Modeling Lithium-Ion Batteries Using Machine
Learning Algorithms for Mild-Hybrid Vehicle
Applications
1st Daniel Jerouschek
2nd Ömer Tan
Department of System Integration and Energy Management
IAV GmbH
Munich, Germany
daniel.jerouschek@iav.de
Department of System Integration and Energy Management
IAV GmbH
Munich, Germany
oemer.tan@iav.de
3rd Prof. Dr. Ralph Kennel
4th Dr. Ahmet Taskiran
Institute for Electrical Drive Systems and Power Electronics
Technical University Munich
Munich, Germany
ralph.kennel@tum.de
Department of System Integration and Energy Management
IAV GmbH
Munich, Germany
ahmet.taskiran@iav.de
Abstract—Voltage prediction in an automotive 48V-mildhybrid power supply system is safety relevant and an enabler for
a better efficiency. Due to the high power to energy ratio in these
power supply systems, an exact voltage prediction is challenging,
so a method to model the lithium ion batteries behavior via an
recurrent neural network is established. Therefore the raw data
is pre-processed with over- and undersampling, normalization
and sequentialization algorithms. With this data base the built
recurrent neural network models are trained and the hyperparametertuning is carried out by the optimization framework
optuna. This training methodology is performed with two battery
types. The validation shows a maximum error of 2.34 V for
the LTO battery and a maximum error of 3.39 V for the LFP
battery. The results demonstrate, that the proposed methodology
is performing in an appropriate error range to utilize it as a tool
to generate a battery model based on available data.
Index Terms—lithium-ion battery (LIB) long short-term memories (LSTM) machine learning (ML) modeling recurrent neural
net (RNN)
I. I NTRODUCTION
The European Union is regulating the CO2 emission for
2021 to a target of 95 g CO2 /km for new passenger cars.
[1] This target is quite challenging for the established original equipment manufacturers, so that the electrification of
the drive train is mandatory to reach this goal. Beside the
battery electric vehicles, with their drawbacks in infrastructure,
costs and range a hybridization of internal combustion engine
vehicles is a promising approach to reduce CO2 emissions. A
mild-hybrid vehicle with a 48 V power supply network is a
cheap and effective variant of electrification. [2] An electric
machine ensures energy recuperation during breaking, as well
a support of the internal combustion engine in acceleration and
load point fitting. Furthermore, belt driven consumers can be
electrified and run with the generated energy. The recuperated
energy has to be stored in an electric energy storage. Adding
extra components to the system is only reasonable if the
whole capability of each component is realized. Ensuring this,
a powerful battery-management system (BMS) with its key
functionalities of monitoring and state estimation is crucial. In
relation to the battery´s capacity the high applied powers lead
to the inference, that the power and voltage prediction is more
critical than the pure state-of-charge estimation. The system is
capable of remaining more frequently in the unlimited voltage
operation range with a better voltage prediction.
Modeling battery voltages can be divided into four categories: Analytical models, electrochemical models, equivalent
circuit models (ECM) and data-driven models. A previous
state-of-charge (SOC) estimation is obligatory for analytical
models and electrochemical models require accurate measurements and large computational costs, thus they are typically
excluded from industrial applications. For ECM precise measurements and a valid SOC model is required to gain models
with high accuracy [3]. Data-driven models are recent fequently discussed in literature. The results show that recurrent
neural networks like long short-term memories (LSTM) [4]
and gated recurrent units (GRU) [5] are more promising than
other approaches like fuzzy logic [6], feedforward neural nets
(NN) [7] and deep NN [8]. In an earlier paper the authors
demonstrated the feasibility of an accurate voltage prediction
for a 48 V battery pack without the utilization of a preceding
SOC estimation [9]. Furthermore, the scope of this paper is:
First, the proof of the applicability of recurrent neural networks
(RNN) models to any battery type and size. Second, to proof
that no expert knowledge is necessary due to the automated
data pre-processing and hyperparameter tuning.
