Ali Al-Hilo 

Aging Characterization of Li-ion Batteries 
 

 

 

 

 

 

 

Vaasa 2022 

School of Technology and Innovations 

    Master’s Thesis in Smart Energy 

 



 

  

 

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Acknowledgments 
 

 

I would like to thank Prof. Hannu Laaksonen for his guidance and 

continuous assistance throughout this master’s thesis. During this journey, I gained 

remarkable insight into scientific research and academic writing. I really appreciate his 

patience and dedication toward the completion of this master thesis as well as every 

single step along the way. His encouragement, trust, and knowledge led me through 

this program.  

  

I would also like to thank my co-supervisor. Chethan Parthasarathy, Ph.D. student, for 

his tremendous efforts and meaningful advice in both the theoretical and practical part 

of this work. Throughout this thesis, he has always been ready and patiently 

responded without hesitation to all my queries. 

  

My sincere gratitude to the School of Technology and Innovations, Electrical 

Engineering, University of Vaasa, Finland, for giving me this great opportunity to study 

and work my master’s thesis in their laboratory. 

 

Last but not least, my deepest thanks to my parents, Mr. Chasib Al-hilo and Mrs. 

Asmaa Al-hilo, for their support and encouragement during all my study levels. Special 

respect and gratitude to my wife Yasmin Al-hello for her unlimited assistance and care. 

 

 

 

 

 

 

 

 



 

  

 

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ABSTRACT:  
 
The depleting nature of fossil energy resources accompanied by increasing demand for energy 
and their influence on increasing the climate change rates and greenhouse gas emissions 
motivated the governments and decision-makers to adopt energy sources that are less harmful 
to the environment and community. Hence, exploiting the potential power of sunlight, water, 
wind, and underground energy was the cornerstone player in achieving cleaner and more 
sustainable energy systems. Unfortunately, it is almost impossible to rely on these resources to 
match the energy demand because of their erratic behavior. Thus, efficient storage systems are 
needed to enhance reliability and increase the dependency on these energy production 
systems by storing excess energy and releasing it when needed.   
 
In the essence of this development, lithium-ion rechargeable batteries stand out to be a 
practical solution for different energy uses, starting from small appliances, transportation, and 
even grid applications. Although at different levels of utilization, all types of Lithium batteries 
experience the problem of aging and capacity degradation. LiBs aging is a unique and 
complicated phenomenon influenced by the interdependency between different internal and 
external factors. Also, the degradation rates, modes, and mechanisms are affected by the 
battery's design, production process, and application field. Hence, it has become indispensable 
to simulate the battery functionality accurately to indicate and fix the possible failures in 
advance.    
 
 Different approaches were employed for tracing and estimating the capacity fade.  
Some models rely on an offline investigation of the battery cell(s), while others succeed in 
scoring high estimation results while the battery is in operation. Data-driven model (DDM) is an 
example of an online model that doesn't need a comprehensive understanding of the battery 
components and the chemical reactions inside. Hence, a specific machine learning type of 
DDM approach called the long-short term memory algorithm (LSTM) was utilized in this thesis. 
LSTM excels in solving a time-dependent problem; hence, it is adopted here as battery aging is 
an accumulated problem affected by its previous state. 
 
Herein, a Lithium titanate oxide (LTO) pouch battery cell was employed and subjected to 
experimental characterization under two different C-rates at a temperature of 25 oC. The test 
results were then treated to extract specific health indicators that are studied in the literature. 
The estimation model was built in a python programming language with the help of data 
manipulation, machine learning, and visualization libraries. The model's outputs were then 
evaluated using metrics like mean absolute error (MSE), and root mean squared error (RMSE). 
_____________________________________________________________________________ 
KEYWORDS: Lithium-ion battery, Aging, LSTM, Capacity fade, Estimation model, Feature 
extraction 

UNIVERSITY OF VAASA 
School of Innovations and Technology 

Author: Ali Al-Hilo 
Title of the thesis:  Aging Characterization of Li-ion Batteries  
Degree: Master of Science in Smart Energy 
Discipline: Smart Energy 
Supervisor: 
Co-Supervisor:                      

Hannu Laaksonen 
Chethan Parthasarathy 

Year: 2022 Pages: 72 



 

  

 

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Contents 

1 Introduction .........................................................................................................8 

1.2 Context and motivation ................................................................................................. 8 

1.2 Thesis purpose ........................................................................................................... 10 

1.3 Thesis contribution ..................................................................................................... 11 

1.4 Structure of the thesis ................................................................................................. 12 

2 Overview of li-ion battery ageing  ............................................................................ 13 

2.1 Component of LIBs and working principle  ....................................................................... 13 

2.2 Ageing types .............................................................................................................. 15 

2.3 External ageing factors of Li-ion batteries ........................................................................ 15 

2.3.1 Impact of temperature .......................................................................................... 15 

2.3.2 Impact of high/low state of charge (SoC) .................................................................. 17 

2.3.3 Impact of high C-rate ............................................................................................ 18 

