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A Recurrent Neural Networks Approach for Estimating the Core Temperature in Lithium-Ion Batteries

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The safety and reliability of Lithium-ion batteries are increasingly critical, especially as more products on the market are powered by them. The core temperature of batteries is one of the important factors to consider when improving safety, longevity, and performance. To overcome the inability to practically obtain direct core temperature measurements, this paper proposes a neural network-based estimation method using a gated recurrent unit. This approach can estimate the core temperature to a high level of accuracy using commonly measured signals such as voltage, current, state of charge, ambient and surface temperatures. Experimental results demonstrate excellent estimation performances over cycling and between different batteries of the same type. The proposed method does not require a strenuous parameter tuning operation, model derivation and simplification, or a deep understanding of the electrochemical processes in the battery. It should be also highlighted that, compared to the other available options in literature, this technique has the advantage of easy implementation.
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Proceedings of the Canadian Society for Mechanical Engineering International Congress 2020
CSME Congress 2020
June 21-24, 2020, Charlottetown, PE, Canada
A Recurrent Neural Networks Approach for Estimating the Core Temperature
in Lithium-Ion Batteries
Olaoluwa Ojo1, Xianke Lin1*, Haoxiang Lang1, Youngki Kim2
1Department of Automotive, Mechanical and Manufacturing Engineering, Ontario Tech University, Oshawa, ON, Canada
2Department of Mechanical Engineering, University of Michigan Dearborn, Michigan, USA
Abstract The safety and reliability of Lithium-ion batteries
are increasingly critical, especially as more products on the
market are powered by them. The core temperature of batteries
is one of the important factors to consider when improving
safety, longevity, and performance. To overcome the inability
to practically obtain direct core temperature measurements, this
paper proposes a neural network-based estimation method
using a gated recurrent unit. This approach can estimate the core
temperature to a high level of accuracy using commonly
measured signals such as voltage, current, state of charge,
ambient and surface temperatures. Experimental results
demonstrate excellent estimation performances over cycling
and between different batteries of the same type. The proposed
method does not require a strenuous parameter tuning
operation, model derivation and simplification, or a deep
understanding of the electrochemical processes in the battery. It
should be also highlighted that, compared to the other available
options in literature, this technique has the advantage of easy
implementation.
Keywords- core temperature estimation, lithium-ion, recurrent
neural networks, GRU
I. INTRODUCTION
The modern awakening to the consequences of climate
change is causing an increase in demand for sustainable products
as seen with electric vehicles (EVs) and renewable energy
sources. The most popular energy storage system for this
application is the Lithium-ion (Li-ion) battery due to its
relatively higher specific power density and energy density
when compared to other chemistries [1, 2]. Li-ion batteries,
however, have drawbacks that depend on temperature.
Temperature outside the optimal operating range has been found
to affect battery safety, longevity [37] and performance [810].
The effects of operating a battery outside these limits could
develop into thermal runaway, reduction in capacity and cycle
life, as well as internal impedance variation. This poses a
problem with electric vehicles since they often require high
discharge or charge currents that generate heat.
In order to prevent these consequences, an accurate
observation of battery temperature is crucial. A popular method
of measuring battery temperature is with surface-mounted
temperature sensors such as thermocouples, thermistors, or
resistance temperature detectors (RTDs). The issue, however,
arises with the realization that the core temperature of a cell can
differ from the surface temperature at high C-rates [11] which
renders the surface temperature measurement imprecise to what
it actually is in the cell. This awareness has piqued interests and
attention in core temperature estimation and predictions. Some
attempts involve the use of adaptive observers [2, 1214] to
estimate the core temperature based on data and models.
Richardson et al proposed an electrothermal-based algorithm
that associates electrochemical impedance spectroscopy (EIS)
with surface temperature measurements for core temperature
estimation [15]. Other literatures have also proposed predicting
the temperature distribution with high fidelity models [16, 17].
Although these methods solve the problem of core temperature
estimation, they can be quite involved for researchers in the field
due to the intense parameter estimation requirement and
complexity of such an approach, as well as the need for an in-
depth understanding of electrochemistry.
This paper introduces an easy to implement neural network
approach that removes this barrier to entry, thereby, allowing
researchers and engineers alike to focus on improving safety and
reliability in Li-ion batteries and the products they power. The
proposed technique is a data-driven approach that uses a
recurrent neural network (RNN) known as the gated recurrent
unit (GRU). This neural network (NN) model receives
commonly measured battery signals such as current, voltage,
SOC, ambient and surface temperatures and delivers highly
