 | 290 | $\mathrm{M}\mathrm{P}\mathrm{a}$ | |

$\mathrm{Poisson}\u2019\mathrm{s}\mathrm{ratio}(v$) | 0.29 | 0.33 | 0.3 | $-$ | |

Strain-rate Sensitivity | C | 100 | 25,000 | 6.844 | $-$ |

P | 10 | 0.95 | 4.12 | $-$ |

Categorical Variable | Number Variable | Dummy Variable | |||
---|---|---|---|---|---|

Cross-section shape | Bistable | 1 | 1 | 0 | 0 |

DUH | 2 | 0 | 1 | 0 | |

STAR | 3 | 0 | 0 | 1 | |

Material type | SS304 | 1 | 1 | 0 | 0 |

Al6061 | 2 | 0 | 1 | 0 | |

ST37 | 3 | 0 | 0 | 1 |

Layer | Neutron Units | Weight | Bias | Activation Function |
---|---|---|---|---|

Dense_1 | 9 | 81 | 9 | Linear |

Dense_2 | 9 | 81 | 9 | ReLU |

Dense_3 | 9 | 81 | 9 | Sigmoid |

Dense_4 | 9 | 81 | 9 | ReLU |

Dense_5 (Output: SEA) | 1 | 9 | 1 | Linear |

Input | Variable | Data Type |
---|---|---|

1 | Dummy 2 Cell Stack (2 stack) | Boolean (0/1) |

2 | Dummy 3 Cell Stack (3 stack) | Boolean (0/1) |

3 | Dummy 2 Cross-Section (STAR) | Boolean (0/1) |

4 | Dummy 3 Cross-Section (DUH) | Boolean (0/1) |

5 | Dummy 1 Material (SS304) | Boolean (0/1) |

6 | Dummy 2 Material (Al6061) | Boolean (0/1) |

7 | Dummy 3 Material (ST37) | Boolean (0/1) |

8 | Inner Spacing | Float (9.8–11.3) |

9 | Thickness | Float (1–3) |

Variables | Value |
---|---|

Epoch | 3000 |

Initialisation | Normal distribution |

Learning batch | 32 |

Epoch step | 300 |

Validation data split | 20% |

Activation Function | ReLU (Rectified Linear Unit), Sigmoid, Linear |

ANN Optimizer | Adam |

Error Parameter | MSE (Mean Squared Error) |

Parameter | Training Set | Validation Set |
---|---|---|

MSE | 2.6315 × 10^{−5} | 0.0129 |

MAE | 0.0013 | 0.0695 |

Parameters | Value | Unit |
---|---|---|

Cross-section | Star | - |

Material | Al6061-T6 | - |

Vertical stack unit | 1 | - |

Inner spacing | 10.2 | mm |

Material thickness | 2.9 | mm |

Input Parameters | Baseline Model | Optimised Model | |||

Value | Unit | Value | Unit | ||

Cross-section | Bistable | - | Star | - | |

Material | $\mathrm{SS}304$ | - | $\mathrm{Al}6061$ | - | |

Vertical stack | $1$ | - | $1$ | - | |

$\mathrm{Inner}\mathrm{spacing}(h$) | $14.6$ | $\mathrm{m}\mathrm{m}$ | $10.2$ | $\mathrm{m}\mathrm{m}$ | |

$\mathrm{Thickness}(t$) | $0.9$ | $\mathrm{m}\mathrm{m}$ | $2.92$ | $\mathrm{m}\mathrm{m}$ | |

Output Parameters | Value | Unit | Value | Unit | |

Mass | $0.0589$ | $\mathrm{k}\mathrm{g}$ | $0.049$ | $\mathrm{k}\mathrm{g}$ | |

EA | $58.7$ | $\mathrm{J}$ | $2772.38$ | $\mathrm{J}$ | |

SEA | $996.93$ | $\mathrm{J}/\mathrm{k}\mathrm{g}$ | $\mathrm{56,596.28}$ | $\mathrm{J}/\mathrm{k}\mathrm{g}$ | |

Predicted SEA | - | $\mathrm{J}/\mathrm{k}\mathrm{g}$ | $\mathrm{54,992.62}$ | $\mathrm{J}/\mathrm{k}\mathrm{g}$ | |

Differences between Predicted and Simulation results | $2.83\%$ | ||||

Comparison between Optimised and Baseline SEA | $5577\%$ |

Material Properties | Value | Unit |
---|---|---|

Material used | Al 2024-T351 [36] | $-$ |

$\mathrm{Density}(\rho $) | $2.78\times {10}^{-6}$ | $\mathrm{k}\mathrm{g}/\mathrm{m}{\mathrm{m}}^{3}$ |

Young’s Modulus (E) | $73.1$ | $\mathrm{G}\mathrm{P}\mathrm{a}$ |

$\mathrm{Yield}\mathrm{Strength}(\sigma $) | $0.324$ | $\mathrm{M}\mathrm{P}\mathrm{a}$ |

