1. Introduction
The rapid growth in demand for electric vehicles has increased the need for lithium
batteries, which are indispensable for energy storage in applications ranging from
electric vehicles (Evs) to portable electronics, owing to their high energy density,
long cycle life, and lightweight design. Thermal management remains a crucial challenge
because poor temperature control can lead to battery degradation, reduced efficiency,
and safety risks, such as thermal runaway [1]. Traditional methods of cooling such as air cooling, water cooling, heat pipes cooling
etc. In addition to conventional methods of cooling, phase change materials have emerged
as an effective solution for thermal regulation in lithium-ion batteries. For instance,
research conducted by Shin et al. [2,3,4] with PCM (Phase Change Materials) integration in lithium polymer pouch batteries
significantly improves heat dissipation, especially in high-temperature environments
with design of neural network. Their work also introduced novel designs for battery
packs with passive thermal management systems for electric vehicles [5], showcasing improvements in battery thermal performance and longevity.
As a result, significant efforts have been made to develop predictive and management
systems for battery temperature to ensure safe and optimal performance. the lack of
images [3]. Numerous studies have been contributed on thermal behavior in LIBs. Panchal et al.
[6] modeled and validated the temperature distributions in prismatic lithium-ion batteries,
investigating the effects of different discharge rates and boundary conditions. This
study highlighted the importance of precise thermal modeling to prevent excessive
heat buildup. Simultaneously, advanced machine learning techniques have emerged to
predict battery thermal management, enhancing thermal performance and providing high
protection and fast and accurate prediction. Jaliliantabar et al. [7] employed artificial neural networks to predict battery temperature across various
operating conditions, demonstrating the effectiveness of machine learning in temperature
prediction. These findings underscore the importance of developing accurate thermal
prediction models for safe and efficient battery operation.
Deep learning techniques, particularly long short-term memory (LSTM) networks introduced
by Yetik O et al. [8], proven effective for time-series data analysis and have been applied in battery
temperature prediction. LSTM models are capable of capturing dynamic changes in battery
temperature during charge and discharge cycles, as shown by Zhu et al. [9], conducted a data-driven analysis of thermal effects in lithium-ion batteries. Additionally,
Kleiner et al. [10] used artificial neural networks to predict core temperature in automotive lithium-ion
batteries in real time, further supporting the role of AI in enhancing battery management
systems. A variety of machine learning models have been applied to predict and optimize
battery parameters, such as the state of charge (SOC) and aging estimation. Talluri
et al. [11] used the k-nearest neighbors (kNN) algorithm to estimate the SOC of lithium-ion batteries,
and Shin et al. [12,13] developed a backpropagation neural network for estimating battery aging. Many learning
algorithms conducted studies on battery thermal management, but there still exists
research gap in the study of lithium polymer pouch battery thermal response has not
been studied at three conditions and the prediction of thermal response of the battery
with machine learning methods are not full filled. Hence in this study addressing
various aspects of battery management on lithium polymer pouch battery.
In this study, experiments were initially conducted on lithium polymer pouch batteries
at three temperature conditions such as $25^\circ$C, $50^\circ$C, and $-10^\circ$C,
to evaluate the thermal responses of the batteries.
1. The key thermal metrics such as battery maximum temperature $T_{\max}$ and temperature
gradient $\Delta T$ were measured at $25^\circ$C, $50^\circ$C, and $-10^\circ$C.
2. Hot soaking and cold soaking experiments were conducted for the first time to evaluate
the most effective PCM for long-term battery protection, even at high temperatures.
3. Following the experimental phase, the data collected was used to train two models
individually: LSTM and random forest (RF) model were trained to predict $T_{\max}$
and $\Delta T$.
4. The performance of both models was compared based on root mean square error (RMSE),
mean absolute error (MAE) and accuracy in terms of percentages. These metrics determine
machine learning method provided more reliable predictions for battery thermal management
under varying conditions.
The rest of this paper is organized as follows. The next section describes analysis
of PCMs for battery thermal management . In the next section we proposed the neural
network aging algorithm for battery thermal management followed by the aging training
model. In the next section the experimental results and discussion with the neural
network performances.
2. Analysis of PCMs for battery thermal management
The battery thermal management system (BTMS) utilizes PCMs to absorb excess heat generated
by the battery during discharge, ensuring that the battery operates within safe temperature
limits. The system provides protection during extreme cold weather conditions. These
dual benefits of the BTMS are illustrated in Fig. 1.
Fig. 1. Battery thermal management with PCM.
Fig. 2 illustrates the main principle of the PCM operation. When the temperature reaches
the melting point during hot conditions, the PCM absorbs excess heat through the process
of melting, thereby cooling the battery. Conversely, in the cold conditions, the PCM
solidifies, releasing stored heat to protect the battery. For better evaluation of
the PCM properties at hot and cold conditions soaking tests were conducted.
Fig. 2. PCM melting & solidification process.