The hereafter article is structured as follows: The process
of data preparation and pre-processing as well as the theory
of RNN are described in Section II. Section III outlines
the application of the previously mentioned pipeline on two
different battery samples. Thereafter, Section IV and V is
allocated to validation results and the conclusion.
II. P IPELINE
This section describes the executed data-pipeline for preparing and training a battery model independent of a specific
battery type.
A. Battery Samples and Data collection
The proposed modeling method is applied to two different
battery types, an LTO and an LFP Battery. The LTO battery
has a Lithium-titanate anode in combination with a nickel
manganese cobalt oxide cathode has a capacity of 11 Ah
and the maximum current is 350 A in charging as well as
in discharging direction. With 450 A maximum current and
a capacity of 20 Ah the LFP battery with its graphite anode
and lithium iron phosphate cathode is more powerful. The
two battery samples were tested in two different mild-hybrid
vehicle environments, whereby the impact to the battery is
only noticeable by the current profiles. In order to gain a valid
battery model with machine learning algorithms an extensive
preceding data collection is mandatory. The data used for
this approach are obtained from testing vehicle measurements
driven in customer-oriented conditions. The data provided by
the BMS is logged with a CAN bus measuring device with
a sampling rate of 10 Hz. With an overall data magnitude
of nearly 2.600 h of measurements for the LFP, and 5.500
h for the LTO battery, respectively a sufficient data set is
obtained. The temperature ranges between approximately 23°C and 60°C for both batteries. After pre-processing the
LTO data set has a volume of 1.028.918 points and the LFP
set has 1.641.058 points. Each set is split into a training and
validation data set with a ratio of ten to one. In contrast to this,
the test data is collected on a hardware-in-the-loop test bench
with a climate chamber, an electric source-sink and the battery
sample. Test-bench measurements benefit from the applicable
conditions, so that a wide temperature and power range can
be validated. The applied current-profiles were taken from the
corresponding vehicles.
B. Methodology for Data Pre-Processing
The logged raw data has to be pre-processed in several
steps to be usable to train a NN. These steps are reducing
the magnitude of data with a simultaneously approximation
of an unbiased feature distribution. Furthermore, the data has
to be prepared to be suitable for the NN.
1) Undersmapling: Undersampling is motivated by a reduction of training time per epoche and the possibility to learn
the behavior adequately. Large datasets require a lot of time
as every single date has to be processed through the entire
network. Data sets generated in a customer oriented way are
inherently unbalanced with regard to the operation strategy
as well to the climate conditions. Undersampling algorithms
are targeting to achieve an equal data distribution over the
relevant feature ranges by reducing the over-represented data.
The algorithm stops before too much data is cut off and a lack
of information occurs.
2) Oversampling: Non-generic measurement data typically
have a lack of data in extreme feature areas. The oversampling
algorithm detects these underrepresented spots and appends
generated data there. Generating data is done by adding artificial noise to the multiplied existing data in these spots, without
changing the basic correlation. This can be accomplished by
using the inertia to small changes of features like temperature
and state-of-charge.
3) Normalization: Due to the differences in the input
feature ranges a scaling of the ranges and values is carried
out. This normalization leads to numerical stability, a better
generalization and a faster training progress with higher learning rates. Equation 1 shows the min-max scaler applied to the
input data.
X̂[:, i] =
X[:, i] − min(X[:, i])
max(X[:, i]) − min(X[:, i])
(1)
Ioffe et al. [10] introduced the batch normalization, where the
normalization is applied to the activations between the neural
network layers in order to limit the covariate shift.
4) Sequentializing: Most of the effects influencing the voltage behavior of a battery depends largely on time. Modeling
these time dependencies with neural networks is achieved
by recurrent layers. Layers like RNN, GRU or LSTM use
sequential data as inputs to calculate the outputs. The sequence
length determines the past time range transferred to the net.
