Exploration of artificial neural network [ANN] to predict the electrochemical characteristics of lithium-ion cells

Article abstract of DOI:10.1016/j.electacta.2007.08.049

CoO anode, as an alternate to the carbonaceous anodes of lithium-ion cells has been prepared and investigated for electrochemical charge-discharge characteristics for about 50 cycles. Artificial neural networks (ANNs), which are useful in estimating battery performance, has been deployed for the first time to forecast and to verify the charge-discharge behavior of lithium-ion cells containing CoO anode for a total of 50 cycles. In this novel approach, ANN that has one input layer with one neuron corresponding to one input variable, viz., cycles [charge-discharge cycles] and a hidden layer consisting of three neurons to produce their outputs to the output layer through a sigmoid function has been selected for the present investigation. The output layer consists of two neurons, representing the charge and discharge capacity, whose activation function is also the sigmoid transfer function. In this ever first attempt to exploit ANN as an effective theoretical tool to understand the charge-discharge characteristics of lithium-ion cells, an excellent agreement between the calculated and observed capacity values was found with CoO anodes with the best fit values corresponding to an error factor of <1%, which is the highlight of the present study.

Full text of DOI:10.1016/j.electacta.2007.08.049

Available online at www.sciencedirect.com
Electrochimica Acta 53 (2007) 1877–1882
Exploration of artificial neural network [ANN] to predict
the electrochemical characteristics of lithium-ion cells
∗
Thirumalai Parthiban, R. Ravi, N. Kalaiselvi
Central Electrochemical Research Institute (CECRI), Karaikudi 630006, India
Received 23 April 2007; received in revised form 13 August 2007; accepted 19 August 2007
Available online 30 August 2007
Abstract
CoO anode, as an alternate to the carbonaceous anodes of lithium-ion cells has been prepared and investigated for electrochemical
charge–discharge characteristics for about 50 cycles. Artificial neural networks (ANNs), which are useful in estimating battery performance,
has been deployed for the first time to forecast and to verify the charge–discharge behavior of lithium-ion cells containing CoO anode for a total of
5
0 cycles. In this novel approach, ANN that has one input layer with one neuron corresponding to one input variable, viz., cycles [charge–discharge
cycles] and a hidden layer consisting of three neurons to produce their outputs to the output layer through a sigmoid function has been selected
for the present investigation. The output layer consists of two neurons, representing the charge and discharge capacity, whose activation function
is also the sigmoid transfer function. In this ever first attempt to exploit ANN as an effective theoretical tool to understand the charge–discharge
characteristics of lithium-ion cells, an excellent agreement between the calculated and observed capacity values was found with CoO anodes with
the best fit values corresponding to an error factor of <1%, which is the highlight of the present study.
©
2007 Elsevier Ltd. All rights reserved.
Keywords: Artificial neural network; Back propagation; Lithium-ion cells; CoO anodes; Charge–discharge cycle
1
. Introduction
lytical equations. Towards this direction, the ANNs have been
applied to model certain complicated processes related to the
field of engineering, viz., aerospace, automotive, electronic,
manufacturing, robotics, telecommunication, etc. ANN method
is now almost a standard modeling technique based on statistical
approach. Particularly, ANN is an inductive or data-based model
for the simulation of input/output mappings. One of the distinct
characteristics of the ANN is its ability to learn from experi-
ence and examples and to get adapted with changing situations
accordingly.
In recent years, multivariate methods and ANNs are used to
predict the capacity behavior of lead-acid batteries [1–7] alone,
wherein literature is replete with reports on the modeling and
prediction of characteristics of lead-acid batteries [8]. In this
regard, ANNs have been used to predict capacity and power
[6,9], gust effects on a grid-interactive wind energy conversion
system with battery storage [10], cycle life and failure mecha-
nism of lead-acid system [11]. On the other hand, ANN has been
deployed for the first time to understand and to predict possibly
the rechargeable lithium-ion cell charge–discharge charac-
teristics through the present study. Since there are no reports
on the modeling and prediction of charge–discharge behavior
Batteries are highly non-linear devices for which there are
no simple and accurate physical models available to predict
the underlying complex phenomena, such as reaction mecha-
nism, charge–discharge behavior, cycle life, capacity retention,
etc. Basically, mathematical models of physical systems are
constructed to facilitate our understanding of mechanisms that
lead to specific responses and to enable response predic-
tions. This creates the need for prediction tools that provide
users with useful information such as remaining working time,
available energy at every desired time of operation, etc. In
this regard, the artificial neural networks (ANNs), one of the
most powerful modeling techniques with very quick return for
the practice could be explored as a possible tool to predict
the charge–discharge characteristics of rechargeable batteries.
Because, ANNs play a vital role in analyzing and predicting
the behavior of systems that cannot be described by any ana-
∗
Corresponding author. Tel.: +91 4565 227550.
E-mail address: kalakanth2@yahoo.com (N. Kalaiselvi).
0
013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.electacta.2007.08.049

