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Shahriar, Saleh Mohammed, Bhuiyan, Erphan A, Nahiduzzaman, Md, Ahsan, Mominul and
Haider, Julfikar (2022) State of Charge Estimation for Electric Vehicle Battery Management
Systems Using the Hybrid Recurrent Learning Approach with Explainable Artificial Intelligence.
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Article

State of Charge Estimation for Electric Vehicle Battery

Management Systems Using the Hybrid Recurrent Learning
Approach with Explainable Artificial Intelligence
Saleh Mohammed Shahriar 1,*, Erphan A. Bhuiyan 2, Md. Nahiduzzaman 1, Mominul Ahsan 3
and Julfikar Haider 4,*

1 Department of Electrical and Computer Engineering, Rajshahi University of Engineering and Technology,
Rajshahi 6204, Bangladesh
2 Department of Mechatronics Engineering, Rajshahi University of Engineering and Technology,

Rajshahi 6204, Bangladesh

3 Department of Computer Science, University of York, Deramore Lane, Heslington, York YO10 5GH, UK

4 Department of Engineering, Manchester Metropolitan University, Chester St, Manchester M1 5GD, UK

* Correspondence: saleh1610004@gmail.com (S.M.S.); j.haider@mmu.ac.uk (J.H.)

Abstract: Enhancing the accuracy of the battery state of charge (SOC) estimation is essential in de-
veloping more effective, dependable, and convenient electric vehicles. In this paper, a hybrid CNN
and gated recurrent unit-long short-term memory (CNN-GRU-LSTM) approach, which is a recur-
rent neural network (RNN) based model with an explainable artificial intelligence (EAI) was used
for the battery SOC estimation, where the cell parameters were explicitly synchronized to the SOC.
The complexed link between the monitoring signals related to current, voltage, and temperature,
and the battery SOC, was established using the deep learning (DL) technique. A LG 18650HG2 li-
Citation: Shahriar, S.M.;
ion battery dataset was used for training the model so that the battery was subjected to a dynamic
Bhuiyan, E.A.; Nahiduzzaman, M.;
Ahsan, M.; Haider, J. State of Charge
process. Moreover, the data recorded at ambient temperatures of −10 °C, 0 °C, 10 °C, and 25 °C are
Estimation for Electric Vehicle fed into the method during training. The trained model was subsequently used to estimate the SOC
Battery Management Systems Using instantaneously on the testing datasets. At first, the training process was carried out with all tem-
the Hybrid Recurrent Learning perature data to estimate the SOC by the trained model at various ambient temperatures. The pro-
Approach with Explainable Artificial posed approach was capable to encapsulate the relationships on time into the network weights and,
Intelligence. Energies 2022, 15, 8003. as a result, it produced more stable, accurate, and reliable estimations of the SOC, compared to that
https://doi.org/10.3390/en15218003 by some other existing networks. The hybrid model achieved a mean absolute error (MAE) of 0.41%
Academic Editor: to 1.13% for the −10 °C to 25 °C operating temperatures. The EAI was also utilized to explain the
Piedad Garrido Picazo battery SOC model making certain decisions and to find out the significant features responsible for
the estimation process.
Received: 10 October 2022
Accepted: 25 October 2022
Keywords: state of charge (SOC); lithium-ion; battery management system (BMS); electric vehicle
Published: 27 October 2022
(EV); deep learning; explainable AI; gated recurrent unit
Publisher’s Note: MDPI stays neu-
tral with regard to jurisdictional
claims in published maps and institu-
tional affiliations.
1. Introduction
In the realm of modern power technologies, energy storage systems or batteries are
considered as a major component with a variety of applications traversing from small
Copyright: © 2022 by the authors. Li-
electrical devices to large scale applications e.g., electric vehicles (EVs) [1]. Due to the sig-
censee MDPI, Basel, Switzerland. nificantly low to zero carbon emissions, low noise, great effectives, and the adaptability
This article is an open access article of EVs in grid administration and interconnection, they are a viable technology for estab-
distributed under the terms and con- lishing a sustainable transportation system in the longer term [2–5]. Due to the absence of
ditions of the Creative Commons At- fuel in EVs, the technical structure is much simpler, compared to a vehicle based on an
tribution (CC BY) license (https://cre- internal combustion (IC) engine. Among the different types of battery technologies, lith-
ativecommons.org/licenses/by/4.0/). ium-ion batteries are preferred in EVs for high power and energy density, greater

Energies 2022, 15, 8003. https://doi.org/10.3390/en15218003 www.mdpi.com/journal/energies

Energies 2022, 15, 8003 2 of 27

reliability, longer lifespan, minimal discharge rate, and improved effectiveness. Moreo-
ver, the cost and capacity of these batteries are being optimized gradually, which eventu-
ally increases their usage in the EV industry. As a primary element in all of the battery
applications with multiple cells, a battery management system (BMS) is necessary to pro-
vide a reliable operation during its consumption, in the EVs. The BMS is capable of sens-
ing the voltage, current, and temperature of the battery cells to minimize overcharging
and over discharging scenarios [6].
The most significant roles of the BMS include the SOC, State of Health (SoH), and the
State of Power (SoP) for the assessment of the battery states [7], which enables the users
to evaluate the battery pack’s remaining charge, predict the battery’s ageing level, and the
amount of power the battery pack can offer at any given time. The SOC estimation is also
vital to maintain appropriate functioning of the EV drive systems, as this metric straight-
forwardly measures a vehicle’s available mileage and is required for the battery balancing
system. The SOC estimation is an undeniable objective as the battery cells endure irregular
characteristics with repetitive acceleration and braking, in the EVs. As there exists no di-
rect and specific method to quantify the SOC, it is essential to estimate it precisely. Typi-
cally, open circuit voltage-based techniques and coulomb counting (CC), have been used
to estimate the SOC, but these are widely acknowledged to have certain drawbacks [8].
The methods primarily use a chart or quadratic fitting to define the relationship between
the SOC and the open-circuit voltage (OCV). Nevertheless, they necessitate the battery
being at rest for more than two hours in order to obtain an accurate SOC value [9]. The
hybrid approach has been proposed in the literature, to provide a holistic modeling ap-
proach for Li-ion batteries [5] where CC, the linear Kalman filter (LKF), and OCV-based
methods were combined for accurately estimating the SOC and to ensure a safe battery
operation within the acceptable SOC limits, prolonging its lifetime. Therefore, the SOC
estimation tasks have largely been replaced by more advanced methods, for instance, ar-
tificial intelligence (AI) based methods. In the subsequent literature review, the focus has
been given on the AI based SOC estimation methodologies.
In recent years, a number of AI algorithms for the SOC estimation have been postu-
lated. These strategies have shown the potential to outperform the traditional methods.
The methods utilize a unique learning capability of the AI model for training, which is
able to correlate the interrelationships and patterns among the cell assessment parameters
(i.e., voltage, current, resistance, and temperature) and the SOC, with the help of a massive
quantity of data. The AI model is then applicable to an unknown data set to estimate the
SOC. Feedforward neural network (FNN) models for predicting the SOC, were presented
by Darbar and Bhattacharya [10], using voltage, current, and temperature measurements
as the input variables. Once confronted with a variety of driving conditions at varying
temperatures throughout training and testing, the proposed scheme was adequate in es-
timating the SOC. However, the real-time data layout arrangement for machine learning
(ML) was still considered a work in progress. Vidal et al. [11] proposed an enhanced back
propagation neural network (BPNN) that used evaluated voltage, current, and tempera-
ture as the input features to estimate the precise SOC. The BPNN algorithm, however, had
a slow computation time and was extremely receptive to the preliminary weight [12], alt-
hough it could show gradient dissemination or dropping into a local minimum dilemma.
To overcome this issue, other authors utilized an artificial fish swarm technique to deter-
mine several optimal BP neural network parameters [13]. Notwithstanding, in the partic-
ular instance of a huge quantity of data, this swarm intelligence optimization algorithm
significantly increased the computational cost.
Numerous different AI approaches did not take into account the battery voltage
modeling, but the SOC was rather explicitly represented as a component of the sampled
signals. For the SOC estimation, the assorted recurrent neural networks (RNNs) were used
with reasonable precision. To estimate the SOC, Chemali et al. [14] proposed the exploi-
tation of a long short-term memory (LSTM) network. The voltage, current, and tempera-
ture measurements were supplied actively into an extensive infrastructure, which could
Energies 2022, 15, 8003 3 of 27