accurate estimations of the core temperature in real time. The
use of the GRU for estimation does not involve any thermal
models, their derivations or simplification, nor does it require an
expertise in electrochemistry. Estimations are accomplished by
training the NN to learn the non-linear relationship between the
variables, and then testing the network on measurements from
processes like constant current constant voltage (CC-CV) cycles
or drive cycle current profiles. This NN approach is able to:
Accurately learn the non-linear thermal relationship
between the voltage, current, state of charge, surface
temperature and the core temperature
Maintain a high level of accuracy over cycling
Extend this estimation experience to other batteries of
the same form-factor and chemistry
To summarize the key contributions of this study, this
approach enables its users to easily set up and estimate core
temperature without an in-depth understanding of the intricacies
of the battery nor the need for model derivation, model
simplification or a strenuous parameter estimation process. It is
a neural network model able to learn the non-linear relationship
between a multivariate input and the core temperature. It has the
potential of scale since only one model needs to be trained with
data from one battery in a pack and beyond.
The remainder of this paper is organized as follow. First, we
introduce the neural network model for estimating core
temperature as well as the training process. Then, a detailed
description of the experiment set up and data collection process
is introduced. Next, several test cases are investigated, and the
results and observations are discussed. Finally, we conclude the
paper.
II. NEURAL NETWORK MODEL FOR CORE TEMPERATURE
ESTIMATION
A. The Gated Recurrent Unit (GRU)
Recurrent Neural Networks (RNNs) are a class of artificial
neural networks that are used for time-varying or sequential data
predictions. The main purpose of an RNN is to allow data to
persist, thereby recognizing patterns from past data and using
those patterns to make estimations or future predictions. An
RNN is a subset of the supervised learning family because of its
ability to learn the relationship between its inputs and the
required output(s). A supervised neural network learns this
relationship by minimizing a loss function with respect to the
model weights. Therefore, as the model learns, the loss decreases
towards a local or absolute minimum following a gradient and
updating the weights. Although a vanilla RNN is able to learn
these sequential relationships, it is unable to maintain
dependencies or intuitions with data further in the past. This
limitation is caused by two issues known as the exploding and
vanishing gradient problems [1820]. These problems occur
when training with the backpropagation through time (BPTT)
method. The exploding gradient drives the weights responsible
for reflecting long-term dependencies to oscillate, while the
vanishing gradient drives these same weights to a norm of zero
(not substantially changing with each new epoch), making
learning incredibly time-consuming or impossible. Gated
recurrent units and long short-term memory neural networks are
variations of the vanilla RNN because they solve the problem of
the exploding and vanishing gradients. They are, hence, better
suited for capturing long-term contexts. The similarity between
both is their ability to remember features from further in the past
without being affected by the gradient problems mentioned
earlier. This found immunity is due to their memory feature and
gates which allow them to easily control the flow of data from
the past. The difference between both, however, is that the GRU
trades off a better memory for faster training due to the reduced
number of weights. Unlike language translation, for example,
the superior memory of the LSTM over GRU is not as important
for core temperature estimation since the context needed for its
estimation need not extend as far into the past.
RNNs have seen rapid growth in research for predicting
sequential data. They can be found in natural language
processing, language translation, music compositions and many
more. RNNs are also experiencing growth in battery research.
Some applications are seen in the prediction of capacity fade [21,
22] and state of charge (SOC) estimation [23, 24]. These
examples are proof that this method is indeed accepted with
confidence in research.
The structure of the GRU neural network is shown in Figure
1. The GRU takes in a number of samples (n) that are
reformatted from the dataset. These samples are formed by
applying a sliding-window across the sequential data obtaining
one new datapoint in every sample. Each sample ( 
    ) is a matrix made up a number of timesteps
(m) consisting of previous and present voltage (
), current (
),
ambient temperature 
and the surface temperature (
)
inputs represented as column vectors by the arrows above the
terms. These inputs along with the previous hidden state or
previous output (). are used to estimate the current hidden
state () which is either sent to another GRU layer or a fully
connected layer as the output. The memory of the GRU layer is
kept in the hidden state and is propagated to subsequent
timesteps.
In a GRU layer, there are 2 gates: the update gate and the
reset gate. The gates are represented by the sigmoid function ().
These functions squash elements in vectors to a range between
0 and 1 thereby allowing or preventing data from flowing further
on. The update gate is responsible for updating entries in the
hidden state, it chooses what part of the hidden state to replace
with the new concatenated inputs. The reset gate is responsible
Figure 1. A GRU architecture unfolded in time
hk
hk-1
xk
tanh
Update Gate
Reset
Gate
hk
1
  