Fig. 3. demonstrates the cyclic process of energy absorption and release by PCMs. At low
temperatures, the PCM is in a solid state and is ready to absorb heat. When the temperature
increases, the PCM absorbs energy and melts, storing heat. When temperatures drop,
the PCM solidifies and releases the stored heat. This characteristic makes PCMs highly
effective for thermal management in various applications, such as insulation, temperature
stabilization in electronics, and energy-efficient building materials. We also proposed
the novel approach of hot soaking and cold soaking for the first time in order to
evaluate the best PCM to that will protect the battery for long time in high and low
temperature conditions.
Fig. 3. PCM phase transitions at different & temperature.
Hot soaking test: The pouch battery is exposed to temperature of $50^\circ$C and this
process is known as hot soaking. During this hot soaking phase, discharge was conducted
after battery reaching to $50^\circ$C and the changes in both PCM and battery temperatures
were monitored.
Cool soaking test: Similarly, the pouch battery is exposed to temperature of $-10^\circ$C
and this process is known as cold soaking. The pouch battery was tested after reaching
a temperature of $-10^\circ$C and changes in both PCM and battery temperatures were
monitored.
During hot soaking the phase transition temperature of expanded graphite PCMs was
assessed under high ambient conditions to study their melting and solidification behavior
depicted in Fig. 4. Hot water at $50^\circ$C was circulated initially to melt the PCMs, followed by
natural cooling. Heat transfer analysis for EG PCMs with phase transition temperatures
of $26^\circ$C and $28^\circ$C revealed distinct responses as follows: EG28 reached
$45^\circ$C, holding steady from $35^\circ$C to $50^\circ$C, then released stored
heat gradually during solidification. Similarly, EG26 reached to $42^\circ$C, maintaining
a stable phase from $39^\circ$C to $50^\circ$C before cooling down.
Fig. 4. PCM transition curve at high temperatures.
The physical model of the lithium polymer pouch battery consists of a separator, electrode,
and anode. During charging and discharging, the movement of electrons increases, resulting
in heat generation within the battery. This heat accumulates as excess thermal energy.
Therefore, an effective BTMS must be designed to dissipate this excess heat.
The heat balance equation in the battery for the proposed system is shown below, accounting
for the heat generation from the battery:
The heat generated by the battery during its charging and discharging cycles is expressed
in Eq. (1). The left term Qgen represents the heat generated within the battery due to chemical
reactions. $I$ is the current passing through the system, $U$ is the open circuit
voltage, $V$ is the instantaneous voltage of the system during current flow, $T$ is
the absolute temperature of the system, $\partial U/\partial T$ is the temperature
coefficient of the open circuit voltage while the subsequent terms describe the heat
balance achieved through the PCM $Q_{\rm PCM}$ is the heat absorbed by the PCM and
$Q_{\rm loss}$ is the heat lost to the environment due to conduction and convection
[14]. The battery specifications are listed in Table 1.
Table 1. Battery specification for the experiment.
|
Parameters
|
Values
|
|
Cell type
|
Li-polymer pouch battery
|
|
Length of cell [mm]
|
135
|
|
Width of cell [mm]
|
225
|
|
Thickness of cell [mm]
|
6.9
|
|
Module Nominal Voltage [V]
|
12
|
|
Cell current [A]
|
15
|
|
Specific heat of cell[j/kg-k]
|
1025
|
|
Battery connection
|
3S1P
|
|
Power [kw]
|
0.5
|
The PCMs were purchased from the Rubitherm technologies (GmbH in Berlin, Germany)
and SGL company (Limburg, Germany). These are the commercial PCMs consists of the
mixture of hydrocarbons derived from the petroleum based of melting and solidifying
points. Table 2 represents the PCMs thermal properties that considered during the experiment condition
[15].
Table 2. Thermal properties of PCM.
|
Type
|
PCMs
|
|
RT15
|
RT31
|
EG5
|
EG26
|
EG28
|
|
Melting
Point (℃)
|
15
|
31
|
5
|
26
|
28
|
|
Specific heat
(kJ/kg K)
|
1.89
|
1.99
|
2.19
|
2.19
|
2.59
|
|
Density
(kg/m3)
|
889
|
889
|
599
|
811
|
815
|
|
Thermal conductivity
(W/Mk)
|
0.2
|
0.2
|
6.5
|
2.5
|
5.5
|
The governing heat energy equation can be expressed as in Eq. (2)
where $m_{\rm pcm}$: Mass of the PCM,
$c_{\rm pcm}$: Specific heat of the PCM,
$h_{\rm pcm}$: Heat transfer coefficient of PCM,
$T_{\rm b}$: Temperature of battery,
$T_{\rm pcm}$: Temperature of PCM,
$h_{\rm e}$: Environment heat transfer coefficient,
$T_{\rm a}$: Aluminum Temperature of battery,
$T_{\rm e}$: Environment Temperature of battery.
The phase change of the PCM at melting and solidification temperatures with its specific
heat expressed as a temperature dependent function. The heat capacity of the PCM cpcm,
is expressed as the sum of sensible cse and latent heat capacity cla and given in
Eq. (3) [18],
where $m$ and $K$ are the latent heat of fusion and the liquid fraction of the PCM.