discover the delineation between both the input series data and the goal SOC. It predicts
the SOC appropriately and learns the hyperparameters on its own. Bian et al. [15] em-
ployed a bi-directional LSTM (Bi-LSTM) which presented a shortcoming that, when de-
coding started without sufficient input sequence data, the decoding efficiency suffered
significantly [16]. Considering the recorded current, voltage, and temperature infor-
mation, another research work [17] employed the gated recurrent unit recurrent neural
network (GRU-RNN) to estimate the battery SOC. Yang et al. [18] employed the velocity
derivative to adjust the network’s weights, in order to increase the GRU network model’s
predictive performance. However, the practical EV operating characteristics for the bat-
teries might vary from these dynamically balanced trajectories, since they could be
changed for various places, users, and time frames. A network based on certain common
features might not be adequate to reliably estimate the SOC underneath a variety of real-
world EV contexts. In the domain of AI, it could lead to algorithmic breakdowns. Moreo-
ver, these methods did not offer the aspects on the mapping of input and output. There-
fore, it is necessary to find out the feature which is responsible for the output result of the
AI model.
In this research, a hybrid CNN-GRU-LSTM (convolutional neural network-gated re-
current unit-long short-term memory network) model with an explainable AI, has been
proposed, that can reliably and more accurately estimate the SOC while self-learning the
network parameters, in order to contribute to the effective battery management for the
EVs. The novel hybrid lightweight model was employed to minimize the SOC estimation
error with a shorter processing time and a smaller memory use, due to a smaller number
of parameters. The explainable AI would help to identify the most important feature from
all of the input features for an accurate SOC estimation when the SOC data at different
temperatures were used together and separately. The hybrid model was compared with
four other models, such as the LSTM, CNN-LSTM, CNN-bi-directional LSTM, and GRU,
to identify the best performing model. Furthermore, the performance of the hybrid model
was compared with the state-of-the-art (SOTA) models to contribute to a better health
management of the EV batteries.
The rest of the paper is organized as follows. Section 2 provides the materials and
methods used in this paper to develop the model, while Section 3 discusses the models’
architecture. Section 4 presents the full experimental results and analysis. Finally, Section
5 draws conclusions, based on the findings.

2. Materials and Methods

2.1. Description of the Dataset
Data related to A LG 18650HG2 Li-ion battery [19] using a 3 Ah LG HG2 cell was
used to train the RNN models. The Li-ion battery was tested in a 0.23 m3 thermal chamber
and a 75 amp and 5 volt Digitron firing circuit was used as the battery tester. The test was
conducted at six different ambient temperatures, ranging from −20 °C to 40 °C. A random
combination of UDDS, HWFET, LA92, and US06, was used in a sequence of eight drive
cycles (mix 1–8). In a compact electric car, the driving cycle power profile was computed
for a single LG HG2 cell. Following each test, the battery was charged at a rate of 1C to 4.2
V with a 50 mA cutoff and a battery temperature of 22 °C or higher. The details of the test
bench and the data logging system are given in [14].
The data of the four ambient temperatures (−10 °C, 0 °C,10 °C, and 25 °C) were chosen
for this work. Four parameters, including voltage, current, temperature, and ampere-hour
(Ah), were selected from the dataset to train the RNN models. The dataset was sampled
to 1 Hz and the SOC was calculated by dividing the Ah data by the capacity of the battery
cell. Then, two parameters were added to the dataset which were the average voltage and
the average current determined by the moving window method. The sample data is
shown in Figure 1.
Energies 2022, 15, 8003 4 of 27

(a)

(b)
Figure 1. Sample data plot for the measured parameters of the terminal voltage, current, tempera-
ture, and battery capacity (Ah) while (a) discharging and (b) charging the battery at −10 °C.

2.2. Overall Design of the Study

The main objective of this work is to propose an optimized deep learning (DL) ap-
proach to estimate the SOC and explain the model with the explainable AI. The initial task
was to collect and preprocess the data for the model training. Then five DL model archi-
tectures, based on CNN and RNN, were built to estimate the SOC of the EV battery in an
optimum way. Then, these five models were trained with the training data and verified
with the test data. A comparison was made among the models and an optimum model
was selected. The optimum model performs better than the other four models, but does
Energies 2022, 15, 8003 5 of 27

not state that it can be used in a BMS as a battery model. Therefore, the optimum model
was also compared with the existing state-of-the-art models, and finally explained with
an explainable AI and the feature importance was calculated using the SHAP library in
Python. An overview of the workflow is shown in Figure 2.

Figure 2. Overall design of the study for the SOC estimation of the EV battery.

2.3. Methodologies Used for the SOC Estimation

The RNN is one kind of artificial neural network (ANN) that is used in the analysis
of sequential data. Nowadays, the RNN is used in the field of natural language processing
(NLP), time series forecasting, voice recognition, and so on [20]. Since the SOC of a lith-
ium-ion battery is estimated through the analysis of sequential data, the RNN can also be
applicable here. Two types of RNN algorithms were used here: the long short-term
memory (LSTM) and the gated recurrent unit (GRU). One dimensional convolution was
also used for the feature extraction purpose from the data.