Vector
Concatenation
Element
-
wise
Addition
Element
-wise
Multiplication
Element
-
wise
Subtraction
for resetting or forgetting irrelevant features in the network. The
mechanics of a GRU cell can be described by the following set
of equations:
where r and z are the reset and update activations, while h and
are the hidden state and its candidates for each sample k. is
the set of weights for input () and is the set of weights for
the previous hidden state (), while the hyperparameter is
the bias applied to the results from each gate. The tanh function
is similar to the sigmoid activation function except it squashes
the vector element between -1 and +1. The neural network (NN)
model used in this paper uses two GRU layers and a fully-
connected layer that receives the hidden state of the last GRU
layer and reduces it to one neuron which becomes the estimated
core temperature () for that timestep. Two layers are used here
to allow the NN to easily extract some abstract relationships
among the inputs. The numbers of neurons for the two GRU
layers are 256 and 128 respectively. Figure 2 illustrates the NN
model layered next to each other.
III. DATA COLLECTION AND TEST CASES
A. Specifications and experiment Setup
Two 2.5Ah lithium iron phosphate (LiFePO4 or LFP) battery
cells from A123 (Batt-A and Batt-B) were chosen for this
experiment. The batteries were put through both driving cycle
current profiles and constant charge/discharge cycles. Data
acquisition was carried out on an in-house test system shown in
Figure 3(A). The test system recorded voltage, current, state of
charge, ambient temperature, surface temperature, and core
temperature data. Temperature measurement was accomplished
by attaching and inserting two T-type thermocouples onto the
surface and into a perforation created at the centre of the positive
terminal of the battery. The test equipment consisted of one
programmable power supply capable of 80V and 60A, an
electronic DC load capable of sinking up to 40A, voltage,
current, and temperature sensing units, a relay module for
switching between the power supply and the electronic load. A
computer is also included for control.
An illustration of the connection of the experimental set up is
presented in Figure 4.
B. Data collection process
Data collection for training and validation is comprised of
multiple cycles of constant charge and discharge while data for
testing was obtained from current profiles based on popular
driving cycles. The training data collection process starts with
charging the battery to maximum capacity, and waiting until the
core and surface temperatures converge ( ). A discharge-
charge cycle is then applied to bring the SOC from 100% to a
target SOC and back to 100%. After each charge and discharge
step, the battery is allowed to cool down until  . The target
SOCs differ in each cycle - they range from 10% to 90% in 10%
increments. This charge-discharge-cooldown cycle for all target
SOCs is regarded here as a set. Six sets are carried out for a
complete dataset. Each set is run at a different C-rate ranging
from 1C 6C.
The testing data is comprised of data collected from running
5 current profiles derived from the EUDC, HWFET, LA92,
UDDS, and US06 driving cycles. All profiles applied to the
battery are applied starting at 80% SOC and within 1C and 6C.
The data collection procedure for the testing data is similar to the
procedure for training and validation data collection. The battery
is initially charged to full, then discharged to 80% SOC, the
system waits to allow the core and surface temperature values to
converge then begins running the current profiles. Each profile
run is also followed by a cooldown period, and then a recharge
to 80% SOC. All five profiles begin at 80% SOC because EV
   
 
   
 
 
   
 
     
(1)
Figure 2. The neural network (NN) model
GRU
GRU
Figure 3. (A) Battery test system; (B) thermocouple placements
(B)
(A)
Surface
Thermocouple
Core
Thermocouple
Power Supply
Electronic Load
Relay Module
and
Microcontroller
Battery
Laptop
TC: thermocouple, MCU: microcontroller
Figure 4. Connection Diagram of the Battery Test System.
Power
Supply
Electronic
Load
Relay
Module
Relay
Control
Data &
Control
Data &
Control
Data &
Control
Temp
Data
Current
Sense
Vsense
(+ve)
Vsense
(-ve)
MCULi-ion Battery
Amb TC
TC
Module
manufacturers typically set a maximum of 80-90% SOC to
prolong battery life.
C. Training Process
The GRU neural network was trained on two Nvidia Tesla
P100 GPUs supplied through a cluster on the Compute Canada
(CC) system. The neural network was modelled on a python-
based neural networks library built on Tensorflow called Keras
for training and inference. A mean square error loss function
( 

