# A Dual-Input Neural Network for Online State-of-Charge Estimation of the Lithium-Ion Battery throughout Its Lifetime

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## Abstract

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_{2}batteries, it is validated that the proposed DIGF network is capable of providing more accurate SOC estimations throughout the battery’s lifetime compared to the existing RNN counterparts. Moreover, it also shows greater robustness against different initial SOCs, making it more applicable for online SOC estimations in practical situations. Based on these verification results, it is concluded that the proposed DIGF network is feasible for estimating the battery’s SOC accurately throughout the battery’s lifetime against varying initial SOCs.

## 1. Introduction

## 2. Methodology

#### 2.1. DIGF Network

#### 2.2. SOC Estimation Procedure

#### 2.2.1. Data Preprocessing

#### 2.2.2. DIGF Network Training

^{−3}, 1 × 10

^{−7}, respectively, according to the literature [41].

#### 2.2.3. SOC Estimation

## 3. Experimental Data

_{2}batteries, provided by the Center of Advanced Life Cycle Engineering at the University of Maryland, were employed to verify the performance of the proposed DIGF network for SOC estimation throughout the battery’s lifetime [43,44]. These data consist of the test results under room temperature from five batteries (named CS2-33, CS2-34, CS2-35, CS2-36, CS2-37, respectively) with rated capacity of 1.1 Ah. During the experiment, all the batteries were charged under a constant current–constant voltage (CC–CV) charging mode and discharged with a constant current. In a CC–CV charging cycle, the battery is first charged with a constant current until its voltage reaches the maximum charge voltage; then, it is charged under a constant voltage. Then, the constant voltage charging stage is terminated when the charge current tapers down to the end-of-charge current. In the discharging cycle, the battery is discharged with a constant current until its voltage drops to the discharge cut-off voltage. The detailed information on the batteries and the test conditions is listed in Table 2.

## 4. Results and Discussion

## 5. Conclusions

_{2}batteries show that the proposed DIGF network is feasible for providing satisfying SOC estimations with stronger robustness against different initial SOCs for batteries throughout their lifetimes. Owing to these advantages given above, it is speculated that this proposed DIGF network has great potential for use in online SOC estimation for lithium-ion batteries in practice with a large range of SOHs and initial SOCs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SOC | state-of-charge |

RNN | recurrent neural network |

GRU | gated recurring unit |

FC | fully connected |

DIGF | dual-input neural network combining GRU layers and FC layers |

SOH | state of health |

EV | electric vehicles |

AHI | ampere-hour integral |

OCV | open-circuit voltage |

ECM | equivalent circuit model |

LSTM | long short-term memory |

RMSE | root mean square error |

CC–CV | constant current–constant voltage |

T | Timestep |

${\mathrm{X}}_{t}$ | input of RNN |

${h}_{t-1},{h}_{t}$ | output of RNN |

$\mu $ | number of features in the RNN input |

$\nu $ | number of features in the RNN output |

${z}_{t}$ | output of update gate |

${r}_{t}$ | output of reset gate |

${h}_{t}^{\prime}$ | candidate state |

${w}_{iz},{w}_{hz},{b}_{z}$ | parameters of update gate in GRU |

${w}_{ir},{w}_{hr},{b}_{r}$ | parameters of reset gate in GRU |

${w}_{in},{w}_{hn},{b}_{n}$ | parameters of candidate state in GRU |

$\sigma ()$ | sigmoid function |

$\mathrm{tan}\mathrm{h}()$ | hyperbolic tangent function |

${x}_{fc}$ | input of FC layer |

${w}_{fc}$ | parameters of FC layer |

$\alpha $ | number of features in the input of FC layer |

$\beta $ | number of features in the output of FC layer |

$ou{t}_{fc}$ | output of FC layer |

$k$ | index of cycle |

${V}_{t}^{k}$ | voltage measurement of battery |

${I}_{t}^{k}$ | current measurements of battery |

$I{n}_{t}^{1}$ | input 1 of DIGF network |

$I{n}_{t}^{2}$ | input 2 of DIGF network |

${f}_{GRU}()$ | function of GRU layer in the DIGF network |

${f}_{FC}()$ | function of FC layer in the DIGF network |

${O}_{t}^{1},{O}_{t}^{2},{O}_{t}^{3},{O}_{t}^{4}$ | output of layer 1, layer 2, layer 3, layer 4 in DIGF network |

