State of Health Estimation of Lithium-ion Batteries Using Convolutional

Neural Network with Impedance Nyquist Plots

Yichun Li, Mina Maleki, Shadi Banitaan and Mingzuoyang Chen

Dept. of Electrical & Computer Engineering & Computer Science, University of Detroit Mercy, Detroit, MI, U.S.A.

Keywords:

Lithium-Ion Batteries, Electric Vehicles, State Of Health, Convolutional Neural Network, Nyquist Plot,

Electrochemical Impedance Spectroscopy, Deep Neural Network, Machine Learning.

Abstract:

In order to maintain the Li-ion batteries in a safe operating state and to optimize their performance, a precise

estimation of the state of health (SOH), which indicates the degradation level of the Li-ion batteries, has

to be taken into consideration urgently. In this paper, we present a regression machine learning framework

that combines a convolutional neural network (CNN) with the Nyquist plot of Electrochemical Impedance

Spectroscopy (EIS) as features to estimate the SOH of Li-ion batteries with a considerable improvement in

the accuracy of SOH estimation. The results indicate that the Nyquist plot based on EIS features provides

more detailed information regarding battery aging than simple impedance values due to its ability to reﬂect

impedance change over time. Furthermore, convolutional layers in the CNN model were more effective in

extracting different levels of features and characterizing the degradation patterns of Li-ion batteries from EIS

measurement data than using simple impedance values with a DNN model, as well as other traditional machine

learning methods, such as Gaussian process regression (GPR) and support vector machine (SVM).

1 INTRODUCTION

The use of lithium-ion (Li-ion) batteries has gained

considerable attention as one of the most promising

means of reducing net carbon dioxide emissions for a

wide range of industrial applications. During the use

of Li-ion batteries, degradation of capacity occurs as

an irreversible process, resulting in diminished perfor-

mance and increased safety operation concerns. State

of health (SOH) is determined as the ratio of the cur-

rent maximum capacity of Li-ion batteries to the max-

imum capacity when the battery is fresh, which is the

degradation indicator of Li-ion batteries that reﬂects

the current health condition of the batteries compared

to its initial health condition. SOH estimation is vital

not only for maintaining the optimal performance of

electric vehicles (EVs) but also for performing health

assessments on Li-ion batteries, which provides vi-

tal information regarding battery maintenance and re-

placement (Rauf et al., 2022). Unlike voltage, current,

and temperature, the SOH of Li-ion batteries cannot

be measured directly with gauges in a battery man-

agement system (BMS). The coulomb counting (Ng

et al., 2009) as a direct capacity measurement has

been widely used in a laboratory environment to mea-

sure the capacity of Li-ion batteries, in which a com-

plete discharge and charge cycle is necessary at each

measurement. Due to the fact that frequent discharg-

ing and charging is a time-consuming process that can

accelerate the aging of Li-ion batteries, it is imprac-

tical to implement the coulomb counting in real-life

applications where a real-time estimation is needed.

Thus, designing robust and reliable battery manage-

ment systems that estimate SOH accurately remains a

challenge.

Recent advances in artiﬁcial intelligence (AI) and

the availability of large Li-ion battery datasets have

resulted in the development of a wide range of data-

driven methods that are capable of estimating the

SOH of Li-ion batteries accurately, in which a contin-

uous capacity estimation task has been converted into

a regression machine learning problem. The quality

of the Li-ion battery dataset has a great deal of signif-

icance since data-driven models are based upon mea-

surable battery data in order to provide a robust esti-

mation of the battery capacity without delving deeply

into electrochemical phenomena inside the battery.

As a result, it remains difﬁcult to select a suitable su-

pervised machine learning model with effective fea-

ture sets for accurate battery SOH estimation. In

recent years, extensive research has been conducted

on extracting degradation patterns from Li-ion bat-

teries and mapping their relationship with capacity

using voltage, current, and temperature from charg-

842

Li, Y., Maleki, M., Banitaan, S. and Chen, M.

State of Health Estimation of Lithium-ion Batteries Using Convolutional Neural Network with Impedance Nyquist Plots.