A trade off between short sequence length with the therefore
resulting worse prediction and longer sequence length with
worse training speed has to be figured out in consideration
of the specific application. In automotive 48 V power supply
systems largely volatile powers are conducted, so that a
sequence length of 12.8 s is sufficient.
C. Theory of RNN Utilization in Battery Models
The Battery behavior is characterized by its highly nonlinear time-dependency with time constants of several seconds.
This time dependency is again dependent of battery states like
the temperature and the SOC. A conventional feedforward
neural net is not meeting the challenge of modeling these
dependencies. For this purpose recurrent neural networks are
a good approach.
1) RNN-Layer: Recurrent neural network layers uses sequential data as inputs to calculate the output. The input in
form of xt with t as the time step are given in the right
order to an RNN cell. Each input is processed in the cell
to two outputs: One output is forwarded as the cell state Ct
to the next cell and one output is forwarded as the output
state ht to the next layer. The functioning of a RNN cell can
be seen in figure 1. The hidden layers are forwarding every
output step calculated by a single RNN cell to the next layer,
whereas the output layer only returns the last value of the
sequence as it represents the predicted value. Simple RNNs
use in the cell calculation only a tanh activation function to
calculate both states. Updating the weights proportional to the
partial derivative of the loss function could lead to a vanishing
gradient problem [11]. Therefore, long term dependencies can
not be modeled with conventional RNNs.
3) Dropout: Overfitting occurs, when a model learns the
input data including the noise too accurately. Dropouts prevent
NN from overfitting, by randomly dropping neurons during
the weight update process in training. The ratio of dropped
neurons in each iteration to total neurons is specified by
the dropout rate. This regularization method is introduced by
Srivastava et. al. [13]. Reducing the probability of overfitting
enables the possibility to train with higher learning rates and
therefore accelerating the training progress.
Fig. 1: Schematic structure of an RNN neuron.
2) LSTM-Layer: LSTM cells show great improvements
on modeling longer time dependencies than RNN, due to
less suffering from the vanishing gradient problem. LSTMs
were first introduced by Hochreiter et al. [12], the principal
architecture of an LSTM cell is shown in 2. Inside an LSTM
cell an extensive calculation takes place, resulting in two
different outputs. The input gate it , the output gate ot and the
forget gate ft are calculated with the previous hidden state
Ct−1 , the input vector and an activation function. W and U
describe the corresponding matrices, b the bias vector and σ
the activation function. These inner gates are affecting the cell
state Ct directly. The calculation of the hidden state vector
ht is performed with an activation function for the cell state
and the output gate. This hidden state ensures a storage of
information over a longer period of time without encountering
the vanishing gradient problem.
ft = σsig (Wf xt + Uf ht−1 + bf )
(2)
it = σsig (Wi xt + Ui ht−1 + bi )
(3)
ot = σsig (Wo xt + Uo ht−1 + bo )
ft = σtanh (WC xt + UC ht−1 + bc )
C
ft
ct = ft ct−1 + it C
(4)
ht = ot σtanh (ct )
(7)
(5)
(6)
(a)
(b)
Fig. 3: Schematic structure of a NN without (a) and with (b)
Dropout
D. Battery Modeling and RNN Hyperparameter Tuning
Fig. 2: Schematic structure of an LSTM cell.
Choosing the right input features as well as tuning the
hyperparameters have a high influence to training speed and
model accuracy.
1) Feature Selection: In literature modeling battery bahavior is performed using the terminal current, battery temperature, actual voltage and the SOC as input for ECMs as
well as for NN. The proposed approach uses only physical
measurable features as input to train the model. The SOC is
not an appropriate feature for input since it is just a predicted
state with no deterministic value in behind. The SOC delivers
the extra information about the current voltage level of the
battery, beside the overvoltages occuring during load. A more
direct way to detect the actual voltage level is the calculation
of Utrend . It is determined as the average of the last voltages
in this sequence and is updated after a certain period of time.