 
 ) was used in conjunction with an
optimizer known as RMSprop that works on the following
principle:
where γ is the momentum term (recommended value of 0.9), η
is the learning rate (0.0001 in this study),
k is the gradient of
the loss function (MSE) with respect to the weights at time step
k, ϵ is a smoothing term that prevents division by zero,
is called the moving average of the squared gradient and
finally, θ is the set of hyperparameters including weights and
biases. The optimizer is what performs the training by
minimizing the loss.
As previously mentioned, each dataset imported into the NN is
sampled with a sliding window, 60 timesteps deep, where the
last timestep is the current timestep to be estimated. In order to
conserve memory, 128 batches of these samples were fed in
each time to the NN for training. The training dataset was split
into an 80%-20% grouping for the training and validation data
respectively. During inference (testing), however, a single
batch was fed in to induce real-time estimation. The neural
network was trained for 200 epochs during which a
contingency for overfitting was implemented simultaneously.
In order to prevent overfitting, the weights of the epoch with
least validation loss were saved and used.
D. Test Cases
1) Core temperature estimation performance: Since the goal
of this study is to accurately estimate the core temperature,
the first test case evaluates the performance of the network.
The neural network’s performance is quantified by the
maximum absolute error (MAE) and the maximum error
(MAX). After validating the performance on the test
dataset collected from Batt-A (dataset-A1), a number of
other test cases are considered to further prove the
capability of this approach.
2) Estimation performance over cycling: The test data and
result referred to earlier for Batt-A is used here as a
benchmark before cycling. Therefore, after collecting the
first iteration of the test dataset for Batt-A (dataset-A1) and
verifying it on the NN model, the result is compared to the
result after cycling. After dataset-A1, Batt-A is cycled 100
times at 10 A and then subjected to a second iteration of
data collection (dataset-A2). The ability of the NN model
to accurately estimate core temperature is then verified on
dataset-A2. In each iteration, a MAE of less than 0.1ºC is
expected.
3) Estimation performance on a second cell of the same type:
In this test case, a second battery (Batt-B) of the same type
and from the same manufacturer is tested. This battery is
also put through the same driving cycle current profiles and
the resulting test dataset is used on the NN model trained
on Batt-A. The purpose of this is to examine the
performance of a model trained once and used on other
cells of the same type in a battery pack.
IV. RESULTS AND DISCUSSION
A. Core temperature estimation performance
The neural network model based on the gated recurrent unit
(GRU) is trained on the training dataset from Batt-A. Training
and testing the network for 200 epochs lasted for less than 5
hours. The chosen number of epochs, as with many other NN
parameters, was an iterative process to ensure the best training
and validation losses without overfitting too long or requiring a
longer training duration. As mentioned earlier, the trained
model weights with the least validation loss were chosen in
order to enable the model to generalize well on unseen data.
Immediately after training the NN model, the model is used for
testing datasets one sample at a time (batch size = 1). The first
iteration of the test dataset from Batt-A (dataset-A1) is fed
through the NN model and the result is shown in Figure 6. In
the figure, the residual or absolute error is plotted first, while
the estimated and measured core temperatures are plotted
below. In this illustration, the NN model is able to produce a
MAE of 0.066ºC and MAX of 0.275ºC. The MAE attained here
outperforms the expected result of 0.1ºC which signifies that the
neural network was able to learn the relationship between the
inputs and the core temperature while maintaining its ability to
generalize on unseen data. The reason for the strong estimation
performance is due to the presence of the surface temperature.
The model is able to primarily take the current, SOC and surface
temperature and infer the core temperature from them. This is
what is meant when the model is said to have learned the
thermal relationship. Without the surface temperature, the NN
model will be unable to learn this thermal relationship.
B. Estimation performance after cycling
After training the neural network model on the training
dataset collected from Batt-A and testing the model on dataset-
A1, Batt-A was put through 100 cycles of charge-discharge
cycles. After cycling, another test dataset was gathered (dataset-
  