DOI: 10.5220/0011672300003411

In Proceedings of the 12th Inter national Conference on Pattern Recognition Applications and Methods (ICPRAM 2023), pages 842-849

ISBN: 978-989-758-626-2; ISSN: 2184-4313

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

ing curves. In practice, however, the charging pat-

terns of users vary, which results in uncertainty in the

charging data collected. Thus, in order to overcome

the limitations of adopting multi-channel battery fea-

tures, including battery voltage, current, and temper-

ature from charging curves, this paper proposes a ma-

chine learning framework, in which Electrochemical

Impedance Spectroscopy (EIS) data from impedance

curves are combined with a convolutional neural net-

work (CNN) to estimate the SOH of Li-ion batteries.

The novelty and contributions of this paper are

summarized as follows.

• EIS features have been demonstrated in previ-

ous work (Li et al., 2021) that they can be efﬁ-

ciently utilized in Li-ion battery State of Charge

(SOC) estimation with better accuracy than a

multi-channel feature set using a deep neural net-

work. Now that SOC estimation has been ex-

tended to SOH estimation, and a promising level

of accuracy has been observed for SOH estima-

tion using the EIS feature set.

• To the best of our knowledge, this is the ﬁrst time

that the Nyquist plot of EIS features has been in-

tegrated with the CNN model as features in order

to estimate the SOH of Li-ion batteries. Accord-

ing to the implementation results, Nyquist plots

of impedance provide more comprehensive infor-

mation on battery aging than simple impedance

values in terms of describing nonlinear and com-

plex degradation processes of lithium-ion batter-

ies, resulting in substantial improvements in SOH

prediction accuracy of Li-ion batteries.

• This study demonstrated that convolutional layers

in the CNN model were more effective in extract-

ing different levels of features from EIS Nyquist

plots and analyzing degradation patterns of Li-

ion batteries than simple impedance values with

a deep neural network (DNN), as well as other

conventional machine learning techniques, such

as Gaussian Process Regression (GPR) and sup-

port vector machine (SVM).

The remainder of the paper is organized as fol-

lows: Section II summarizes the recent state-of-art re-

search work regarding the SOH estimation of Li-ion

batteries. Section III describes the utilized EIS dataset

and the proposed machine learning framework. Sec-

tion IV highlights the results and comparisons ob-

tained from the employed models with the EIS feature

set. Finally, the conclusion is drawn in Section V.

2 RELATED WORK

This section summarizes related published work re-

garding the SOH estimation of Li-ion batteries. In

spite of the challenge of designing a BMS that is

capable of estimating SOH accurately, it is vital to

ensure the reliability and safety of Li-ion batteries

for various applications. Therefore, the development

of novel methods for the states estimation of Li-ion

batteries has received signiﬁcant attention in recent

years. Generally, the majority of research studies con-

ducted so far can be divided into two broad categories,

model-based models and data-driven models.

The model-based methods are highly dependent

on the domain knowledge of multi-physics phenom-

ena of Li-ion batteries, including electrochemistry

and aging characteristics. The Kalman ﬁlter has been

proposed in (Saxena et al., 2019) for the estimation of

SOC and SOH of Li-ion batteries. In (Daigle et al.,

2016), An Equivalent Circuit Model (ECM) was de-

veloped by Daigle and Kulkarni to predict battery ca-

pacity when batteries were discharged. An extended

Kalman ﬁlter (EKF) and an enhanced self-correcting

equivalent circuit model were used by Plett (Plett et

al., 2004) to achieve an online capacity estimation

of the Li-ion battery cell. According to (Lin et al.,

2017), two sliding mode observers can be used to de-

termine the SOC and SOH of Li-ion batteries coupled

with a reduced order electrochemical model (EM).

Because EMs contain a large number of partial differ-

ential equations, their solution requires a signiﬁcant

amount of computational power.

The use of model-based methods involves the de-

velopment of complex mathematical models that are

designed to account for the long-term dependencies

of battery degradation and to describe the degradation

process. However, the lack of domain knowledge re-

garding model construction precludes the use of these

methods in real-world applications since it is infeasi-

ble to identify all the hidden complex and highly non-

linear degradation characteristics. In contrast, data-

driven models utilize machine learning techniques to

provide an accurate estimation of the SOH of Li-ion

batteries, thereby overcoming the lack of generality in

model-based approaches for different types of batter-

ies. As a consequence of the advantages of using ma-

chine learning techniques, data-driven methods rely

solely on experimental data collected from the battery

without taking into account battery aging mechanisms

and internal electrochemical reactions.