2.3.1. Long Short-Term Memory (LSTM)

The LSTM is specifically developed to prevent the problem of long-term dependency
[20]. It is its default behavior to remember information for long periods of time. In Figure
3, ck is denoted as the cell memory where k is denoted as time. The LSTM has three gates:
forget, input, and output. The forget gate decides which information has to be erased from
the cell memory and is defined by Equation (1) [14].
Fk = σ (wf·[hk−1,xk] + bf) (1)
where, the sigmoid function, which is denoted by σ, is used and this provides the values
of either 0 or 1. Mainly this sigmoid function decides whether the information in c k−1 has
to be erased or not. Here, wf, hk−1, xk, and bf, are weight metrics, previous layer hidden state
vector, input vector, and the bias of the network, respectively.
Energies 2022, 15, 8003 6 of 27

Figure 3. The internal architecture of a LSTM unit containing all of the parameters and gates.

The input gate keeps the new information in the unit memory ck. The input gate is
described by Equations (2) and (3).
ik = σ (wk ·[hk−1,xk] + bk) (2)

c˜k = tanh(wc ·[hk−1,xk] + bc) (3)

where the “input gate layer” ik, which is built with a sigmoid layer, chooses which values
have to be updated first. Following that, a tanh layer generates the c˜k vector of the new
candidate values that could be added to the state. Now, the outputs of Equations (1)–(3)
are combined to update the unit memory ck, defined by Equation (4).
ck = fk ∗ ck−1 + ik ∗ c˜k (4)
where, ck is the unit memory. Now, the principle of the output gates will be discussed. The
output has to be provided, based on the cell unit memory ck. First, a sigmoid function is
used to perform the task related to which part of the unit memory will be used, as the
output (Equation (5)).
Ok = σ (wo [hk−1,xk] + bo) (5)
where bo is the bias. Now, the cell unit memory ck is passed into a tanh function to make
the values from −1 to 1. Then, it is multiplied by the output of the Equation (4) to obtain
the output hk (Equation (6)).
hk = Ok ∗ tanh(ck) (6)
where hk is the output. The main problem of the past RNN, was that previous inputs faded
away with time. However, in the LSTM, the cell memory is controlled by the input and
the forget gates. Thus, a long-term dependency problem is solved [21].

2.3.2. Gated Recurrent Unit (GRU)

Although the accuracy of the LSTM with three gates is very good, it is a complex
model. Therefore, an updated version of the LSTM has emerged, and this is called the
gated recurrent unit (GRU), which has an update gate and a reset gate. The reset gate
controls how to integrate a new input with prior inputs in its memory, while the update
gate specifies how much of the previous memory should be retained. The long-term de-
pendencies can be explicitly modeled using this gating method. The network learns how
Energies 2022, 15, 8003 7 of 27

its memory should function by learning the settings for its gates. Figure 4 explains the
whole process in the GRU.

Figure 4. The internal architecture of a GRU containing all of the parameters and gates.

The reset gate is denoted by ‘r’ and the update gate is denoted by ‘z’. Equations (7)–
(10) represent the whole GRU process [22]. The GRU reduces the complexity of the LSTM
and works very well with small datasets.

zk = σ (wz·[hk−1,xk]) (7)

rk = σ (wr·[hk−1,xk]) (8)

h͂k = tanh(w [rk ∗ hk−1,xk]) (9)

hk = (1 − zk) ∗ hk−1 + zk ∗ h͂k (10)

where rk is the reset gate and zk is the update gate.

2.3.3. CNN for the Feature Extraction

A one-dimensional (1D) convolutional layer was used in this work. In a normal two-
dimensional (2D) CNN, the kernels or filters stretch across both the spatial dimensions of
an image, from left to right and from top to bottom. Moreover, the kernels in 1D-CNN
layers only stretch in one dimension, which in this case is the temporal dimension. As a
result, they can extract temporally relevant information [23]. The causal padding was used
before running the filter. This is a unique sort of padding that mostly uses one-dimen-
sional convolutional layers, that are particularly useful in time series analysis. As the time
series provides the sequential data, it aids in the addition of zeros at the beginning and
the prediction of the early time step values.

2.3.4. Explainable AI Tool

The explainable AI is a new feature of ML and DL that can explain a ML or DL model.
In the process of ML or DL, at first, a model is trained with some input features and the
outputs. Following the training of the model, if the input features are provided, the model
provides an output result. However, the individual impact of the input features on the
output is unknown. For example, in this SOC estimation model, if five inputs (voltage,
current, temperature, average voltage, and average current) are provided, the model
Energies 2022, 15, 8003 8 of 27

provides the SOC of the battery, but the model cannot determine the importance of each
input feature, which can be explained by the explainable AI.
The Shapley Additive exPlanations (SHAP) is a library using Python, which is used
to calculate the feature importance of a model. At first, SHAP takes a trained model, and
with a sample dataset provided to SHAP, it makes predictions using the obtained dataset
by shuffling the values in a single column. It calculates how much the loss function suf-
fered from shuffling, using these forecasts and the true target values [24]. The importance
of the variable just shuffled, is measured by the performance degradation. Then, it restores
the data to its previous state (undoing the shuffle from step 2). Then, it repeats the step
with the next column in the dataset, until it has computed the importance of all of the
columns.
Lundberg and Lee’s recent work [25] on ML algorithms has created new ways to
comprehend the model outputs. Based on the average of the geometrical contribution
across all potential permutations of the features, the Shapley value is determined. The
following mathematical expression is used for calculating the traditional SHAP value.
|𝑇|! (𝑛 − |𝑇| − 1)!
∅𝑗 = ∑ [𝑓(𝑇 ∪ {𝑗}) − 𝑓(𝑇)] (11)
𝑛!
𝑇⊆𝑁{𝑗}
where Φj stands for the contribution of feature j and N represents all features set. Then, n
denotes the number of the features in set N, T is the subset of N that contains feature j and
without knowing the feature values, the base value, or f(N), is the expected result for each
feature in N. The SHAP value of each feature for a given observation, is added up to esti-
mate the model result for that observation. As a result, the explanation model is defined
by Equation (12).
𝑀

𝑔(𝑧 ′ ) = ∅0 + ∑ ∅𝑗 𝑧𝑗′ (12)

𝑗=1

where M is the features number and z′ is the input [26].

3. Architecture of the Employed Learning Networks

A total of five RNN models were employed for the SOC estimation. The models were
built using TensorFlow, which is an open-source library that uses Python, and that is
widely used in the field of ML and DL. These models were built, based on five types of
layers, namely, a one-dimensional convolution layer, a LSTM layer, a bi-directional LSTM
layer, a GRU layer, and a dense layer. Google Collab was used as the programming envi-
ronment. The voltage, current, battery temperature, average voltage, and the average cur-
rent were used as the input features and the SOC in % was used as the output. Adam was
used as the optimizer, with the benefit of fixing the learning rate of the model itself [27].
An algorithm, regarding the whole process is given in Algorithm 1.