3. Proposed neural network aging algorithm for battery thermal management
Temperature is a primary factor that negatively impacts battery performance; therefore,
effective thermal management is essential to keep the battery operating within safe
limits. Battery aging, which determines battery lifespan, is influenced by temperature
($T$), as described in [19].
where $k$: aging rate; $A$: exponential factor of battery materials, $E$: activation
energy (J/mol), $R$: universal gas constant (J/mol$\cdot$K), $T$: battery temperature
(K). As the temperature $T$ increases, the exponential term decreases, thus increase
$k$ and causes aging. In this section, machine learning algorithms are developed to
predict battery temperature. Subsequently, to ensure the battery remains within safe
temperature limits, appropriate PCMs were identified.
3.1 Method 1: LSTM Algorithm
Fig. 5 illustrates the internal structure of a LSTM cell, which is a type of recurrent neural
network (RNN) used to learn and retain long-term dependencies in time-series data.
The input represents the current data point in the time series. This could be temperature
data or other relevant features that are passed into the LSTM cell. The forget gate
($f_t$) is responsible for deciding which information from the previous cell state
($C_{t-1}$) should be discarded or kept as expressed in Eq. (7).
Fig. 5. LSTM Training process.
Input gate ($\sigma$ and $\tanh$): The input gate ($i_t$) controls how much new information
should be added to the cell state. It consists of two components as in Eqs. (8) and (9).
A sigmoid function ($\sigma$) decides which parts of the input are important. $b_c$
is the candidate cell update.
A tanh function squashes the input data into a range between $-1$ and $1$, creating
candidate values that could be added to the cell state. The input gate thus decides
which new information will update the cell state $C_t$.
Cell State Update: The cell state is the internal memory of the LSTM cell that retains
long-term dependencies. The previous cell state is multiplied by the forget gate output
to discard irrelevant information. Then, the candidate values from the input gate
are added to the updated cell state. This process ensures that important information
is retained while irrelevant data is discarded. The corresponding equation was expressed
in Eq. (10).
Output gate ($O_t$): The output gate decides what the LSTM cell's output will be based
on the updated cell state. The cell state is passed through a tanh function (which
scales it between $-1$ and $1$), and then the sigmoid function ($\sigma$) determines
which parts of the cell state will be output as the next hidden state ($h_t$) as
expressed in Eqs. (11) and (12). This hidden state is passed on to the next LSTM cell and can be used as a prediction.
where $W_o$ and $b_o$ are the weight matrix and bias for the output gate.
3.2 Method 2: RF Algorithm
The process begins by taking the original dataset temperature, voltage and the current
data and creating multiple random subsets of the training data. Each subset is used
to train an individual decision tree, allowing the model to capture different aspects
of the data. The idea is to reduce overfitting and improve generalization by introducing
entropy in the data that each tree as shown in Eq. (13).
For each subset of training data, a separate decision tree is built. These decision
trees are trained independently and make predictions based on their respective data.
In the context of temperature prediction, each tree learns different relationships
between input features such as ambient temperature, battery temperature at various
points, discharge rate and the target variable such as the predicted battery temperature.
Once the decision trees are trained, each tree makes its own prediction for the target
variable such as temperature. Decision Tree 1, Tree 2, and Tree 3 in the shown in
Fig. 6 are independent predictions for the battery temperature based on the new input data.
Fig. 6. RF method process.
The final step in the RF method is to aggregate the predictions from all the individual
trees. This is typically done by averaging the predictions of all trees. The idea
is that the collective wisdom of multiple trees provides a more accurate and robust
prediction than relying on any single tree, as each tree may capture different patterns
in the data.
For regression, the output is the average of all tree predictions as shown in Eq.
(14).
This proposed BTMS is shown in Fig. 7(a) battery module integrated with PCM for thermal management. The battery cells are
positioned at the center, with PCM layers placed on both sides to absorb and dissipate
heat.
During high temperatures, the PCMs absorb heat by melting, preventing overheating.
In cold conditions, the PCMs solidify and release stored heat, maintaining battery
performance. This passive thermal management system helps regulate temperature and
improve battery efficiency in electric vehicles.
4. Proposed Battery Aging Training
The two methods are the LSTM approach and the RF method. Both methods rely on data
collected from the battery, such as voltage, current, and temperature, and use predictive
models to estimate key parameters like the maximum temperature $T_{\max}$.
Generally, heat generation is expressed as sum of reversible and irreversible heat
generation term, and given as below, the irreversible heat source term is the difference
between voltage and open circuit voltage (OCV) while reversible heat source term is
the change of entropy change of OCV over given temperature.
where $O_{\rm ocv}$: Open circuit voltage,
$U_{\rm T}$: Terminal voltage,
$T_{\rm B}$: Temperature of the battery.
When cell is charged or discharged, the temperature of the cell varies, and accordingly
ion diffusion in solid are affected. The temperature of cell as energy Eq. (16) under isothermal condition is [17]:
where $\rho$: Density of the cell,
$C_{\rm p}$: Heat capacity of the cell,
$q_{\rm gen}$: Heat generation rate per unit volume.