The update process is a method to reduce the exposure bias
problem in teacher forcing algorithms. The four input features
to predict the voltage for the next step are:
•
•
•
•
Terminal current It
Temperature Tt
Terminal voltage Ut
Voltage trend Utrend
2) Hyperparametertuning: Hyperparameters of neural networks have an effect on training speed and accuracy of the
model. To optimize the accuracy of a NN the hyperparameters
must be tuned. The grid search algorithms drawback is a
computational and time intense method, for what reason the
optuna algorithm is applied for hyperparameter tuning. Optuna
is a hyperparameter optimization framework based on bayesian
optimization algorithms. Optuna minimizes the given objective
function. In this approach the objective funciton is set to the
maximum absolute error on the test set. This metric shows
the modeling accuracy even in very hard to predict areas.
The tuneable hyperparameters have to be defined including
a range or a list of specific values. Each trial chooses the
hyperparameters based on the results of the previous trials
in view of the objective function. In case one trial is pretty
unpromising optunas successive halving pruner prunes a trial.
This pruner is a non-stochastic best arm identification method
initially introduced by Jamieson et al. [14]. This leads to an
efficient way to optimize the hyerparameters. Tuning every
hyperparameter in one single optuna study would be very
computational itense, due to the huge variable space. Table
I shows hyperparamters, which were tuned previously. This
predefinition is reasonable, as these parameters are independent from each other. The usage of LSTM layers and batch
normalization is justified in subsection II-C and in II-B,
respectively. A sequence length of 128 steps is a trade-off
between an extensive training time and a too short timedependency. The large training data set makes it necessary
to use bigger batch sizes to avoid overfitting. The learning
rate of 0.0002 is determined empirically, as well as the loss
function and the optimizer. The hyperparameters of figure
TABLE I: Pretuned hyperparameters for the LTO and LFP
model.
Hyperparameter
Type of RNN
Learning rate
Number of epochs
Batch size
Optimizer
Loss function
Sequence length
Batch normalization
Value
LSTM
0.0002
100
1024
Adam
MSE
128
On
II are tuned via the optuna hyperparamtertuning algortithm.
They have to be tuned in parallel, as they are influencing
each other directly. More hidden layers respectively neurons
demand higher dropout rates to prevent overfitting and vice
versa.
III. A PPLICATION OF P IPELINE TO BATTERIES AND
TARGETS
The created pipeline for data preparation and model tuning
is easily applicable to measurement data of different battery
types. Hereafter two applications were conducted to the battery
samples introduced in chapter II-A.
1) Training progress: Fig 4 shows the training progress
over epochs for both battery samples. The LTO sample takes
59 s training per epoche, whereas the LFP battery takes 95
s training per epoche, both trained on a NVIDIA RTX 2080
Ti GPU with 11 GB RAM using the TensorFlow backend.
The differences in training time arises from the different
architectures proposed from the optuna algorithm.
Fig. 4: Training progress for loss and validation loss of LTO
and LFP models
2) Proposed Model Architecture: The results of the applied
optuna algorithm is shown in table II. Comparing the two
architectures, the LTO chemistry has a smaller NN size with
only two hidden RNN layers and 79 neurons each, compared
to 105 neurons in each of the three RNN layers of the LFP
chemistry. This could be substantiated by the flat open-circuit
voltage (OCV) curve of LFP, where more sampling points
were needed. In contrast to the theory, that larger networks
need higher dropout rates, the LFP network is optimized to a
dropout rate of 0.16, compared to 0.4 at LTO. Two attached
dense layers seem to be suitable for both applications.
IV. VALIDATION U SING T EST-B ENCH M EASUREMENTS
Contrary to the training data set, the validation consists of
test bench measurements, with the advantage of the possibility
to condition and load the battery samples with extreme values.
The climate chamber is capable of temperatures in the whole
battery samples´ operating areas. Furthermore, an electrical
pre-conditioning is feasible, as well as a wide voltage and
TABLE II: Hyperparameters tuned by optuna algorithm for
the LTO and LFP model.