Algorithm 1: The model building and training method for the SOC estimation
• Voltage, Current, Temperature, Average Voltage, Average Current
Inputs • Input Shape = (5,1); Which corresponds (Number of Features, Window Size)
• Here, Number of Features = 5, Window Size = 1
Output • Five trained models and their performance parameters
• Building a model with just LSTM and dense layers
• Building a model with the addition of a one-dimensional convolution layer before the LSTM layers
Model
• Building a model transforming the uni-directional LSTM layers into bi-directional.
Building
• Building a model with just the GRU and dense layers
• Building a hybrid model with a one-dimensional convolution, and GRU and LSTM layers
Model • Defining the loss function as Mean Absolute Error (MAE)
Compiling • Defining the optimizer as “Adam”.
Energies 2022, 15, 8003 9 of 27

Training • Training the five models with training data and calculating the training errors.
and Testing • Testing the five models with test data and calculating the test error. (Errors are Mean Absolute Er-
Models ror, Root Mean Squared Error, and Maximum Error)

3.1. Learning Network 1: LSTM

Recurrent neural networks with a unique ability to disingenuously recognize se-
quences over extended periods of time, are known as long short-term memory (LSTM)
networks. It is the best option for modeling sequential data and is therefore used to un-
derstand the intricate complexities of sentient behavior. The term “cell state” refers to the
long-term memory. The preceding data is kept in the cells because of their recursive na-
ture. Three LSTM layers with each layer consisting of 512 units, were added to the model.
Then, a flatten layer was used to make the data three-dimensional to one-dimensional,
followed by four dense layers, which have 1024, 1024, 512, and 128 units, respectively with
the activation function “ReLU”. Finally, one dense layer of one unit was incorporated as
the output layer. The architecture of the LSTM model is presented in Figure 5.

Figure 5. Architecture of the LSTM model.

3.2. Learning Network 2: CNN-LSTM

The convolutional neural network (CNN) layers for the extraction of features on the
input data are merged with the LSTMs, to endorse the sequential prediction in the CNN
LSTM architecture. The CNN-LSTMs were created for concerns involving the prognostics
of the visual time series, as well as the implementation of producing explanations from
the visual patterns. The model architecture of the CNN-LSTM was almost same as the
LSTM model with the key difference of a one-dimensional convolution layer, before the
LSTM layers, which was added for the feature extraction purposes (Figure 6). It extracts
the main features of the data before entering it into the LSTM layers. A total of 128 filters
were used for the convolution process.
Energies 2022, 15, 8003 10 of 27

Figure 6. Architecture of the CNN-LSTM model.

3.3. Learning Network 3: CNN-Bi-Directional LSTM

A bi-directional LSTM, also known as a Bi-LSTM, is a sequential computational
framework, that consists of two LSTMs, one of which receives the input in forward time
order, and the other receives the input in backward time order. The CNN-bi-directional
LSTM architecture is almost the same as the CNN-LSTM model, except for the bi-direc-
tional LSTM layers, instead of the uni-directional LSTM layers, as shown in Figure 7. The
rest of the architecture is the same. The input runs in two directions in a bi-directional
LSTM. The input flows in one way, either backward or forwards, with the conventional
LSTM. However, with the bi-directional LSTM, the information flows in both directions,
preserving both the future and the past. When jobs requiring sequence to sequence are
essential, the Bi-LSTM is typically used.

Figure 7. Architecture of the CNN bi-directional-LSTM model.

3.4. Learning Network 4: GRU

A gated recurrent unit (GRU) is a component of a particular type of recurrent neural
network, that is designed to use the interconnection made through a series of nodes, to
carry out machine learning activities involving memory and grouping, such as speech
recognition. The main distinction between the GRU and LSTM, is that while the LSTM
has three gates—input, output, and forget—the GRU only has two gates, update and reset.
The GRU has fewer gates than the LSTM, making it less complicated. In the GRU model,
three layers with each layer consisting of 64 units, were added in place of the LSTM layers,
followed by a flatten layer and three dense layers with 1024, 1024, and 512 units with the
activation function ”ReLU”. Then, one dense layer with one unit was used as the output
layer. The complexity of the GRU model is much less than that of the LSTM based models.
The architecture of the GRU model is shown in Figure 8.

Figure 8. Architecture of the GRU model.

Energies 2022, 15, 8003 11 of 27

3.5. Learning Network 5: Hybrid CNN-GRU-LSTM

First, an explanation is needed why a CNN-GRU-LSTM hybrid model should be
built. Although the LSTM is capable to solve the long-term dependency problems of the
RNN and shows accurate results on large datasets, it needs more parameters and memory,
in order to be executed, in contrast to the GRU. Hence, a combination of the LSTM and
the GRU layers can provide the solution to the long-term dependency problem, but at the
same time be less complex and less time-consuming.
At first, a one-dimensional convolution layer containing 128 filters was added for the
feature extraction purpose, followed by a GRU layer of 64 units. Next, a LSTM layer of 64
units and a flatten layer were incorporated sequentially. Then, two dense layers, which
have 1024 and 512 units, were added with the activation function “ReLU”. Finally, one
dense layer of one unit was used as the output layer. The architecture of the CNN-GRU-
LSTM hybrid model is shown in Figure 9.

Figure 9. Architecture of the hybrid CNN-GRU-LSTM model.

3.6. Summary of the Learning Networks

The structural comparative analysis of the different learning network models is
shown in Table 1. According to the number of parameters and layers, the hybrid CNN-
GRU-LSTM is the most lightweight model and the CNN-Bi-LSTM is the heaviest.

Table 1. Summary of the model characteristics.

No. of Model Depth (No. No. of CNN No. of Dense (Hid-

Models No. of RNN Layers
Parameters of Layers) Layers den) Layers
LSTM 9,513,729 7 0 3 4
CNN-LSTM 9,774,849 8 1 3 4
CNN Bi-LSTM 22,101,761 8 1 3 (Bi-directional) 4
GRU 1,729,217 6 0 3 3
CNN-GRU-LSTM 925,313 5 1 2 2

4. Quantitative Analysis and Validation of the Learning Networks

4.1. Performance Valuation Metrices
The mean absolute error (MAE), defined by Equation (13), was used as the loss func-
tion for training the model.
𝑁
1
𝑀𝐴𝐸 = ∑|𝑆𝑜𝐶(𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)𝑘 − 𝑆𝑜𝐶(𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑)𝑘 | (13)
𝑁
𝑛=1
Energies 2022, 15, 8003 12 of 27

where N is the length of the data. Following the training, the models were tested with the
test data. The root mean squared error (RMSE) defined by Equation (14) and the maxi-
mum error defined by Equation (15) were chosen as the test criteria of the models, as well
as the MAE.

𝑁
1
𝑅𝑀𝑆𝐸 = √ ∑(𝑆𝑜𝐶(𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)𝑘 − 𝑆𝑜𝐶(𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑)𝑘 )2 (14)
𝑁
𝑛=1

𝑀𝑎𝑥 𝐸𝑟𝑟𝑜𝑟 = 𝑀𝐴𝑋(|𝑆𝑜𝐶(𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)– 𝑆𝑜𝐶(𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑)|) (15)

4.2. Training with the Data of the Four Ambient Temperatures Altogether
In this experimental analysis, the data of all four ambient temperatures (10 °C, 0 °C,
10 °C, and 25 °C) were used collectively to train the five models with 669,956 training data.