The heat flux between cell and surrounding and expressed as in Eq. (17),
where $k$: Heat transfer coefficient,
$m$: Thickness of cell,
$T_{\rm e}$: Ambient temperature.
For small change in the battery the temperature increased and their effects will be
observed in the future work.
Fig. 7. Proposed Model1 LSTM layout for training.
4.1 Training model by LSTM model
In the LSTM method, the voltage, current, time, and temperature data collected from
the battery are processed through the LSTM network. The model predicts temperature
by learning the time-dependent patterns in the input data. As the data moves through
the LSTM cell's gates such as forget, input, and output gates, the model selectively
retains important past information and discards irrelevant data. The ability to capture
long-term dependencies allows the LSTM model to predict how the temperature evolves
over time as depicted in Fig. 7. Based on past temperature data and other input variables, the model predicts the
future maximum temperature $T_{\max}$. This method is highly effective in capturing
sequential trends, such as gradual increases or decreases in temperature over time,
ensuring that the predicted temperatures closely follow the actual battery behavior
over various cycles. The split data was train data is 80%, test data is 20%, batch
size of 32, Adam optimizer is used with the learning rate of 0.001, layers considered
are 50 units followed by the dense layer with 1 unit that gives the output as temperature.
4.2 Training model by RF model
In the RF method, the input data are voltage, current, time, and temperature used
to train multiple decision trees. Each decision tree learns different aspects of the
relationships between these inputs and the maximum temperature $T_{\max}$. Unlike
the LSTM method, which focuses on time sequences, the RF model relies on building
multiple independent decision trees that use subsets of the data as illustrated in
Fig. 8. To build the RF model the number of trees (estimators) estimators considered are
100 and the random state is 42.
Fig. 8. Proposed Model2 RF layout for training.
Each tree makes its own prediction of $T_{\max}$ based on the given inputs, and the
final predicted temperature is obtained by averaging the outputs of all the trees.
This ensemble approach improves robustness and reduces overfitting, resulting in accurate
predictions of $T_{\max}$ across different temperature conditions. RF captures complex
interactions between variables but does not account for time dependencies as the LSTM.
Fig. 9. Experiment setup for temperatures.
The key components of the setup include a discharge Unit, battery module & PCM, data
logger, and computer for data analysis. The experimental setup consists of a lithium
polymer pouch battery module integrated with various PCMs to manage temperature during
discharge as represented in Fig. 9. A DC resistor load bank simulates real-world discharge conditions, while thermal
sensors placed at five key points on the battery surface capture real-time temperature
data. This data is recorded by a data logger and processed by a computer, which runs
predictive models like LSTM and RF to analyze the battery's thermal performance. The
experimental procedure involves charging and discharging a lithium battery pack to
analyze thermal management aspects, including peak temperature $T_{\max}$ and $\Delta
T$. The following steps are as experiment procedure
Step 1: Battery charging: The lithium battery pack, consisting of three cells, is
charged to a voltage of 3.9~V using a constant current of 8 A, then allowed to rest
for one hour.
Step 2: Post-charging stabilization: After charging is complete, the entire battery
pack undergoes a stabilization period to ensure even temperature distribution.
Step 3: Discharge process: The battery pack is discharged to a cutoff voltage of 2.7
V using a constant current, simulating typical usage.
Step 4: Data collection: Voltage and current measurements are continuously recorded
during discharge and transmitted to a computer via sensors, capturing real-time data
on thermal behavior.
Step 5: Repetition and temperature monitoring: Steps (1) to (4) are repeated for each
cycle. During each cycle, $T_{\max}$ data is gathered, especially focusing on any
rapid temperature increases and corresponding thermal gradients.
Step 6: Data transmission for model training: The collected data is then fed into
LSTM and RF models for training, aimed at predicting thermal behavior.
Step 7: Model training and learning: The LSTM and RF models are trained on the data
to learn patterns related to $T_{\max}$ and $\Delta T$.
Step 8: Comparison and evaluation: The actual thermal gradients and $T_{\max}$ values
are compared against the model's predictions.
Error analysis: Metrics such as mean absolute error (MAE), root mean square error
(RMSE), and accuracy are used to assess prediction accuracy and identify any deviations
in temperature estimation. The accuracy of the predicted output is evaluated by calculating
the error between the predicted and actual temperature values. This is expressed as
the mean absolute error (MAE), defined as the average absolute difference between
the actual and predicted values, as shown in Eq. (18).
where $N$ is the sample number, $P_i$ is the value of predicted temperatures and $E_i$
is the exact temperature. In this paper, the above equation. The root mean square
deviation is expressed as in Eq. (19),
where $I$ is the variable, $s$ is the number of non-missing data points, $l_2$ is
actual observations and the $l_1$ is the estimated value.