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T. Parthiban et al. / Electrochimica Acta 53 (2007) 1877–1882
of lithium-ion cells, it is aimed through the current study to
exploit the same for a lithium-ion system containing CoO
anode.
weighted input signals to that neuron:
Netj = ΣWij Xi
It is well known that the problems associated with the
deployment of existing category lithium battery anodes such
as graphite/carbonaceous anodes [12], tin-based oxides [13],
metal–metal alloys [14], ternary metal borides, silicides and
nitrides [15,16], etc., have placed greater emphasis upon the
need to identify certain novel/alternate anodes ultimately. As a
result, new class of metal oxide [17] and vanadate anodes [18]
are being investigated off late and among the variety of 3d-
metal oxide anodes, CoO anode has been chosen for the present
study, based on our earlier investigation [19]. Further, the exper-
imental results obtained from the charge–discharge analysis of
Li/CoO half cells containing an electrolyte made up of 1:1 (v/v)
where Wij is the weight-connection to neuron j in the current
layer from neuron i in the previous layer and Xi is the input
signal of neuron. The Netj of the weighted inputs is transformed
with a sigmoid transfer function, which is used to get the output
level. This function is as follows:
1
Yj =
−Netj
1
+ e
where yj is the output of neuron j. Generally, the root mean
squared error (RMSE) is used as the error function for finalizing
the training and testing process [23]. The goal of training a net-
work is to change the weights between the layers in a direction
that minimizes the error E:
EC:DEC dissolved in 1 M LiPF were compared with the pre-
6
ꢀ
ꢁ
0
.5
dicted values of ANN with a view to understand the possibility
of arriving at the best fit values ultimately. Also, the study high-
lights on the possibility of exploiting ANN technique to predict
the charge–discharge capacity values of Li/CoO half cells with
the lowest error value (<1%).
1
E =
2
n(ΣpΣ (y − t )
k
pk
pk
The error E of network is defined as the squared differences
between the target values ‘t’ and the outputs ‘y’ of the output
neurons summed over p training patterns and k output nodes.
With this background, the study deals with the possibility of
deploying ANN technique for lithium-ion battery performance
prediction, via comparison of predicted and observed specific
capacity values of lithium-ion cells containing CoO anodes upon
extended charge–discharge cycling process.
1
.1. Methodology of modeling/artificial neural network
Artificialneuralnetworkmodelingisessentiallya‘blackbox’
operation linking input to output data using a particular set of
non-linear basis functions. ANNs consist of simple synchronous
processing elements, which are inspired by biological nervous
systems [20] and the basic unit in the ANN is the neuron [21].
ANNs are trained using a large number of input data with corre-
sponding output data (input/output pairs) obtained from actual
measurement so that a particular set of inputs produces, as nearly
as possible, a specific set of target outputs. Training consists of
adjusting the weight associated with each connection (synapse)
between neurons until the computed outputs for each set of data
inputs are as close as possible to the experimental data out-
puts. It is well known that during the design and training of
ANNs, factors such as (i) architecture of the ANN; (ii) train-
ing algorithm; and (iii) transfer function need to be considered
eventually.
The term “architecture of the artificial neural network” refers
to the number of layers in the ANN and the number of neurons
in each layer. In general, it consists of an input layer, one or more
hidden layers and one output layer. The number of neurons in
the input layer and the output layer are determined by the num-
ber of input and output parameters, respectively. In order to find
the optimal architecture, number of neurons in the hidden layer
has to be determined (this number will be determined based on
the ANN during the training process by taking into consider-
ation the convergence rate, mapping accuracy, etc.). The most
widely used network type is multi-layered feed-forward network
2. Experimental method (synthesis of CoO) and method
of approach (ANN)
2.1. Preparation of CoO anode
ThecompoundCoOselectedforthepresentinvestigationwas
◦
synthesized via thermal decomposition of CoCO3 at 850 C. A
weighed amount of CoCO3 powder was heated inside a tubu-
◦
lar furnace at a temperature of 800 C in an atmosphere of
flowing argon. Generally, the synthesis of CoO is reported to
associate with common impurities of Co3O4 and so the process
of high-temperature calcination was carried out under the influ-
ence of argon gas flow. Also, the precursor mixture kept inside
the furnace was subjected to a process of intermittent grinding
at least twice, i.e., at the end of every 6 h, to ensure reaction mix-
ture homogeneity and phase purity of the formed final product.
Again, the process of heating was extended for another 3 h, espe-
cially to obtain CoO with maximum purity and stability by way
of expelling the CO2 gas completely from the selected carbonate
precursor. Also, the post heat treatment after 12 h is expected to
exclude the co-existence of trace amounts of cubic Co3O4 from
the final product thoroughly. The compound CoO obtained as
ultra fine powders at the end of 15 h. heat treatment in argon gas
flow was subjected further to electrochemical characterization,
viz., charge–discharge studies.
[
[
22,23] trained with the back-propagation learning algorithm
24–34]. The BPN algorithm is based on the selection of a suit-
able error function, whose values are determined by the actual
and predicted outputs of the network. The model with lowest
prediction error is being used as the final and optimal model.
The activation function of a neuron is defined as the sum of the
The anode electrode was prepared by coating a slurry that
contained a mixture of synthesized metal oxide powder (80%
by weight), carbon (10%) and PVdF binder (10%) over a cop-
per foil and the details pertinent to the same are mentioned