In (Choi et al., 2019), as a result of exploiting and

applying multi-channel charging proﬁles of the bat-

tery voltage, current, and surface temperature to deep

learning models, numerical results indicate that the

State of Health Estimation of Lithium-ion Batteries Using Convolutional Neural Network with Impedance Nyquist Plots

843

proposed multi-channel method delivers up to 58%

mean absolute percentage error (MAPE) improve-

ment by deploying various neural networks in com-

parison with the use of only voltage charging proﬁles.

The feed-forward neural network (FFNN) has been

deployed in (Chaoui et al., 2017) to estimate the SOH

of Li-ion batteries by using input features, including

battery terminal voltage, current, and ambient temper-

ature from charging curves, which enables the neural

network to extract the dynamic characteristics from

Li-ion batteries and map them to the capacity. To es-

timate the SOH of Li-ion batteries, a gate recurrent

unit-convolutional neural network (GRU-CNN) was

proposed in (Fan et al., 2020), which can extract the

shared information and time dependencies from the

charging curve and limit the maximum prediction er-

ror to 4.3%. The authors in (Yang et al., 2022) have

utilized the battery data from charging/discharging

curves and fed them into various CNN-based SOH

estimation models, indicating the effectiveness of the

proposed models in predicting the SOH of Li-ion bat-

teries.

The data-driven methods mentioned above all rely

heavily on the charging curve data, but the charging

patterns of users are difﬁcult to predict, resulting in

randomness in the battery charging data. As an al-

ternative to using battery voltage, current, and tem-

perature from charging curves, EIS has gained in-

creased interest from researchers in recent years for

its non-destructive nature and capability to analyze

the impedance spectrum of batteries.

It has been demonstrated in (Li et al., 2021) that

the EIS feature set was more effective and efﬁcient in

predicting Li-ion battery capacity than battery volt-

age, current, and temperature from charging curves.

Incorporating cycle numbers with EIS features in (Li

et al., 2022) improved the SOH estimation accuracy

by up to 50% compared to those relying solely on

EIS features. The authors in (Kim et al., 2022) pro-

pose an unsupervised machine learning model called

EIS-based InfoGAN (EISGAN), which extracts vari-

ables that can precisely formulate battery degradation

from the EIS feature set with low-frequency ﬂuctu-

ations. An acceptable level of prediction accuracy

can be achieved with a mean absolute error (MAE)

of 0.71 and a root mean square error (RMSE) of 0.91,

respectively, for testing on a single cell. Moreover,

a CNN model has been deployed with EIS measure-

ment data to estimate the SOH of Li-ion batteries in

(Pradyumna et al., 2022), where the maximum esti-

mation error was found to be 0.57 (% capacity) and

the RMSE was found to be 0.233 (% capacity).

Despite the high dimensionality of EIS features,

it has been challenging to select the quantitative fea-

tures that correlate with battery degradation when us-

ing EIS measurements to predict the SOH of lithium-

ion batteries. Hence, a CNN model has been devel-

oped in this paper, in which the convolutional layer is

employed to extract the most useful features from the

input data automatically without omitting any critical

characteristics of the battery data.

3 MATERIAL AND

METHODOLOGY

This section discusses Zhang’s EIS dataset (Zhang et

al., 2020), one of the largest publicly available EIS

datasets to date, as well as how EIS features were ex-

tracted and restructured in different ways to charac-

terize battery degradation patterns. Also, a proposed

machine learning framework will be described where

the CNN and DNN models were deployed to extract

the aging characteristics from EIS features to estimate

the SOH of Li-ion batteries. The proposed machine

learning framework in this work is presented in Fig-

ure 1.

3.1 Data Acquisition

Various non-linear mechanisms and complex decline

trajectories are involved in the degradation of Li-ion

batteries. In order to train a machine learning model

that will accurately predict the SOH of Li-ion batter-

ies, reliable battery aging data are essential.