5. Experimental Results and discussion
The results depicted in Fig. 10 represents the $T_{\max}$ of the battery with PCM and No PCM at $25^\circ$C, with
selected PCMs and evaluated $T_{\max}$ and also evaluated $\Delta T$. Table 6 represents the comprehensive comparison of PCMs manage temperature over time at $25^\circ$C.
According toFig. 11, the No PCM reaches the highest temperature of $37.0^\circ$C maximum temperature
shown in Table 6. In contrast, all PCMs effectively reduce the temperature rise. EG28, as depicted
in both the graph and table, is the most effective, maintaining a much lower maximum
temperature, reducing it by $\Delta T$ $8.1^\circ$C, reaching around $28.9^\circ$C.
EG26 temperature are recorded as $29.9^\circ$C and the $\Delta T$ is $7.1^\circ$C,
respectively.
Fig. 10. Comparison of $\pmb{T_{\max}}$ at $\pmb{25^\circ}$C.
Fig. 11. Comparison of $\pmb{T_{\max}}$ at $\pmb{50^\circ}$C.
Similarly, the RT15 and RT31 samples show moderate temperature control, with RT15
reducing the temperature by $\Delta T$ of $3.0^\circ$C and RT31 $\Delta T$ by $4.3^\circ$C.
The expanded graphite materials consistently show better thermal management, with
EG28 achieving the greatest reduction. Together, these results confirm that PCMs,
especially EG28, are effective in managing temperature increases under these conditions.
FromFig. 11, and Table 3, the hot soaking period is observed until 100 minutes and after that started to discharge
each battery pack. No PCM sample reaches a $T_{\max}$ of $50.7^\circ$C rapidly. Expanded
graphite PCMs significantly reduce this peak temperature, with EG28 showing the best
performance, reducing the temperature with the thermal gradient $\Delta T$ of $13.7^\circ$C
and $T_{\max}$ $37.0^\circ$C, followed closely by EG26, with $T_{\max}$ of $37.9^\circ$C
and $\Delta T$ is $12.8^\circ$C. RT15 and RT31 observed temperature of $T_{\rm max}$
as $45.9^\circ$C and $44.0^\circ$C with $\Delta T$ of $4.8^\circ$C and $6.7^\circ$C,
respectively.
Table 3. Temeprature of PCM at $\pmb{25^\circ}$C.
|
PCM
|
Tmax
|
DT
|
|
(°C)
|
(°C)
|
|
|
No PCM
|
37.0
|
-
|
|
|
RT15
|
34.5
|
3.0
|
|
|
RT31
|
32.7
|
4.3
|
|
|
EG5
|
31.1
|
5.9
|
|
|
EG26
|
29.9
|
7.1
|
|
|
EG28
|
28.9
|
8.1
|
|
The sample without PCM indicates $T_{\max}$ rises sharply and maintains the highest
temperature, while the PCMs keep the temperature significantly lower. EG28 $T_{\max}$,
as shown, maintains the lowest temperature throughout the discharge period, confirming
its superior thermal regulation properties.
Both the graph and table illustrate that EG28 and EG26 are the most effective in reducing
temperature, particularly during the discharge phase.Fig. 12, demonstrates the effectiveness of different PCMs at $-10^\circ$C. Cold soaking period
is observed until 80 minutes and then discharge of battery pack is started after reaching
each cell to $-10^\circ$C. The No PCM sample reaches the lowest temperature of $-3.21^\circ$C,
while PCMs significantly increase $T_{\max}$. The maximum temperature reached by each
PCMs surrounded batteries are $1.93^\circ$C, $0.85^\circ$C: $3.43^\circ$C, $3.34^\circ$C,
$4.29^\circ$C for RT15, RT31, EG5, EG26 and EG28. The data reveals that No PCM exhibited
the highest peak temperature, reaching $-3.21^\circ$C more rapidly.
Table 4. Temeprature of PCM at $\pmb{50^\circ}$C..
|
PCM
|
Tmax
|
DT
|
|
(°C)
|
(°C)
|
|
|
No PCM
|
50.7
|
-
|
|
|
RT15
|
45.9
|
4.8
|
|
|
RT31
|
44.0
|
6.7
|
|
|
EG5
|
44.2
|
6.5
|
|
|
EG26
|
37.9
|
12.8
|
|
|
EG28
|
37.0
|
13.7
|
|
Fig. 12. Comparison of $\pmb{T_{\max}}$ at $\pmb{-10^\circ}$C.
This indicates that the absence of a PCM results in poor thermal regulation and a
higher rise in temperature EG28 is the most effective, raising the temperature by
$7.51^\circ$C to $4.29^\circ$C, followed by EG5 and EG26 with similar performance.
The graph shows that PCM-treated samples maintain higher temperatures during both
cold soaking and discharge periods, with EG28 consistently providing the best thermal
retention. From Table 5, overall, EG28 offers the greatest temperature stability at $-10^\circ$C.
In contrast, EG28 achieved the lowest maximum temperature of $4.29^\circ$C, demonstrating
its superior thermal control properties.