Hyperparameter
Units per layer
Number of LSTM layers
Number of dense layers
Dropout rate
LTO
79
2
2
0.4
LFP
105
3
2
0.16
current range coverage with a power supply and an electric
load. This ensures, that the models accuracy is also validated
in the hard-to-predict areas, where the battery samples has high
non-linear behavior of the OCV and the internal resistance.
The measurement procedure of a validation profile is as
follows:
•
•
•
•
(a)
Electrical conditioning to requested SOC
Thermal conditioning for at least 12 h
Apply current profile
Export measured data
The validation set of the LTO sample focuses on real-life
driving current profiles by using scaled measured currents
to reach the batteries´ current and voltage boundaries. The
temperature of the 12 profiles in the set ranges between 20°C and 50°C. The LFP validation set consists of ten profiles
and is focused on high-current peaks with extreme voltage
drops in both directions. Beside single current peaks of about
1 s, this validation set contains even of short volatile profiles.
A temperature range between -10°C and 25°C is reached in
this set. During training and inference the prediction takes
place only within one sequence, whereas in most applications
a prediction for a longer period of time is required. In this
section the influence of the actual predicted voltage to the next
step is investigated, as there is no teacher forcing algorithm
applied in this model. Small errors in the beginning could
lead to an instability of prediction. Figure 5 shows one
validation of the LTO model at -23°C in a low SOC area.
The error is not biased, so a prediction instability due to
the prediction feedback procedure is non-existent. The offset in the beginning is to be substantiated in the fact, that
the validation is conducted on one single battery sample,
whereas the modeling takes place on different batteries with
their individual properties due to differences in manufacturing
and ageing. The optimization algorithm is aligned to reduce
the maximum error in the validation set. This leads to a
different voltage drop shape between prediction and ground
truth. The electrochemical effects in the battery cell results in
an exponential voltage course. The predicted voltage is more
angular and has a small overshoot when the load stops. Beside
this effect, the biggest errors are occurring during the volatile
phase, as the overvoltages are hard to predict. In this validation
profile an MSE of 0.59 V² and an MaxError of 2.28 V is
reached, respectively an MSE of 0.53 V² and an MaxError of
2.34 V in the whole validation set.
Figure 6 shows one validation profile of the LFP model at
-10°C in a middle SOC range. The error does not increase
(b)
Fig. 5: Voltage (a) and Error (b) of a validation profile of the
LTO Batttery at -23°C and a low SOC.
dramatically after the current peak, so a prediction instability
due to the prediction feedback procedure is non-existent in
this model either. The LFP shows also a similar behavior like
the LTO in the voltage relaxation after the voltage peak. The
exponential decrease is not of the same shape as the ground
truth, but the extent of the voltage peak is predicted well.
Although the biggest error occurs during the voltage peak, it
is just an issue of shape and timing. Within the peak the error
crosses the zero point line but without reaching more than 0.37
V as a maximum Error. The off-set could be explained similar
to the one in the LFP model, as there are differences in every
battery sample. An overall MSE of 0.37 V² and an MaxErrror
of 3.39 V in the validation set can be determined.
A comparison between the two models shows that the LFP
model has a better MAE, but a worse MaxError. This may be
a result of the flat OCV curve of LFP battery cells in medium
SOC ranges. Altogether both models have similar accuracies.
V. C ONCLUSION
In this paper, a new battery voltage modeling method was
proposed, specifically without using the SOC as an input feature. Firstly, the raw data is prepared in a pipeline with under-,
oversampling, normalization and sequentialization algorithms.
Secondly, the RNN-LSTM model is built considering the
selected features. The training algorithm uses the optimization
framework optuna to find the optimum in the hyperparameter
TABLE III: Validation errors of the test set profiles.
Profile
LTO
LFP
MAE [V]
0.56
0.33
MaxError [V]
2.34
3.39
MSE [V2 ]
0.53
0.37
(a)
(b)
Fig. 6: Voltage (a) and Error (b) of a validation profile of the
LFP Batttery at 0°C and a medium SOC.
space.