In light of the difﬁculty of conducting battery ag-

ing experiments, researchers have evaluated their pro-

posed prediction algorithms based on publicly avail-

able battery datasets. A comprehensive dataset of EIS

measurements, as speciﬁed in (Zhang et al., 2021),

was selected for this experiment, which was con-

ducted by continuously charging and discharging 12

Eunicell LR2032 lithium-ion coin cells made of Li-

CoO2/graphite.

Battery internal impedance plays an important

role in determining its operational voltage, rate ca-

pability, and efﬁciency, and can even have a signiﬁ-

cant impact on its practical capacity. In general, the

measurement approach involves applying a sinusoidal

current or voltage with a certain amplitude and fre-

quency, and measuring the amplitude and phase shift

of the output voltage or current (Li et al., 2020). Re-

peating this procedure for various frequencies, typi-

cally between kHz and MHZ, yields a characteristic

impedance spectrum. More than 20,000 EIS spectra

of 12 commercial Li-ion batteries have been collected

in the EIS dataset (Zhang et al., 2021). The samples

were cycled at different temperatures, speciﬁcally,

ICPRAM 2023 - 12th International Conference on Pattern Recognition Applications and Methods

844

Figure 1: The proposed supervised machine learning framework.

eight cells were cycled at 25°C, two cells at 35°C,

and the remaining cells were cycled at 45°C. EIS

measurement data are collected spanning a frequency

range from 0.02 HZ to 20 KHZ, in which 60 sample

points were conducted at each charging/discharging

cycle.

3.2 Feature Extraction

Due to the complexity and non-linearity of the Li-ion

battery aging process, selecting the most signiﬁcant

patterns from the EIS feature set plays an important

role in describing the degradation of Li-ion batter-

ies. In this work, the Nyquist plot of EIS features has

been extracted based on different cycle numbers of

charging/discharging of Li-ion batteries, while sim-

ple impedance values also have been restructured to

characterize the battery aging patterns.

3.2.1 Nyquist Plot

By varying the applied frequency in an EIS mea-

surement, considerable information can be gathered.

Nyquist plots have been commonly used to visualize

the complex values of impedance values. A Nyquist

plot at one sample point where the real part of the

impedance is plotted against the imaginary part was

presented in Figure 2, where each blue dot represents

a complex value of the impedance, and 60 different

blue dots were collected at each frequency point.

In order to visualize how the Nyquist plot can

reﬂect the degradation of Li-ion batteries, several

Nyquist plots with respect to various SOH of Li-ion

batteries have been shown in Figure 3, where the plot

curves of impedance shift as the result of battery ag-

ing.

3.2.2 Impedance Values

The EIS measurement data have been restructured in

different ways to describe the aging patterns of Li-ion

batteries. For various deep learning models, different

data representations may be needed to take advantage

Figure 2: Nyquist plot of impedance at one sample point.

Figure 3: Nyquist plots of impedance at different SOH.

of each deep learning model. Instead of represent-

ing the EIS features of Li-ion batteries, another com-

monly adopted way to describe the data is to use a

single column array to formulate the impedance val-

ues, where EIS measurement data are organized as a

120 x 1 array.

State of Health Estimation of Lithium-ion Batteries Using Convolutional Neural Network with Impedance Nyquist Plots

845

3.3 Data Processing

A data processing step is essential before feeding

the input data into the machine learning model. In

this step, EIS measurement data are normalized and

restructured before being fed into a neural network

model.

3.3.1 Data Normalization

Normalization of data refers to the process of reorga-

nizing information in a database to reduce redundancy

and enhance its efﬁciency by making all features on

the same scale. The Min-Max function was used to

normalize EIS measurement data in this study:

scaled

− x

min

max

− x

min

(1)

In this case, x

represents each element in fea-

ture column n, and x

min

and x

max

are the minimum

and maximum values for each feature column, respec-

tively. Impedance value in each feature column will

be scaled between 0 and 1 at the end of the normaliza-

tion, which enables each feature in EIS measurement

data of equal importance.

3.4 Model Selection

A CNN framework has been proposed to estimate the

SOH of Li-ion batteries in this study, while a DNN

model has also been deployed with the same EIS mea-

surement data in order to compare the performance of

the models.