Table 5. Temeprature of PCM at $\pmb{-10^\circ}$C..
|
PCM
|
Tmax
|
DT
|
|
(°C)
|
(°C)
|
|
|
No PCM
|
-3.21
|
-
|
|
|
RT15
|
1.93
|
5.15
|
|
|
RT31
|
0.85
|
4.06
|
|
|
EG5
|
3.43
|
6.65
|
|
|
EG26
|
3.34
|
6.56
|
|
|
EG28
|
4.29
|
7.51
|
|
5.1 Effect of temperature gradient at $\pmb{25^\circ}$C
Figs. 13(a)-13(e) represent, both the LSTM and RF models that used to predict the maximum temperature
$T_{\max}$ during the discharge cycle for different PCMs, including RT15, RT31, EG5,
EG26, and EG28.
Fig. 13. Comparison of $\pmb{T_{\max}}$ with Experiment at $\pmb{25^\circ}$C with
LSTM & RF models in battery during discharge (a) RT15, (b) RT31, (c) EG5, (d) EG26,
and (e) EG28.
The experimental results showed that the $\Delta T$ values for the battery are $2.4^\circ$C,
$3.6^\circ$C, $5.4^\circ$C, $6.4^\circ$C, and $7.5^\circ$C, respectively. LSTM predicted
results of $\Delta T$ temperatures are obtained as $2.39^\circ$C, $3.5^\circ$C, $5.3^\circ$C,
$6.2^\circ$C, and $7.2^\circ$C. RF predicted results of $\Delta T$ are $2.05^\circ$C,
$3.2^\circ$C, $5.2^\circ$C, $6.1^\circ$C, and $7.19^\circ$C.
5.2 Effect of temperature gradient at hot condition of $\pmb{50^\circ}$C
From Figs. 14(a)-14(e), the experimental results showed that the $\Delta T$ values for the battery are depicted
as $13.8^\circ$C, $16.9^\circ$C, $18.2^\circ$C, $19.6^\circ$C, and $20.8^\circ$C,
respectively. LSTM predicted results of $\Delta T$ temperatures are obtained as $12.54^\circ$C,
$15.6^\circ$C, $17.2^\circ$C, $18.7^\circ$C, and $19.5^\circ$C. RF predicted results
of $\Delta T$ are $13.9^\circ$C, $17.5^\circ$C, $19.5^\circ$C, $19.49^\circ$C, and
$19.3^\circ$C.
Fig. 14. Comparison of $\pmb{T_{\max}}$ with Experiment at $\pmb{50^\circ}$C with
LSTM & RF models in battery during discharge (a) RT15, (b) RT31, (c) EG5, (d) EG26,
and (e) EG28.
5.3 Effect of temperature gradient at cold condition of $\pmb{-10^\circ}$C
From Figs. 15(a)-15(e), the experimental results showed that the $\Delta T$ values for the battery are evaluated
as 6.2$^\circ$C, 5.2$^\circ$C, 6.2$^\circ$C, 7.0$^\circ$C and 10.0$^\circ$C respectively.
LSTM predicted results of $\Delta T$ temperatures are obtained as 5.9$^\circ$C, 5.1$^\circ$C,
5.9$^\circ$C, 6.9$^\circ$C and 9.9 C. RF predicted results of $\Delta T$ are 5.7$^\circ$C,
4.9$^\circ$C, 4.9$^\circ$C, 6.8$^\circ$C and 9.8$^\circ$C. The results depicts that
the LSTM predicted temperature gradients are having high accuracy when compared to
the RF predicted values.
Fig. 15. Comparison of $\pmb{T_{\max}}$ with Experiment at $\pmb{-10^\circ}$C with
LSTM & RF models in battery during discharge (a) RT15, (b) RT31, (c) EG5, (d) EG26,
and (e) EG28.
5.4 Performance comparison between LSTM and RF methods
LSTM predicts temperature based on time sequences by learning patterns over time.
RF predicts temperature by averaging the outputs of multiple trees, focusing on the
relationships between variables without considering time dependencies. Both methods
provide reliable predictions of $T_{\max}$, but LSTM yields better accuracy when compared
to the RF model. The performance comparison was explained in the following:
5.4.1 Analysis of normal temperature at $\pmb{25^\circ}$C
At normal operating conditions of 25$^\circ$C, the performance of the BTMS was
evaluated using both the LSTM and RF models. RT15, RT31, EG5, EG26, and EG28, PCMs
were tested and evaluated the key thermal parameters such as maximum temperature $T_{\max}$
and temperature gradient $\Delta T$ predicted by both models. In terms of PCM performance,
EG28 emerged as the best performing PCM at 25$^\circ$C, achieving the lowest RMSE
0.03 and MAE 0.23 with LSTM. This indicates that EG28 and EG26 are particularly effective
at maintaining thermal stability under normal temperature conditions, reducing temperature
fluctuations and improving overall battery performance.