All these steps are applicable to every type of lithium-ionbatteries, as the presented implementation for an LFP and
an LTO 48 V battery stack shows. The feature selection
enables real-time applications, since only physical measurable
parameters were used. The modeling accuracy is in the region
of 1% or between 0.33 V and 0.56 V. The maximum error
is below 7%, validated over a wide temperature and power
range. The recommended usage of the proposed algorithm can
be understood as a tool to generate a voltage battery model,
neither with the need for expert knowledge nor premodeling
the SOC. Future work could improve the model accuracy in
the edge feature regions as well as building up a transmission
from the voltage model to a power prediction model.
ACKNOWLEDGMENT
R EFERENCES
[1] European Comission, “Reducing co2 emissions from passenger cars
- before 2020,” 2021. [Online]. Available: https://ec.europa.eu/clima/
policies/transport/vehicles/cars en
Mean temp [°C]
15.6
4.7
Mean voltage [V]
44.9
45.5
[2] M. Schudeleit, C. Sieg, and F. Küçükay, “The potential of 48v hev in
real driving,” 2015.
[3] A. H. Ranjbar, A. Banaei, A. Khoobroo, and B. Fahimi, “Online
estimation of state of charge in li-ion batteries using impulse response
concept,” IEEE Transactions on Smart Grid, vol. 3, no. 1, pp. 360–367,
2012.
[4] A. Khalid, A. Sundararajan, I. Acharya, and A. I. Sarwat, “Prediction of
li-ion battery state of charge using multilayer perceptron and long shortterm memory models,” in 2019 IEEE Transportation Electrification
Conference and Expo (ITEC). IEEE, 19.06.2019 - 21.06.2019, pp.
1–6.
[5] C. Li, F. Xiao, and Y. Fan, “An approach to state of charge estimation
of lithium-ion batteries based on recurrent neural networks with gated
recurrent unit,” Energies, vol. 12, no. 9, p. 1592, 2019.
[6] X. Hu, S. E. Li, and Y. Yang, “Advanced machine learning approach
for lithium-ion battery state estimation in electric vehicles,” IEEE
Transactions on Transportation Electrification, vol. 2, no. 2, pp. 140–
149, 2016.
[7] M. Charkhgard and M. Farrokhi, “State-of-charge estimation for lithiumion batteries using neural networks and ekf,” IEEE Transactions on
Industrial Electronics, vol. 57, no. 12, pp. 4178–4187, 2010.
[8] E. Chemali, P. J. Kollmeyer, M. Preindl, and A. Emadi, “State-of-charge
estimation of li-ion batteries using deep neural networks: A machine
learning approach,” Journal of Power Sources, vol. 400, pp. 242–255,
2018.
[9] D. Jerouschek, Ö. Tan, R. Kennel, and A. Taskiran, “Data preparation
and training methodology for modeling lithium-ion batteries using a long
short-term memory neural network for mild-hybrid vehicle applications,”
Applied Sciences, vol. 10, no. 21, p. 7880, 2020.
[10] S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep
network training by reducing internal covariate shift.” [Online].
Available: http://arxiv.org/pdf/1502.03167v3
[11] I. Goodfellow, Y. Bengio, and A. Courville, Deep learning.
Cambridge, Massachusetts and London, England: MIT Press, 2016.
[Online]. Available: http://www.deeplearningbook.org/
[12] S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural
computation, vol. 9, no. 8, pp. 1735–1780, 1997.
[13] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever,
and Ruslan Salakhutdinov, “Dropout: A simple way to prevent
neural networks from overfitting,” Journal of Machine Learning
Research, vol. 15, no. 56, pp. 1929–1958, 2014. [Online]. Available:
http://jmlr.org/papers/v15/srivastava14a.html
[14] K. Jamieson and A. Talwalkar, “Non-stochastic best arm identification
and hyperparameter optimization.” [Online]. Available: https://arxiv.org/
pdf/1502.07943