3.4.1 Convolutional Neural Network

There has been considerable interest in using convo-

lutional neural networks as a powerful tool for deal-

ing with computer vision problems, where CNNs are

used to classify and differentiate between various ob-

jects contained in an image. In this study, a CNN

framework has been proposed and presented in Fig-

ure 4. There are 1657 Nyquist plots each with a size

of (1657x420) that have been fed into the CNN model

where two convolutional layers each with a max pool-

ing layer after are followed by there fully connected

dense layers to extract the aging patterns from the im-

ages and map the relationships to the capacity value

of Li-ion batteries.

Typically a CNN model is composed of multi-

ple layers with different functionalities, including in-

put layer, convolutional layers, pooling layers, ﬂat-

ten layer, hidden layers, and output layer. The pur-

pose of the Convolution Operation is to extract high-

level features from the input image, such as edges. In

CNN models, multiple convolutional layers are usu-

ally required since the architecture is designed to take

into account high-level features as additional convo-

lutional layers are added. Similar to the convolutional

Layer, the Pooling layer is designed to reduce the spa-

tial size of the convolved feature, which decreases

the computation complexity and results in a more ef-

ﬁcient model. Now that the input image has been

converted into a form suitable for multi-level percep-

trons, the image should be ﬂattened into a column

vector in order to feed it into a feed-forward neural

network that employs backpropagation for each itera-

tion of training. With the help of the optimization al-

gorithm, the model is able to distinguish dominating

and certain low-level features in images and classify

them accordingly.

3.4.2 Deep Neural Networks

The DNN is one of the most promising deep learning

techniques, particularly when a large amount of data

is involved, which can be used to learn the dynamics

and nonlinear degradation patterns of Li-ion batteries

for a regression SOH estimation task. Generally, a

DNN model refers to a simple feed-forward neural

network, which consists of multiple layers, includ-

ing the input layer, hidden layers, and output layer.

The selection of the number of layers and the number

of neurons in each speciﬁc layer make a signiﬁcant

difference in the prediction performance of models,

where the tuning of hyperparameters in a DNN model

should be taken into consideration carefully. Previous

works (Li et al., 2022), (Chemali et al., 2018) have

provided an insight into what combination of the hy-

perparameters should be selected in the DNN model

with the comparable input data size to estimate the

SOH of Li-ion batteries due to the complexity and

time-consuming nature of hyperparameters optimiza-

tion. The input data in the input layer is composed

of 120 neurons, are fed sequentially to two hidden

layers with 64 and 32 neurons in each one, respec-

tively. ReLU function was assigned as the activation

function in both hidden layers and the output layer to

formulate the nonlinear aging process of Li-ion bat-

teries. Adam algorithm was utilized to optimize the

loss function computed by mean squared error (MSE)

in each iteration to adjust the weights and bias of the

DNN model. Also, a dropout layer with a dropout

rate of 0.1 was added after the hidden layers to avoid

the potential overﬁtting during the training phase. The

hyperparameters deﬁned in the DNN model have been

presented in Table I.

ICPRAM 2023 - 12th International Conference on Pattern Recognition Applications and Methods

846

Figure 4: The proposed CNN framework.

Table 1: DNN Hyperparameters.

Hyperparameter Selection Options

Input size 120 x 1

Number of hidden layers 2

Number of neurons in the

ﬁrst hidden layer

Number of neurons in the

second hidden layer

Output size 1

Optimization algorithm Adam

Dropout rate 0.1

Activation function for hid-

den & output layers

ReLU

Loss function Mean squared error

Batch size 32

3.5 Evaluation

Mean square error and mean absolute error are two

widely used evaluation metrics for regression ma-

chine learning problems. And they were utilized

to evaluate the performance of employed CNN and

DNN models in this study.

3.5.1 Mean Squared Error

Mean square error is deﬁned as the mean of the square

of the difference between real and predicted values in

statistics. In this case, it is computed by taking the

mean of the square of the difference between the true

capacity y

true

and the predicted one y

predicted

as shown

in:

MSE =

∑

predicted

− y

true

)

(2)

The smaller value of MSE indicates better SOH

prediction accuracy of Li-ion batteries.