5.4.2 Analysis of normal temperature at $\pmb{50^\circ}$C
In hot conditions battery temperature rises more rapidly, requiring efficient thermal
management. EG28, with the best thermal stability in hot conditions. By comparing
the performance, the EG28 shows the less RMSE and MAE of the LSTMs are observed as
032 and 0.22 and with the RF RMSE and MAE are obtained as 0.75 and 0.62. In this case
the temperature is not increasing rapidly with the expanded graphite PCMs and the
rubitherm phase change materials. Because RT15 and RT31 PCMs will melt fastly than
the EG PCMs due to the high thermal conductivity.
5.4.3 Analysis of normal temperature at $\pmb{-10^\circ}$C
In cold conditions $-10^\circ$C, thermal management focuses on maintaining battery
performance as the PCM solidifies, releasing stored heat. At the cold condition of
temperature $-10^\circ$C the PCM performance, EG28 PCM emerged as the best-performing
PCM at $25^\circ$C, achieving the lowest RMSE value of 1.53 and MAE value of 1.51
with LSTM. Similarly, the less performance is obtained with RF of 1.51 RMSE and MAE
is 1.08. This indicates that EG28 is particularly effective at maintaining thermal
stability under severe cold temperature conditions, reducing temperature fluctuations
and improving overall battery performance.
Although PCMs offer numerous advantages, their limited availability presents a minor
drawback.
5.5 Discussion between LSTM and RF Methods
Tables 6-8 compare the accuracy of LSTM and Random Forest methods at temperatures of 25$^\circ$C,
50$^\circ$C, and $-10^\circ$C. Overall, LSTM consistently shows slightly higher accuracy
than RF particularly at lower temperatures, with minimal differences across the different
PCMs and temperature conditions. In terms of accuracy, both methods show high performance,
with percentages ranging from 94% to 99%. LSTM consistently shows higher accuracy
than RF across most PCMs and temperature conditions. The overall performance is expressed
as the division of the Tpcm temperature recorded with the PCM and TNo pcm no PCM battery
temperature.
Table 6. Comparison of the perfomance at $\pmb{25^\circ}$C..
|
PCM
|
RMSE
|
MAE
|
|
LSTM
|
RF
|
LSTM
|
RF
|
|
|
RT15
|
0.2
|
0.4
|
0.17
|
0.3
|
|
|
RT31
|
0.2
|
0.3
|
0.26
|
0.21
|
|
|
EG5
|
0.1
|
0.3
|
0.25
|
0.12
|
|
|
EG26
|
0.3
|
0.2
|
0.18
|
0.19
|
|
|
EG28
|
0.03
|
0.2
|
0.23
|
0.19
|
|
Table 7. Comparison of the perfomance at $\pmb{50^\circ}$C..
|
PCM
|
RMSE
|
MAE
|
|
LSTM
|
RF
|
LSTM
|
RF
|
|
|
RT15
|
1.59
|
0.88
|
0.96
|
0.71
|
|
|
RT31
|
1.02
|
0.98
|
0.73
|
0.71
|
|
|
EG5
|
0.91
|
1.14
|
0.75
|
0.85
|
|
|
EG26
|
0.52
|
0.88
|
0.41
|
0.69
|
|
|
EG28
|
0.32
|
0.75
|
0.22
|
0.62
|
|
Table 8. Comparison of the perfomance at $\pmb{-10^\circ}$C..
|
PCM
|
RMSE
|
MAE
|
|
|
LSTM
|
RF
|
LSTM
|
RF
|
|
RT15
|
1.42
|
1.91
|
1.20
|
1.02
|
|
RT31
|
1.40
|
1.74
|
1.09
|
1.19
|
|
EG5
|
1.45
|
1.62
|
1.13
|
1.22
|
|
EG26
|
1.66
|
1.19
|
1.13
|
0.79
|
|
EG28
|
1.53
|
1.51
|
1.07
|
1.08
|
At 25$^\circ$C, LSTM achieves accuracies of 95% to 99%, generally outperforming RF,
which ranges from 93% to 97%. At 50$^\circ$C, LSTM accuracy ranges between 97% to
99%, while RF accuracy is slightly lower, varying from 95% to 98%. At $-10^\circ$C,
LSTM again shows a slight edge, with accuracies between 95% and 97%, compared to RF's
range of 94% to 96%. Overall, LSTM demonstrates superior accuracy compared to the
RF method across all temperatures and PCMs, highlighting its robustness for this application.
Table 9. Comparison of LSTM &RF methods.
|
PCM types
|
At 25°C
|
At 50°C
|
At-10°C
|
|
LSTM
(%)
|
RF
(%)
|
LSTM
(%)
|
RF
(%)
|
LSTM
(%)
|
RF
(%)
|
|
RT15
|
99
|
97
|
98
|
96
|
97
|
94
|
|
RT31
|
98
|
97
|
97
|
98
|
97
|
96
|
|
EG5
|
99
|
96
|
97
|
95
|
97
|
96
|
|
EG26
|
95
|
95
|
98
|
96
|
97
|
95
|
|
EG28
|
97
|
93
|
99
|
97
|
95
|
96
|
Fig. 16(a) illustrates the change in loss values for both the training and validation datasets
over 100 epochs. The loss metric here likely represents mean squared error (MSE) for
a regression task or categorical cross-entropy for a classification task.