4.2.1. Training and Test Results of the LSTM Network

Following 15 epochs, the training mean absolute error (MAE) of the LSTM model
was 0.93%. It took 55 min and 34 s for the whole training process with a total of 9,513,729
trainable parameters in the LSTM network. Following the training, the model was tested
with the test data of the four ambient temperatures, separately, and the results are given
in Table 2. The average MAE and RMSE of the LSTM model, based on the four ambient
temperature data, were found as 0.81% and 1.17%, respectively. The remarkable point of
the results was that no convolution layer was used for the feature extraction. Since the
MAE was used as a loss function, the main goal of the training process was to reduce the
MAE. The model performed best at 0 °C temperature where the MAE was only 0.64%,
compared to the highest MAE of 0.9% at 10 °C.

Table 2. Test results of the LSTM model.

Temperature Number of Required Time

MAE (%) RMSE (%) Max Error (%)
(°C) Test Data (s)
−10 39,293 4.03 0.79 1.11 4.17
0 42,530 4.12 0.64 0.89 4.65
10 44,284 4.26 0.90 1.56 8.43
25 47,517 5.14 0.87 1.10 4.50
Average 0.80 1.17 5.44

The plot of the measured and predicted SOC values of the LSTM model with the test
data of −10 °C, is given in Figure 10a. Instead of plotting the data for all temperatures, the
results of −10 °C is plotted as determining the SOC at lower ambient temperatures, is more
critical than in higher temperatures [14,28]. From the graph, it was found that the model
worked better with very small errors while charging, but generated more errors during
the discharging process. Because of the experimental process, it is known that the battery
was charged at a constant voltage process of 4.2 V. At the beginning of the charging pro-
cess when the battery is empty, the current flow is normally higher. The current flow is
subsequently decreased with the passage of charging time because the battery becomes
gradually full of charge. Therefore, the charging process is quite simple, whereas dis-
charging is not, as the battery is not discharged with a constant load, rather with the power
profile of different drive cycles. When the battery is used in an electric vehicle, the load
can be changed at almost every moment. Another remarkable phenomenon that happens
during the discharging process is the regenerative braking, which is normally a charging
process, where the loss of kinetic energy does not happen while braking, rather the energy
is again stored in the battery. Therefore, the process of discharging is more complex
Energies 2022, 15, 8003 13 of 27

making it very challenging to predict the accurate SOC while discharging, compared to
the prediction of the SOC during the charging. This can be demonstrated by very smooth
lines of the SOC during the charging process, compared to the noisy lines during the dis-
charging process (Figure 10a). The plot of the absolute errors of the LSTM model on test
data of −10 °C is shown in Figure 10b. The maximum error of the test data at −10 °C
(4.17%), presented in Table 2, was also evidenced in Figure 10b. The error can be both
positive and negative. As the optimization of the model was built, based on the mean
absolute error, the absolute error is plotted for better understanding.

(a)

(b)
Figure 10. Performance of the LSTM model at −10 °C (a) measured and predicted SOC values and
(b) absolute errors from the test data.

4.2.2. Training and Test Results of the CNN-LSTM Network

The CNN-LSTM network contained 9,774,849 trainable parameters and after 15
epochs, the training mean absolute error (MAE) was recorded as 0.91%, with 1 h 57 min
and 24 s required for the whole training process. Adding a convolution layer with 128
filters, increased the training time by almost 1 h, reduced by 0.02% the training error, and
increased a total of 261,120 trainable parameters. Following the training, the model was
tested with the test data of the four ambient temperatures, separately, and the test results
are shown in Table 3.
Energies 2022, 15, 8003 14 of 27

Table 3. Test results of the CNN-LSTM model.

Number of Test RMSE Max Error

Temperature (°C) Required Time (s) MAE (%)
Data (%) (%)
−10 39,293 10.12 0.82 1.23 9.30
0 42,530 11.04 0.70 1.12 9.28
10 44,284 12.10 0.89 1.65 8.37
25 47,517 13.40 0.49 1.00 11.50
Average 0.73 1.25 9.61

It was observed that the CNN-LSTM model showed a superior performance at 25 °C

and a relatively poor performance at 10 °C. The average MAE and RMSE of the CNN-
LSTM model, based on the four ambient temperature data, were 0.73% and 1.25%, respec-
tively. Therefore, from the test result, it was clear that adding a convolution layer reduced
the total mean absolute error, but the maximum error was increased. The testing time
increased significantly, compared to the LSTM model because of the convolution layer,
which extracted the feature from the data, and it is normally a time-consuming process.
The plot of measured values and predicted values of the CNN-LSTM model on the test
data at −10 °C is presented in Figure 11a. The graph was also almost identical to the LSTM
model performance graph with a better performance for the charging time SOC estima-
tion, compared to that during the discharging. The absolute errors of the CNN-LSTM
model on the test data at −10 °C is plotted in Figure 11b with a maximum error of 9.3%,
which was higher than that of the LSTM model. It should be noted that only at a fewer
points, were the error was so high. However, the overall test MAE of all of the temperature
data of the CNN-LSTM model decreased to 0.73%, compared to 0.81% in the LSTM model.
Therefore, though adding a convolution layer made the model more complex, the overall
performance of the CNN-LSTM improved.

(a)
Energies 2022, 15, 8003 15 of 27

(b)
Figure 11. Performance of the CNN-LSTM model at −10 °C (a) measured and predicted SOC values
and (b) absolute errors from the test data.

4.2.3. Training and Test Results of the CNN Bi-Directional-LSTM Network

During the CNN bi-directional-LSTM (CNN Bi-LSTM) model training, the MAE was
found to be 0.87%, after running 15 epochs which took almost 3 h 55 min 32 s, which were
about four and two times higher than the LSTM and CNN-LSTM models, respectively.
The total number of 22,101,761 trainable parameters in the CNN Bi-LSTM model was
more than double the previous two models. Adding the number of parameters means
adding more complexity. Though the MAE was reduced by almost 0.04%, than that of the
CNN-LSTM model, it required a huge amount of time for training. Therefore, this CNN
Bi-LSTM model can be used where time and memory complexities are of minor im-
portance, compared to the error. Following the training, the model was tested with the
test data of the four ambient temperatures (Table 4).

Table 4. Test results of the CNN bi-directional-LSTM model.