${C}^{0}$ | battery’s rated capacity |

$dq$ | interpolation interval |

$N$ | number of interpolation samples |

${x}_{train}^{i}$ | unnormalized current/voltage in the training dataset |

${x}^{i}$ | unnormalized voltage/current in the training or testing datasets |

${x}_{norm}^{i}$ | normalized voltage/current in the training or testing datasets |

$n$ | index of iteration during training process |

${\theta}_{n}$ | all parameters of DIGF network |

${L}_{n}\left({\theta}_{n-1}\right)$ | loss function |

${\beta}_{1},{\beta}_{2}$ | decay rates of Adam optimizer |

$\eta $ | learning rate of Adam optimizer |

$\u03f5$ | constant term of Adam optimizer |

M | number of samples in the training dataset |

$SO{C}_{e,j}$ | experimental SOC |

$SO{C}_{m,j}$ | estimated SOC |

$L$ | total number of the estimated SOCs in cycle |

${t}_{end}$ | duration of the discharge cycle |

${C}^{k}$ | $\mathrm{battery}$ |

$SO{C}_{t}^{k}$ | $\mathrm{battery}$$\text{}$ |

$SO{H}^{k}$ | $\mathrm{battery}$ |

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**Figure 7.**Boxplot of RMSEs of SOC estimations under different initial SOCs for battery CS2-37 throughout its lifetime by LSTM, GRU, and DIGF networks.

**Figure 8.**SOC estimations for CS2-37 at cycle 200 by LSTM, GRU, and DIGF networks: (

**a**) initial SOC = 95%;

**(b**) initial SOC = 90%; (

**c**) initial SOC = 85%; (

**d**) initial SOC = 80%; (

**e**) initial SOC = 75%; (

**f**) initial SOC = 70%.

Hyperparameter | Layer 1 | Layer 2 | Layer 3 | Layer 4 | Layer 5 |
---|---|---|---|---|---|

μ | 50 | 50 | - | - | - |

β | - | - | 50 | 50 | 1 |

Specification | CS2-33 | CS2-34 | CS2-35 | CS2-36 | CS2-37 |
---|---|---|---|---|---|

Cell Chemistry | LiCoO_{2} cathode | ||||

Weight (w/o safety circuit) | 21.1 g | ||||

Dimensions | 5.4 × 33.6 × 50.6 mm | ||||

Rated capacity (Ah) | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 |

Constant charge current (A) | 0.55 | 0.55 | 0.55 | 0.55 | 0.55 |

Maximum charge voltage (V) | 4.2 | 4.2 | 4.2 | 4.2 | 4.2 |

End-of-charge current (A) | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 |

Discharge cut-off voltage (V) | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 |

Discharge current (A) | 0.55 | 0.55 | 1.1 | 1.1 | 1.1 |

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**MDPI and ACS Style**

Qian, C.; Xu, B.; Xia, Q.; Ren, Y.; Yang, D.; Wang, Z.
A Dual-Input Neural Network for Online State-of-Charge Estimation of the Lithium-Ion Battery throughout Its Lifetime. *Materials* **2022**, *15*, 5933.
https://doi.org/10.3390/ma15175933

**AMA Style**

Qian C, Xu B, Xia Q, Ren Y, Yang D, Wang Z.
A Dual-Input Neural Network for Online State-of-Charge Estimation of the Lithium-Ion Battery throughout Its Lifetime. *Materials*. 2022; 15(17):5933.
https://doi.org/10.3390/ma15175933

**Chicago/Turabian Style**

Qian, Cheng, Binghui Xu, Quan Xia, Yi Ren, Dezhen Yang, and Zili Wang.
2022. "A Dual-Input Neural Network for Online State-of-Charge Estimation of the Lithium-Ion Battery throughout Its Lifetime" *Materials* 15, no. 17: 5933.
https://doi.org/10.3390/ma15175933