Fig. 16. Training and validation accuracy over epochs.
As shown, the initial epochs experience a significant decrease in loss, indicating
rapid learning. After around 10 epochs, both training and validation loss stabilize
near zero, suggesting that the model has effectively learned the data pattern and
achieved low prediction error.Fig. 16(b) demonstrates the model's accuracy on the training and validation datasets across
100 epochs. The high accuracy on both datasets indicates that the model can make accurate
predictions, meeting the expected performance standards.
Fig. 17, represents the correlation heatmaps for the predictions made by the LSTM and RF
models. The correlation heatmaps indicate how well the models' predictions match the
actual data, with values close to 1.00 representing perfect correlation. The correlation
between the predicted values and actual values is 1.00 for both categories 0 and 1.
This indicates that the LSTM model perfectly predicted these values. The overall correlation
heatmap shows that the LSTM model has a strong ability to capture and predict the
relationships in the temperature data, whereas for the RF method the correlation values
are 1.00 for category 1 and 0.99 for category 0, indicating a very strong correlation
between predicted and actual values, though not as perfect as the LSTM model for category
0.
Fig. 17. Training and validation accuracy over epochs.
Despite this, the RF model still provides highly accurate predictions, performing
well when predicting temperature without relying on time-series data. The minor difference
between the two models is visible in category 0, where the correlation drops slightly
to 0.99, indicating a small degree of error. Recent studies [20,21,22] indicates that the proposed hybrid cooling system, combining PCM with liquid and
air cooling, achieves a $\Delta T$ of 2.9$^\circ$C, 3.8$^\circ$C, and 7.6$^\circ$C.
In comparison, the proposed approach achieves a significantly higher $\Delta T$ of
13.7$^\circ$C, even under similar conditions as those in the referenced studies.
6. Conclusion
In this study, we proposed a method for predicting the maximum temperature $T_{\max}$
of lithium polymer pouch batteries using machine learning models LSTM and RF integrated
with PCMs by performing the experiments at 25$^\circ$C, 50$^\circ$C, and $-10^\circ$C
to choose best PCM The following conclusions were drawn from this research:
1. EG28 proved to be the most effective PCM across all temperature conditions, consistently
maintaining the lowest $T_{\max}$, offering the best thermal regulation for battery
safety and efficiency, with a prediction accuracy of 99% using the LSTM model.
2. EG26 emerged as the second-best PCM, demonstrating strong heat absorption at high
temperatures and effective heat retention in cold environments, with a prediction
accuracy of 97% to 98%.
3. Both LSTM and Random Forest models were used for temperature prediction. The LSTM
model achieved slightly higher accuracy, with up to 99% accuracy in predicting $T_{\max}$,
while the RF model reached up to 97% accuracy.
4. The correlation heatmaps showed that the LSTM model achieved near-perfect predictions
1.00 correlation, while the RF model delivered highly accurate results with a correlation
of 0.99 for certain predictions.
5. The results demonstrated that machine learning models, especially RF, are reliable
tools for predicting battery temperature, ensuring safer and more efficient thermal
management systems.
In the future, further work could focus on integrating additional machine learning
algorithms or hybrid models to further optimize temperature predictions and thermal
management systems for various battery chemistries and conditions.
ACKNOWLEDGMENTS
This research was supported by the “Regional Innova- tion Strategy (RIS)” through
the National Research Foun- dation of Korea(NRF) funded by the Ministry of Education
(MOE)(2023RIS-007).
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Author
Seong Jun Yoon is a Ph.D student at Busan University of Foreign Studies, South
Korea. Also, he researched about battery thermal management with new medium called
phase change materials, and observed good result in that research. Her interested
area of research is thermal management in Electric Vehicle and Artificial Intelligence
Talluri Teressa received her Ph.D. degree from Busan University, Korea, in 2022.
Working as research assistant in KITECH, South Korea from 2022. She received her Master
degree in Thermal Engineering from Jawaharlal University, India. Worked as assistant
professor in KL university, India. Her research interests include hybrid autonomous
electric vehicles and electric vehicles.
Angani Amarnathvarma is a senior researcher in the Korea Institute of Industrial
Technology since 2021. He received his M.S, and Ph.D. degrees in Electronic Engineering
from the Busan University of Foreign Studies, Busan, Korea, in 2018 and 2021 respectively.
Between 2020and 2021, he worked as a managing director in the Korea electric mobile
company. His current research interested area includes the application of intelligent
control to robot systems, adaptive control and Deep learning with neural networks
on 4WS steering wheel.
Hee Tae Chung is a Professor in the Department of Electronic and Robot Engineering,
in Busan University of Foreign Studies, Busan, Korea since 1997. He received his M.S.,
and Ph.D. degrees in Electronic Engineering from the Kyungpook National University,
Dague,Korea, in 1988 and 1996 respectively. Between 1996 and 1997, he worked as a
Patent Examiner in the Korean Industrial Property Office. His current research interested
area includes the application of intelligent control to robot systems, adaptive control
and Deep learning with neural networks.