Temperature Number of Required Time Max Error

MAE (%) RMSE (%)
(°C) Test Data (s) (%)
−10 39,293 20.52 0.64 1.05 5.23
0 42,530 20.52 0.67 0.97 5.78
10 44,284 20.29 0.89 1.62 8.00
25 47,517 21.75 0.55 1.07 9.11
Average 0.69 1.18 7.03

The average MAE and RMSE of the CNN Bi-LSTM model, based on the four ambient
temperature data, were recorded as 0.69% and 1.18%, respectively, which were either sim-
ilar to or better than the previous two models. Though it required more time to calculate
the SOC, the error was on a satisfactory level. The testing time was almost double that of
the CNN-LSTM model and four times greater than that of the LSTM model, possibly due
to the bi-directional layers. In the normal uni-directional LSTM, the data passes in only
the forward direction, whereas the data passes in both the forward and backward direc-
tions in the bi-directional layers. It was also observed that, similar to the CNN-LSTM
model, the CNN Bi-LSTM model performed best at 25 °C and worst at 10 °C.
The plot of the measured values and predicted values of the CNN Bi-LSTM model,
based on the test data at −10 °C during the charging and discharging, showed a similar
trend to that of the previous models (Figure 12a). From Figure 12b and Table 4, a
Energies 2022, 15, 8003 16 of 27

maximum error value of 5.23% was found for the CNN Bi-LSTM model on the test data
at −10 °C, which was in between the previous two models. The overall lower MAE of the
CNN Bi-LSTM model indicated a sign of a better performance than the previous two mod-
els.

(a)

(b)
Figure 12. Performance of the CNN bi-directional-LSTM model at −10 °C (a) measured and pre-
dicted SOC values and (b) absolute errors from the test data.

4.2.4. Training and Test Results of the GRU Network

For the GRU model, after 15 epochs, a MAE of 0.88% was found, which took almost
1 h 29 min and 45 s for the training, with a total of 1,729,217 trainable parameters. The
GRU is a more lightweight model than the LSTM, with a smaller number of parameters
than the three previous LSTM-based models. Based on the similarity, the GRU model ar-
chitecture was similar to the LSTM model. The main difference identified was that the
three layers of the LSTM model had 512 units, compared to the 64 units in the GRU model,
indicating that it is less complex than the LSTM model. The CNN Bi-LSTM showed a very
good performance in predicting the SOC but with the shortcomings of the complex model,
a longer calculation time, a high number of parameters, and a larger memory space. There-
fore, the optimization can be carried out using the GRU model instead of the LSTM
Energies 2022, 15, 8003 17 of 27

models, as it achieved almost the same training error as the CNN Bi-LSTM model. The
test results of the GRU model are presented in Table 5.

Table 5. Test results of the GRU model.

Temperature Number of Test RMSE Max Error

Required Time (s) MAE (%)
(°C) Data (%) (%)
−10 39,293 5.15 1.17 1.58 8.34
0 42,530 5.13 0.76 1.05 7.13
10 44,284 5.11 1.19 2.00 10.36
25 47,517 5.71 0.94 1.48 10.12
Average 1.02 1.53 8.99

The average MAE and RMSE of the GRU model, based on the four ambient temper-
ature data, were found as 1.02% and 1.53%, respectively. Though a smaller training error
was found in the GRU model, the test results were poorer than the LSTM models. Some
sort of over fitting was observed in the test results of the GRU model, but the testing time
was smaller due to it being a lightweight model.
From Table 5, the GRU model performed well at 0 °C and the highest errors were
found at 10 °C. The absolute error results on the test data at −10 °C can be observed in
Figure 13a. Overall, the GRU model could not predict the SOC as correctly as the LSTM
based models, but the complexity and testing times of the model were reduced with a
reduction of the trainable parameters. When the GRU model was compared to a similar
type, such as the LSTM model, which showed a 0.2% less MAE than the GRU model be-
cause the LSTM model performed better with large datasets. The absolute error graph of
the GRU model on the test data at −10 °C (Figure 13b) showed that the max error of 8.34%
was present only at one point, while at other points, all absolute error values were below
6%.

(a)
Energies 2022, 15, 8003 18 of 27

(b)
Figure 13. Performance of the GRU model at −10 °C (a) measured and predicted SOC values and (b)
absolute errors from the test data.

4.2.5. Training and Test Results of the Hybrid CNN-GRU-LSTM Network

In order to take advantage of the best functional features of the individual models, a
hybrid CNN-GRU-LSTM network was proposed. For reaching the optimized point, the
GRU layer reduced the complexity and the LSTM layer made the necessary steps to obtain
a better result in the large dataset. Moreover, the CNN layer carried out the feature ex-
traction task very well.
Upon the completion of 15 epoch runs, a MAE of 0.82% was achieved with the total
trainable parameters of 925,313 in the hybrid CNN-GRU-LSTM network. It was very light-
weight, compared to the other four models, due to the one GRU layer and the one LSTM
layer, while the other models have three LSTM or GRU layers. Other LSTM-based models
had 512 units in every layer, in contrast to the 64 units in the hybrid model. Though it had
a smaller number of parameters, it showed a better training performance than the other
four models, with least amount of training time (53 min and 22 s). The MAE and the train-
ing time were both improved in this hybrid model. The test results for the hybrid model
are given in Table 6.

Table 6. Test Results of the hybrid CNN-GRU-LSTM model.

Temperature Number of Max Error

Required Time (s) MAE (%) RMSE (%)
(°C) Test Data (%)
−10 39,293 5.15 0.86 1.30 5.70
0 42,530 5.16 0.61 1.00 4.80
10 44,284 4.31 0.90 1.62 11.50
25 47,517 5.01 0.63 1.00 9.80
Average 0.75 1.23 7.95

The average MAE and RMSE of the hybrid CNN-GRU-LSTM model, based on the
four ambient temperature data, were recorded as 0.75% and 1.23%, respectively, which
were similar to the LSTM based models but better than the GRU model with a smaller
number of layers and units. The test results and the absolute errors of the hybrid CNN-
GRU-LSTM model on the test data of −10 °C can be observed in Figure 14a and Figure
14b, respectively. The model performed best at 25 °C and worst at 10 °C.
Energies 2022, 15, 8003 19 of 27

(a)

(b)
Figure 14. Performance of the hybrid CNN-GRU-LSTM model at −10 °C (a) measured and predicted
SOC values and (b) absolute errors from the test data.

4.2.6. Comparative Analysis among the Five Models

It is highly important to choose an optimized model for the SOC of a lithium-ion
battery management system, which will be governed by model error, prediction time, and
number of trainable parameters. A higher error obviously reduces the prediction accu-
racy, which is undesirable. As well, as the SOC is used in the battery energy management
of an electric vehicle, a longer prediction time to calculate the SOC would slow down the
BMS response. Furthermore, a higher number of trainable parameters would increase the
size of the model and hence the memory requirement.
All of the five models tested in this work, performed quite well, hence it is challeng-
ing to select the best model, as almost every model performed better than the others with
the test data obtained at any particular temperature. A comparison was made with the
overall error, prediction time, and number of trainable parameters, and presented in Fig-
ures 15 and 16.
Energies 2022, 15, 8003 20 of 27

MAE RMSE

1.8
1.6
1.4
Error 1.2
1
0.8
0.6
0.4
0.2
0
LSTM CNN-LSTM CNN Bi-LSTM GRU CNN-GRU-LSTM

Models

Figure 15. MAE and the RMSE of the five RNN models.