$\mathrm{Poisson}\u2019\mathrm{s}\mathrm{Ratio}(v$) | $0.33$ | $-$ |

$\mathrm{Failure}\mathrm{Strain}({\u03f5}_{f}$) | $0.2$ | $-$ |

Floor Modelling | Value | Unit | ||

$\mathrm{Dimension}(\widehat{x}\times \widehat{z}$) | $200\times 200$ | mm | ||

$\mathrm{Thickness}(\widehat{y}$) | $2$ | mm | ||

Battery Modelling | Value | Unit | ||

$\mathrm{Dimension}(\widehat{x}\times \widehat{z}$) | $150\times 92$ | mm | ||

$\mathrm{Thickness}(\widehat{y}$) | $30$ | mm | ||

Element model | Fully Integrated Solid | - | ||

$\mathrm{Density}(\rho $) | $1.76\times {10}^{-6}$ | $\mathrm{k}\mathrm{g}/\mathrm{m}{\mathrm{m}}^{3}$ | ||

Young’s Modulus (E) | $0.904$ | $\mathrm{G}\mathrm{P}\mathrm{a}$ | ||

Tensile Cut-off (TSC) | $108$ | MPa | ||

DAMP Factor | $0.5$ | - | ||

Plate Modelling | Upper Plate | Lower Plate | ||

Value | Unit | Value | Unit | |

$\mathrm{Dimension}(\widehat{x}\times \widehat{z}$) | $208\times 208$ | mm | $208\times 208$ | mm |

$\mathrm{Thickness}(\widehat{y}$) | $0.4$ | mm | 0.25 | mm |

Configuration | Cell Resize | Cell Arrangement | Total Dimension | Structural Volume |
---|---|---|---|---|

1 | 100% | $6\times 6\times 1$ | $165.4\times 165.4\times 30\mathrm{m}\mathrm{m}$ | $\mathrm{140,271}\mathrm{m}{\mathrm{m}}^{3}$ |

2 | 100% | $6\times 4\times 1$ | $165.4\times 111.2\times 30\mathrm{m}\mathrm{m}$ | $\mathrm{95,695.6}\mathrm{m}{\mathrm{m}}^{3}$ |

3 | 80% | $8\times 8\times 1$ | $175.5\times 175.5\times 24\mathrm{m}\mathrm{m}$ | $\mathrm{124,980}\mathrm{m}{\mathrm{m}}^{3}$ |

4 | 50% | $12\times 8\times 2$ | $163.9\times 109.7\times 30\mathrm{m}\mathrm{m}$ | $\mathrm{89,017.2}\mathrm{m}{\mathrm{m}}^{3}$ |

**Table 15.**Visualisation of the battery thickness deformation for four configurations during impact. The battery is the most deformed for simulation using configuration 3 and least deformed using configuration 1.

Configuration 1 | Configuration 2 | Configuration 3 | Configuration 4 | Time |
---|---|---|---|---|

$0\mathrm{m}\mathrm{s}$ | ||||

$0.5\mathrm{m}\mathrm{s}$ | ||||

$1\mathrm{m}\mathrm{s}$ | ||||

$1.5\mathrm{m}\mathrm{s}$ | ||||

$2\mathrm{m}\mathrm{s}$ |

Configuration | Volume (mm^{3}) | Mass (kg) | EA (J) | SEA (J/kg) | Maximum Deformation (mm) |
---|---|---|---|---|---|

1 | 140,271 | 0.379 | $225.4$ | $595.2$ | $-7.21$ |

2 | 95,695.6 | 0.258 | $225.3$ | $872.2$ | $-7.33$ |

3 | 124,980 | 0.337 | $126.3$ | $374.4$ | $\mathrm{FAIL}$ |

4 | 89,017.2 | 0.240 | $181.1$ | $753.6$ | $-9.69$ |

$0.25\mathrm{m}\mathrm{s}$ | $0.5\mathrm{m}\mathrm{s}$ | $0.75\mathrm{m}\mathrm{s}$ | |

$1\mathrm{m}\mathrm{s}$ | $1.25\mathrm{m}\mathrm{s}$ | $1.5\mathrm{m}\mathrm{s}$ | |

$1.75\mathrm{m}\mathrm{s}$ | $2\mathrm{m}\mathrm{s}$ |

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**MDPI and ACS Style**

Fatiha, I.C.; Santosa, S.P.; Widagdo, D.; Pratomo, A.N.
Design Optimisation of Metastructure Configuration for Lithium-Ion Battery Protection Using Machine Learning Methodology. *Batteries* **2024**, *10*, 52.
https://doi.org/10.3390/batteries10020052

**AMA Style**

Fatiha IC, Santosa SP, Widagdo D, Pratomo AN.
Design Optimisation of Metastructure Configuration for Lithium-Ion Battery Protection Using Machine Learning Methodology. *Batteries*. 2024; 10(2):52.
https://doi.org/10.3390/batteries10020052

**Chicago/Turabian Style**

Fatiha, Indira Cahyani, Sigit Puji Santosa, Djarot Widagdo, and Arief Nur Pratomo.
2024. "Design Optimisation of Metastructure Configuration for Lithium-Ion Battery Protection Using Machine Learning Methodology" *Batteries* 10, no. 2: 52.
https://doi.org/10.3390/batteries10020052