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Explora: Environment
and Resource Artificial neural networks

Table 1. Number of samples per characterization test
Test Number of samples at different temperatures
−10 and 10°C 25 and 35°C 45 and 60°C
Capacity 3 3 3
HPPC
OCV
Thermal pulse
Electrical and thermal model validation
High-current 3
Abbreviations: HPPC: Hybrid pulse power capability; OCV: Open-circuit voltage.
Table 2. Lifetime testing matrix

Condition Number of samples Temperature (°C) C‑rate Rest time (min) Depth of discharge (%)
Discharge Charge
I 3 25 1 0.5 60 100
II 3 25 1 0.5 15 100
III 3 25 1 4 60 100
IV 3 25 4 0.5 60 100
V 3 45 1 0.5 60 100
VI 3 25 Dynamic profile for validation
VII 3 10 1 0.5 60 100

the impact of the charging rate, the charging current was approach for dynamic systems, making them suitable for
increased from 0.5C (3 A) to 4C (12 A), while other factors modeling battery degradation. FNNs excel in predicting a
remained unchanged. single output, such as capacity degradation, which aligns
Moreover, a dynamic discharging profile, instead of a with the requirements of this study. Therefore, a FNN
constant one, was applied to validate the lifetime model. architecture was employed to build the lifetime model.
Finally, the end-of-life of the cell was fixed at 60% of the Figure 3 illustrates a typical two-layer FNN configuration,
initial capacity. with the corresponding mathematical expressions
presented below: 48
2.4. Electrothermal model development
ij (∑
i (∑
v
A comprehensive battery model was developed by y =σ L l=1 ω σ L j=1 v x + ) + w i ) i =12,, …, m (I)
lj
lj
j
0
integrating and validating specialized sub-models into a
unified modeling framework. This framework incorporates where V and W represent the weight matrices, while
electrical, thermal, and lifetime models (Figure 2). The v and w denote the firing thresholds. The function
j0
i0
entire model was created using the MATLAB/Simulink® σ(.) serves as the mapping function. The inputs to the
2024 platform. The electrothermal component simulates network are the n signals x , x ..., x , and the outputs are
n
1
2
both the electrical and thermal behaviors of the battery y , y ..., y . After initializing the network’s weights and
2
m
1
cell, capturing key parameters, such as voltage, SoC, and biases, it is ready for training. Within this framework,
temperature. Meanwhile, the aging model is designed the FNN was trained using three input parameters:
to estimate the degradation of the cell over time and to temperature, current, and cycle number, alongside the
update the cell’s capacity and IR using results from both lifetime characterization data (Section 3.2). The network
the electrical and thermal models. utilized 10 hidden neurons, and the dataset was divided
accordingly, with 75% used for training and 25% for
2.5. Lifetime model development validation and testing. All these processes—training,
ANNs have demonstrated high accuracy in battery validation, and testing—were conducted in the MATLAB/
estimation tasks. 27-31 Among these, feed-forward neural Simulink® 2024 environment to ensure compatibility with
networks (FNNs) stand out as a particularly effective the electrothermal model.
Volume 2 Issue 1 (2025) 4 doi: 10.36922/eer.7228