T. Parthiban et al. / Electrochimica Acta 53 (2007) 1877–1882
1879
elsewhere [35] Further, laminated pouch cells of 6 in. × 4 in.
dimensions were fabricated and subjected to charge–discharge
cycling studies at a constant current (C/10) rate.
2
.2. ANN training approach: (software development)
Generally, steps to be followed to develop an ANN model
are: (i) database collection; (ii) analysis and pre-processing of
thedata;(iii)trainingoftheANN;(iv)testofthetrainednetwork;
and (v) use of the trained ANN for simulation and prediction.
Accordingly, data obtained by experimental measurement of
CoO/Li cells were split into two data sets, one of which is a
training set and the other is the test set.
Fig. 2. Cycleability behavior of CoO compound.
In the present ANN model, the input layer has one neuron
(
(
charge–discharge cycles), the hidden layer has three neurons
training data selection method) and the output layer has two
capacity fade of <10% up to 50 cycles. The discharge plateau
observed around 0.8 V may be attributed to the decomposition
of CoO to form metallic Co particles of nano-size, which are
dispersed in lithia (Li2O) matrix. The nano-sized Co and the
pseudo-amorphous nature imparted to the CoO matrix during
the process of first discharge are believed to be maintained in
the following cycling steps also, based on the cycling behavior of
CoOanodeupto50cycles. ThusthecompoundCoOundergoesa
reversible decomposition process and substantiates the observed
fairly high capacity values upon extended cycling.
It is already reported [36] that the insertion of lithium causes
the local structure around cobalt atoms to become asymmetric,
and the small sized Co particles are believed to evolve gradually
with a well-separated distribution in the lithia matrix. As a result,
during the successive extractions of lithium, the reduced cobalt
particles are reported to return reversibly to the high-temperature
cubic phase of CoO, thus substantiating the minimum capacity
fade of <10% up to 50 cycles. From this, it may be concluded
that CoO seems to be a good candidate as far as the magni-
tude and the retention of specific capacity are concerned. The
coulombic efficiency of the synthesized CoO anode is found to
be satisfactorily good, as evidenced from Fig. 2 an indication that
the oxide material chosen for the present study qualify itself as
one of the possible candidates of existing category metal oxide
anodes, by way of possessing an appreciable storage capacity for
lithium.
neurons such as Qdc and Qc (Qdc = discharge capacity and
Qc = charging capacity). With initial random weight, learning
rate and momentum values, preprocessed training data was
applied to the BPN network and the optimal number of neu-
rons in the hidden layer was determined. Training was stopped,
when the prediction error was found to be the lowest. The objec-
tive of the training procedure is to find a set of possible weights
that permit the network to estimate/predict the ANN output, in
order to minimize the error. ANN model with the lowest pre-
diction error was used as the final and optimum model. Using
these optimum values, the network was tested for the unknown
(
test) data (data not presented to the network during training).
The procedure was repeated for different sets of training-test
data also and the software for ANN method was developed in
Visual Basic.
3
. Results and discussion
3
.1. Charge–discharge characteristics of CoO anodes in
lithium-ion cells (experimental results)
The lithium storage capacity and the cycling efficiency of
cobalt oxide electrode was examined through charge–discharge
measurements carried out between 0.0 and 3.5 V at a constant
current rate of C/10 (Fig. 1). The compound CoO exhibits a
capacity of ∼300 mAh/g upon first discharge, and a subsequent
3.2. Deployment of ANN technique for cycle life prediction
of CoO anode (theoretical values)
Generally, ANNs have the capability to transform and reduce
complicated, coupled systems into an inductive framework for
mathematical analysis and data-based modeling [37]. To verify
the estimation/prediction ability of the ANN models developed
(trained), different sets of test data (specific capacity values of
charge–discharge cycles) were presented to the network. Subse-
quently, the estimated and predicted values were compared with
the measured specific capacity values, up to 50 charge–discharge
cycles. It is quite interesting to note that the estimated and
predicted values are in good agreement with the experimental
values. Graphs plotted for training and estimated/predicted data
for different training data approach are shown in Figs. 3–6.
Fig. 1. Charge–discharge behavior of CoO.