3.5.2 Mean Absolute Error

Mean Absolute Error represents an average value of

the sum of the absolute difference between actual and

predicted results. In this case, it is computed by taking

the mean of the sum of the absolute value of the differ-

ence between predicted capacity y

predicted

and actual

capacity y

true

, which is shown in:

MAE =

∑

predicted

− y

true

(3)

The smaller MAE value indicates a better predic-

tion result.

4 RESULTS AND DISCUSSION

In this work, two different data representations are

derived from normalized EIS measurement data, the

Nyquist plot of impedance in binary images and 120 x

1 single-column vectors, respectively, in order to for-

mulate the degradation mechanism of Li-ion batteries

through CNN and DNN models. Input data have been

divided into 90% training data and 10% testing data

to assess the generalization ability of trained models.

In addition, 10% of the training set was split into a

validation set to prevent the models from overﬁtting

during the training phase. For the statistical analysis

and evaluation of the SOH prediction of Li-ion bat-

teries, CNN and DNN models were implemented in

Python based on TensorFlow.

The deployed CNN model extracted and learned

the changing patterns of the curves of the impedance

plot to predict the SOH of Li-ion batteries, while

the DNN model can only learn the features from the

single-column impedance array due to the limitation

of its simple structure. The prediction results indi-

cate both the DNN and CNN models were capable of

State of Health Estimation of Lithium-ion Batteries Using Convolutional Neural Network with Impedance Nyquist Plots

847

characterizing the dynamic and nonlinear aging pat-

terns of Li-ion batteries from EIS measurement data.

Moreover, because of that, convolutional layers prior

to dense layers that are fully connected can effec-

tively extract aging patterns from Nyquist plots, and

Nyquist plots contain much more detailed informa-

tion regarding the battery degradation process than

simple impedance values, which resulted in a signif-

icant accuracy improvement of the SOH prediction

in CNN model as compared to the DNN model. As

an additional step, simple impedance values were fed

into traditional machine learning methods, including

SVM and GPR models. It is evident from the results

that the CNN model with Nyquist plots as features

achieved an improved SOH prediction accuracy with

MSE and MAE errors of 0.0458 and 0.1292, respec-

tively, outperforming other methods presented in Fig-

ure 5.

As an alternative to the impedance plot, a single-

column array is used to represent the impedance

value, which is composed of a real part of the

impedance value followed by a imaginary part of

it. The Nyquist plot shows the actual ﬂuctuation

of impedance, while the single-column impedance

array only reﬂects the impedance values of the Li-

ion batteries. Accordingly, the prediction results on

the Nyquist plot shows an considerable accuracy im-

provement compared to the single-column impedance

array in SOH prediction, which explains why the

Nyquist plot is better suited to characterizing Li-ion

battery degradation patterns than the single-column

impedance array by using the CNN model.

Figure 5: Performance comparison between CNN model

with Nyquist Plot and DNN, SVM and GPR models with

simple impedance values.

5 CONCLUSIONS

This study proposed a CNN framework for estimat-

ing the SOH of Li-ion batteries using deep learning

techniques. Firstly the EIS feature set has been ex-

tracted and normalized using the Min-Max function

from the raw EIS measurement dataset. Next, the EIS

feature set was restructured into two different forms,

the Nyquist plot and simple impedance values, in or-

der to to be fed into different neural networks and

traditional machine learning models. Based on sim-

ulation results on one of the largest publicly available

EIS datasets, the EIS features set in the Nyquist plot

form contains more detailed information than simple

impedance values regarding the battery aging process

owing to its ability to reﬂect the impedance change at

various SOH stages. Furthermore, the results demon-

strated that the content that reﬂects the ﬂuctuation of

impedance in the Nyquist plots makes a difference

in the SOH prediction compared to single-column

impedance array. Additionally, the CNN model with

two convolutional layers, which incorporates Nyquist

plots as features, signiﬁcantly improved SOH pre-

diction accuracy when compared to the DNN model

and other machine learning models that rely solely on

simple impedance values. Future studies should take

into account more various EIS data representations

and evaluation metrics in order to overcome critical

scenarios in the operations of EVs, and ensure the re-

liability and robustness of the SOH prediction of Li-

ion batteries in real world.

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