It was clear from the graphs that the CNN Bi-LSTM determined the SOC most cor-
rectly, but its prediction time and number of trainable parameters were the highest among
the tested models. However, the hybrid CNN-GRU-LSTM showed almost the same errors
as the CNN-LSTM model, but its prediction time and number of trainable parameters
were either equal to or smaller than the other models. Therefore, the hybrid model could
be considered as the optimum one among the five models tested.

Processing time Number of Trainable Parameters

Number of trainable parameters (Millions)

90 25

80

70 20
Processing time (sec)

60
15
50

40
10
30

20 5
10

0 0
LSTM CNN-LSTM CNN Bi-LSTM GRU CNN-GRU-LSTM
Models
Figure 16. Comparison of the models with respect to the processing time and trainable parame-
ters.
Energies 2022, 15, 8003 21 of 27

4.3. Training with the Data of the Four Ambient Temperatures Separately
It is also important to train the optimum hybrid model with separate temperature
data, to determine its performance. Following the training with the separate temperature
data, the training MEAs were found as 0.42%, 0.46%, 0.38%, and 0.35%, for −10 °C, 0 °C,10
°C, and 25 °C, respectively, where the 0.82% training MAE was found while training with
all of the temperature data altogether. Therefore, it can be concluded that if the models
are developed with the data obtained at the different ambient temperatures separately,
the error can be reduced.
Following the training, the model was tested with the test data and the results are
shown in Table 7 and Figure 17. The best performance was obtained for the model devel-
oped with the data at 25 °C. The higher error at 0 °C could be due to an increase in the
battery’s internal resistance [14].

Table 7. The test result when the CNN-GRU-LSTM model is trained using separate temperature
data.

Temperature (°C) MAE (%) RMSE (%) Max Error (%)

−10 0.64 0.97 6.25
0 1.30 1.50 5.80
10 0.65 1.10 7.60
25 0.41 0.61 4.20

MAE RMSE
1.6
1.4
1.2
1
Error

0.8
0.6
0.4
0.2
0
-10 0 10 25
Temperature (oC)

Figure 17. MAE and the RMSE of the CNN-GRU-LSTM model in the four different temperatures.

4.4. Comparative Analysis with the State-of-the-Art (SOTA) Models

The hybrid CNN-GRU-LSTM model was also compared with other SOTA models,
reported in the literature, using the performance parameters including the MAE and
RMSE (Table 8). Chemali et al. [14] proposed a LSTM-RNN model that could predict the
SOC. However, this LSTM-RNN network had 1000 units in the hidden layer. They found
their best result while training their model with the fixed temperature data at 25 °C which
was 0.68% of the MAE. Chemali et al. [28] proposed a deep neural network (DNN) ap-
proach and obtained their best result of a 0.61% MAE at 0 °C. A Panasonic 2.9 Ah
NCR18650PF battery was used in these two proposals. Du et al. in [29] proposed an ex-
treme learning machine battery model, which can estimate the SOC under a maximum
error of 1.5%, when the test was performed with a Samsung 2.6 Ah battery. Meng et al.
[30] proposed an adaptive unscented Kalman filter with a support vector machine to cal-
culate the SOC using a Kokam 70 Ah battery, and achieved the SOC under a 2% MAE.
Energies 2022, 15, 8003 22 of 27

Maheshwari et al. [31] proposed the sunflower optimization algorithm extender Kalman
filter method and determined the SOC from 0.82% to 1.37%of the MAE on a LG 18650HG2
3 Ah dataset.
The hybrid CNN-GRU-LSTM model proposed in this work achieved only a 0.41%
MAE at a 25 °C ambient temperature, in contrast to the lowest error of a 0.61% MAE at 25
°C, found in the previous works. At −10 °C and 10 °C ambient temperatures, 0.64%, and
0.65% MAE errors were found, respectively. At 0 °C temperature, a 0.61% MAE was found
when the model was trained with the four temperature data altogether. Therefore, with
the 25 °C temperature data, the model performed best, which reduced by almost 0.2% the
MAE from the previous work. At −10 °C, 0 °C, and 10 °C, the performance was also better
than the previous studies and the proposed hybrid model was lightweight and less com-
plex than the others. For instance, even the best performing LSTM-RNN model [14] had
1000 hidden units in the hidden layers, compared to only 64 hidden units in the hybrid
model. Therefore, it can be concluded that the proposed hybrid model can outperform the
SOTA models.

Table 8. Comparative analysis for the five studies.

Temperature Ambient Lithium-Ion Battery

Type of Model MAE (%) Reference
Data Use Temp. (°C) Specification
0 2.088
Together 10 0.782
Panasonic 2.9 Ah
LSTM-RNN 25 0.774 [14]
NCR18650PF
10 0.807
Fixed
25 0.68%
−20 0.22
−10 1.4
Together 0 0.9 Panasonic 2.9 Ah
DNN [28]
10 1.9 NCR18650PF
25 1.1
Fixed 25 0.61
Extreme Learning
Together 25 <1.5 MAX Samsung 2.6 Ah [29]
Machine
Adaptive Unscented Kalman
Filter with Support Vector Together 25 to 42 <2.0 Kokam 70 Ah [30]
Machine
Sunflower Optimization Al- 10 1.24
LG 18650HG2
gorithm Extended Kalman N/A 25 0.82 [31]
3 Ah
Filter 40 1.37
−10 0.86
0 0.61
Together
10 0.90
25 0.63 LG18650HG2
Hybrid CNN-GRU-LSTM Current study
−10 0.64 3 Ah
0 1.30
Fixed
10 0.65
25 0.41

4.5. Explaining the Hybrid CNN-GRU-LSTM Model with the Explainable AI

4.5.1. Model Trained with the Four Ambient Temperature Data Altogether
The Python SHAP library was used to determine the feature importance. At first, the
model that was trained with the data altogether, was tested with SHAP and presented in
Energies 2022, 15, 8003 23 of 27

Figure 18, which revealed that, from the five inputs, the average voltage was the most
important input feature. The prediction of the SOC depends on the average voltage the
most and on the nonlinear behavior of the battery voltage. Since the average voltage is the
average of the voltages (the present voltage and the previous voltage values) of a moving
window, which is a statistical method to quickly identify the changes in the residual mean
value and standard deviation [32], it contains a lot of information on the previous condi-
tion of the SOC. It is the main requirement of the RNN, that the previous important input
and output, should be considered for the present output. Following the average voltage,
the present voltage is another important input feature. As the average voltage contains
information about the previous and present states altogether, the instantaneous voltage
information is also an important feature for the SOC estimation. Furthermore, the average
current containing the information on the present and previous loads on the battery, is
also important information for the SOC estimation. As the battery behavior changes with
the ambient temperature, its importance is shown in the SHAP chart. The instantaneous
current was shown to be a less important feature, as its impact was very low in the SOC
estimation. Therefore, the CNN-GRU-LSTM model could detect the input feature im-
portance from the dataset on the SOC estimation more correctly, based on SHAP values.