  
 
(2)
Figure 5. Batt-A train dataset
A2) and validated on the NN model. The resulting plot is shown
in Figure 7. The performance of the NN model on dataset-A2 is
very close to that on dataset-A1. The MAE and MAX values of
0.074ºC and 0.365ºC respectively are only a fraction less
accurate than those seen in the first test case despite 100 cycles
in-between them. Nevertheless, the result is within the expected
maximum absolute error (MAE) of 0.1ºC. The experimental
results demonstrate the performance of the NN model over
cycling.
A way to potentially improve the capability of the model to
accurately estimate the core temperature irrespective of the
cycle life spent is to include the dataset from cycling during
training, in other words, using both the regular training data and
the data from cycling 100 or more times to train the model. This
will enable the model to learn the long-term relationship
between the change in voltage and core temperature. Therefore,
as the impedance of the battery increases with longer cycles,
and the voltage variation changes, the model is able to adapt and
accurately estimate core temperature.
C. Estimation performance on a second battery of the same
type
The purpose of this subsection is to test the capability of the
model on other batteries of the same type. Successfully
accomplishing this means that data from only one battery is
needed to train the model in practice. To test this hypothesis,
data collected from Batt-B is put through the NN model trained
earlier (on data from Batt-A). The result is shown in Figure 8.
It is evident from the plot that the NN model is still able to
accurately estimate the core temperature of another battery
achieving a MAE of 0.063ºC and MAX of 0.297ºC. This
outcome confirms the ability of the NN model to generalize,
thereby performing well on different datasets. The good
performance is, however, limited to datasets from batteries of
the same type. The reason for this is the similar elements
batteries of the same type share such as dimensions, materials,
assembly, and manufacturing process. These physical attributes
add to the thermal properties of the batteries such as heat
capacity, therefore, enabling them to consistently produce
similar temperature curves given the same input.
In light of this, the NN approach has the potential to be
scaled to battery modules and packs provided they are of the
same type and supply the required data needed for inference. To
implement on other battery chemistries or formfactors, it would
be more appropriate to train the network on data from the new
battery type.
V. CONCLUSION
The temperature of lithium-ion batteries is a critical factor
affecting the safety and reliability in battery-powered devices.
Since the internal or core temperature of a lithium-ion battery is
often higher than that of the surface, the accurate estimation of
core temperature is essential in battery management. This paper
proposes a solution that uses a neural network model based on
the gated recurrent unit to make precise estimations of the core
temperature. This data-driven approach has the advantage of
easy implementation because it does not involve any model
derivation, reduction, or a strenuous parameter tuning
operation, as demonstrated by experimental results. The neural
network model showed the ability to learn the relationship
between the surface and core temperature as well as the impact
of the voltage, current, SOC and ambient temperature on its
estimations. The neural network model was also found to
perform well over cycling as well as on other batteries of the
same type and build. This simple but effective structure
highlights the possible extension of the proposed model to
battery modules (and even packs). The results from these test
cases are proof of the capability and viability of this method in
research and production.
VI. FUTURE WORK
Although the neural network has a strong ability to estimate
the core temperature of a lithium-ion cell, there are areas of
improvement that will be explored in future work. One of which
is the increased robustness to cycling over the entire life of a
battery. One possible solution mentioned in the paper is to train
Figure 6. Core estimation result trained and tested on Batt-A
Figure 7. Batt-A core estimation result after 100 cycles
Figure 8. Estimation result trained on Batt-A and tested on Batt-B
the model on both the data allocated for training and the data
collected during cycling. Training the model with these two will
possibly help the model learn the relationship between voltage
and core temperature better. Another possibility is to train and
save multiple models based on the number of cycles exhausted
by the battery. Hence, as the battery operated in practice is
cycled, a model that has been trained for its specific cycle range
is used. Another area of improvement is to test the NN model
in different harsh environments such as hot and frigid
conditions as well as a scaled-up test with multiple batteries in
a battery pack.
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... For battery temperature prediction, a combined fully connected neural network (FCN) and long short-term memory (LSTM) was implemented to estimate the battery surface temperature [31]. Also, LSTM alone was applied to estimate the core battery temperature [32]. The datadriven methods presented in the literature showed high prediction accuracy and reduced computation power during the prediction compared to other numerical methods. ...
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