1
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T. Parthiban et al. / Electrochimica Acta 53 (2007) 1877–1882
Methods adopted:
Method (estimation
E)/prediction (P))
Training set
Test set
(
Estimation
Estimation
Even cycle data selected Odd cycle data from 1 to
from 1 to 50 cycles
Random cycle data
selected from 1 to 50
cycles
50 cycles
Remaining cycle data
from 1 to 50 cycles
Estimation and
prediction
Random cycle data
selected from 1 to 25
cycles only
Remaining cycle data up
to 50 cycles
Prediction
All 25 cycles data (up to Remaining cycle data
25 cycles) (26–50 cycles)
Fig. 3. Estimation (interpolation) of odd cycle charge–discharge behavior—
even cycle data training approach.
In other words, Fig. 3 shows the estimation (interpolation) of
odd cycle charge–discharge behavior for even cycle training data
approach, which is a commonly reported methodology in the
literature [7,38]. On the other hand, estimation (interpolation)
of in-between cycles for charge–discharge behavior for random
data training approach (up to 50 cycles) is a newer approach
and the results pertaining to the same are furnished in Fig. 4.
Similarly, prediction (extrapolation) of data for a total of 50
cycles for charge–discharge behavior for random data training
approach (up to 25 cycles) and the prediction (extrapolation) of
data for a total of 50 cycles for charge–discharge behavior for
all the consecutive 25 cycles training data approach are depicted
in Figs. 5 and 6, respectively. Herein, it is worth mentioning that
literature has no reports on the training of random cycle data so
also the extrapolation of data, based on chosen category training
imparted to the system. To be more precise in authenticating the
ANN approach to estimate/predict the charge–discharge values
of lithium-ion cells containing CoO anodes, the selection of ran-
dom data testing and the extrapolation of the same for random
data as well as for all the 50 cycles data were made, which is the
significance of the present study.
Fig. 4. Estimation (interpolation) of intermediate cycles charge–discharge
behavior—random data (up to 50 cycles) training approach.
Further, Figs. 7 and 8 show the graphs plotted for experimen-
tal versus estimated/predicted data for different training data
approach with the best fit values (correlation coefficient). It is
obvious from all the figures that an excellent agreement between
the experimental and estimated/predicted capacity values are
observed, an indication that ANN models can also be used for
extrapolation of data with some extended range. This is an inter-
esting observation, since literature reports that ANNs are not
Fig. 5. Prediction (extrapolation) of extended cycle charge–discharge
behavior—random data (up to 25 cycles) training approach.
Fig. 6. Prediction (extrapolation) of extended cycle charge–discharge
behavior—all 25 data (up to 25 cycles) training approach.
Fig. 7. Experimental vs. predicted values (Qdc).

T. Parthiban et al. / Electrochimica Acta 53 (2007) 1877–1882
1881
Table 1
Error values obtained for the different training data approach
Training data approach
RMSE
Correlation coefficient
Hidden layer neurodes
Qdc
Qc
Even cycles (E)
Random 50 (E)
Random 25 (E and P)
All 25 (P)
0.0081436
0.0080256
0.0027328
0.0099867
0.9837
0.9841
0.9797
0.965
0.9783
0.9785
0.9731
0.8747
3
3
3
3
special relevance to the random 50 cycles training data approach
with a correlation coefficient of ∼0.98. Thus, it is demonstrated
that ANN could be deployed as an effective theoretical tool to
estimate/predict the cycle life characteristics of Li-ion cell with
CoO anodes. As an extension of this work, studies on the pre-
diction of extended cycle life performance behavior of variety
of alternate anodes deployed in lithium-ion cells using ANN
technique are underway.
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Fig. 8. Experimental vs. predicted values (Qc).
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