Figure 18. Feature importance of the hybrid CNN-GRU-LSTM model trained with the four temper-
ature data altogether.

4.5.2. Models Trained with Separately with the Four Ambient Temperature Data
The feature importance graph, based on the models trained on the four ambient tem-
peratures separately is shown in Figure 19. The top important features at all four temper-
atures, sequentially, were identified as average voltage, voltage, and average current,
though the value of the importance (SHAP value) were variable at different temperatures.
The least important features (current and battery temperature) altered their positions be-
tween 4th and 5th places. If the importance of temperature was observed, it was noticed
that the most impact was made on the model trained with the data of 10 °C. Therefore,
the temperature could be placed at the 4th position before the current, in terms of the
feature importance. However, in the other three models, the position of the feature im-
portance of the temperature was 5th, and current was 4th. The model trained with 25 °C
data showed temperature as the least important feature. The trained model with 0 °C and
−10 °C data, the temperature showed some importance as a feature.
Now, further analysis is required to understand the importance of the input features.
The models that were trained with the four temperature data altogether, the temperature
feature importance was high possibly due to the fact that the SOC behavior of the battery
was constantly changing with the change of temperature. However, when the model was
trained with the data of the four temperatures separately, the temperature was the least
Energies 2022, 15, 8003 24 of 27

important feature in three circumstances out of four. This could be explained by the fact
that, when the model was trained with the data of the same ambient temperature, the
battery behavior was remained constant.

(a) (b)

(c) (d)
Figure 19. Feature importance of the hybrid CNN-GRU-LSTM model trained with the data of (a)
−10 °C (b) 0 °C, (c) 10 °C and (d) 25 °C.

4.6. General Discussion

The diversity of battery advancements will increase, due to the high demand for EVs,
and as all types of batteries have distinct electrical and chemical constituents and func-
tionalities, this will create a great deal of instability and provide difficulties for a compre-
hensive SOC estimation.
The proposed hybrid CNN-GRU-LSTM battery model can estimate the SOC with a
very little amount of error, which is very helpful for the BMS of EVs because, the SOC is
very significant and critical information for the BMS and the EV driver. Since the proposed
battery model is very lightweight, it will consume a very small amount of memory in the
BMS and the SOC estimation time will be very short, which will help the BMS to respond
faster. Another feature of this work is the novel hybrid model of the LSTM and GRU lay-
ers, where two RNN layers have been used. The LSTM units are more accurate than the
GRU in the long dataset, but two LSTM layers would increase the complexity of the
model. Therefore, one LSTM layer and one GRU layer were used, which ensured both the
accuracy and lightweightedness of the model. The hybrid CNN-GRU-LSTM model can
estimate the SOC consuming less memory in the BMS, with the least calculation time and
the least amount of error, which are the key qualities of an ideal battery model for a BMS.
The existing studies focused on estimating the SOC but it is still unknown which
input features are more important in the SOC estimation. The determination of the input
feature importance is a novel and crucial aspect of this work, as it can add a new dimen-
sion to the development of the BMS. Since, the average voltage and voltage are the most
important input features, more precision while measuring the battery voltage will
Energies 2022, 15, 8003 25 of 27

enhance the BMS performance. Moreover, since the average voltage was measured using
the moving window method, an increment of the size of the moving window will boost
up the accuracy of the SOC. From the description of the dataset, the data (voltage, current,
and temperature) were collected at the sample rate of 1 Hz. From the input feature im-
portance bar chart, the voltage is a more important input feature than the current and
temperature. Therefore, the sample rate of the voltage can be increased, while implement-
ing the battery model to the BMS.

5. Conclusions
The study proposed a hybrid CNN-GRU-LSTM network to predict the SOC of lith-
ium-ion batteries in the most optimized way. A total of five RNN models (LSTM, CNN-
LSTM, CNN Bi-LSTM, GRU and CNN-GRU-LSTM) were built, trained, and tested to
identify the optimum model, by comparing the performance parameters, such as the error
values, prediction time, and number of trainable parameters. The SOC is very important
and vital information for the BMS and the EV driver, and the proposed model can estimate
it with a very small amount of error (best result: 0.41% MAE at 25 °C), which is very help-
ful for the BMS of the EVs. Two RNN layers were used in this model’s LSTM and GRU
layers. In the lengthy dataset, the LSTM units were more accurate than the GRU, but add-
ing two LSTM layers would make the model more complex. Therefore, one LSTM layer
and one GRU layer were used, guaranteeing the model’s accuracy and portability. The
hybrid CNN-GRU-LSTM model has the key characteristics of the perfect battery model
for a BMS as it can estimate the SOC while using less memory (11,170,968 bytes) in the
BMS, with the least amount of calculation time (0.000113 s/sample), and with the least
amount of error.
This hybrid CNN-GRU-LSTM model, demonstrated to be a robust tool for battery
management systems, as it estimated the SOC correctly, within the shortest amount of
time and consumed a small amount of memory in the BMS. When all of the temperature
data (−10 °C, 0 °C, 10 °C, and 25°C) were used together, the MAE ranged between 0.61%
to 0.90%. Furthermore, the MAE values were with the range of 0.41% to 1.3% when the
temperature data was used separately. The hybrid model used the least number of input
parameters (925,313) and consumed the least amount of processing time (training time
and testing time), when compared to the other models. The explainable AI has identified
the average voltage as the most influential parameter, in order to accurately estimate the
SOC. This brings a new dimension to effectively manage the EV battery system.
The hybrid model reduced the MAE by 0.20% over the existing best battery model,
with the least number of parameters, which outperforms the existing models. It produced
a 32.79% better accuracy than the existing models in the literature. The number of units
was also reduced in this hybrid model, compared to other existing work, as it made the
hybrid model more lightweight. In future, the most optimum model for determining the
State of Health (SoH) and State of Energy (SoE) will be proposed. Moreover, the BMS has
some special requirements for machine learning-based SOC computational methods. For
example, the BMS should have a powerful CPU/GPU for receiving a fast response. The
future task would be focused on reducing the computational burdens.

Author Contributions: Conceptualization, S.M.S. and E.A.B.; methodology, S.M.S., E.A.B., and
M.N.; validation, S.M.S., E.A.B., M.N., M.A., and J.H.; formal analysis, S.M.S., E.A.B., M.N., M.A.,
and J.H.; investigation, S.M.S., E.A.B., and M.N.; data curation, S.M.S., E.A.B., and M.N.; writing—
original draft preparation, S.M.S., E.A.B., M.N., M.A., and J.H.; writing—review and editing, S.M.S.,
E.A.B., M.N., M.A., and J.H.; visualization, S.M.S., E.A.B., M.A., and J.H.; supervision, M.N., M.A.,
and J.H. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Energies 2022, 15, 8003 26 of 27

Data Availability Statement: The data presented in this study are available in the article.
Acknowledgments: The authors would like to thank the team at the Manchester Met. University
and the University of York for supporting this research work and preparing the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.

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