2.3.4 Impact of mechanical stresses ................................................................................ 19 

2.4 Description of common aging mechanisms   .................................................................... 20 

2.4.1 Solid electrolyte interphase (SEI) layer ..................................................................... 21 

2.4.2 Lithium plating .................................................................................................... 22 

2.4.3 Particle fracture ................................................................................................... 24 

2.4.4 Transition metal dissolution (TMD) .......................................................................... 25 

2.4.5 Cathode electrolyte interphase (CEI) ........................................................................ 26 

2.4.6 Binder decomposition ........................................................................................... 26 

3 Artificial neural networks ...................................................................................... 27 

3.1 LSTM ........................................................................................................................ 29 

4 Modelling of Li-ion LTO cell capacity fade ................................................................... 32 



 

  

 

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4.1 Methodology ............................................................................................................. 32 

4.2 Test arrangement and procedures  ................................................................................ 33 

4.3 Data preprocessing  .................................................................................................... 36 

4.5 Feature extraction and selection ................................................................................... 37 

4.6 Implementation of the LSTM ........................................................................................ 41 

5 Results and discussion .......................................................................................... 43 

6 Conclusion  ........................................................................................................ 46 

References ................................................................................................................ 48 

Appendices ............................................................................................................... 57 

Appendix 1. Python programming code ............................................................................... 57 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 

  

 

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Figures 

Figure 1 A schematic of a lithium-ion battery and its components (L. Guo et al., 2021) ..................... 14 

Figure 2. a) Expected cell cycle life under varied operating temperatures. b)  Calendar aging at 50% Soc 

under different temperatures. ....................................................................................... 16 

Figure 3 Calndar aging at 25 oC for different SoC (Xu et al., 2018) ................................................. 18 

Figure 4 Specific battery cell aging under different C-rates at fixed room temperature. (Dubarry et al., 

2011) ........................................................................................................................ 19 

Figure 5 Cause-effect relation of some aging factors on battery degradation, adopted from (Li et al., 

2019). ........................................................................................................................ 20 

Figure 6  Schematic of SEI layer formation (Edge et al., 2021) ....................................................... 22 

Figure 7 Voltage plateau during relaxation phase (X. G. Yang et al., 2018) ...................................... 24 

Figure 8 The architecture of LSTM unit (P.Venugopal et al. 2021) .................................................. 30 

Figure 9 Equipment used for cell testing .................................................................................. 35 

Figure 10 Capacity degradation over cycle for a) 1C test b) 5C test ................................................ 37 

Figure 11 The cell voltage during CCCV phase for a) 1C test and b) 5C test at different degradation levels.

 ................................................................................................................................ 38 

Figure 12 The cell energy during CCCV phase for a) 1C test and b) 5C test at different degradation levels.

 ................................................................................................................................ 39 

Figure 13 Correlation map for both test ................................................................................... 41 

Figure 14 Loss function of a) 1C test, b) 5C test ......................................................................... 43 

Figure 15 prediction performance for a) 1C model & b) 5C model ................................................. 45 

 

Tables 
 

Table 1 Factors enhance Lithium plating (X. G. Yang et al., 2018) .................................................. 23 

Table 2 Specification of the battery cell ................................................................................... 33 

Table 3 The extracted features ............................................................................................... 40 

Table 4 LSTM model parameters ............................................................................................ 42 

Table 5 comparison of model results for both tests. ................................................................... 44 



 

  

 

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List of Abbreviations 

Ah   Ampere hour 

SoC    State of Charge 

ESS                                  Energy storage systems 

BESS   Battery Energy Storage Systems 

VRES   Variable renewable energy sources  

BMS    Battery Management System 

EMS    Energy management system 

LiB   Lithium-ion battery 

LTO    Lithium Titanate Oxide 

ECM   Equivalent circuit model 

PBS   Physical- based model  

DDM   Data driven model  

CCCV    Constant current/constant voltage 

CC   Constant current 

GHG   Greenhouse gas  

DOD   Depth of discharge 

ANN   Artificial neural network 

FFNN   Feedforward neural networks 

FBNN   Backpropagation neural networks 

LSTM- RNN  Long-short term memory recurrent neural network  

LAM                                Loss of active material 

LLI   Loss of lithium ion 

IR    Internal resistance  

Li+   Lithium ions 

EV   Electrical vehicle  

SEI   Solid electrolyte interphase 

SSE   solid-state electrolyte  



 

  

 

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SSBs   solid-state batteries 

TMD   Transition metal dissolution  

CEI    Cathode electrolyte interphase 



 

  

 

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1 Introduction  

This chapter aims to explain the background and the scope of this thesis, identify the 

addressed questions, and presents the main contribution. 

 

1.2 Context and motivation 

In recent years, the greenhouse gas (GHGs) emissions rates from energy activities have 

been grown rapidly to records that have not seen before (37 629.7 MtCO2eq 

compared to 34 187.1 MtCO2eq in 2010) (Greenhouse Gas Emissions from Energy 

Data Explorer – Analysis, 2021). Although there was a remarkable decline in values 

during 2020 following the economic and social restrictions during the Covid-19 

pandemic time, scientists expected the emissions to bounce again starting from 2021 

(Tollefson, 2021). This increased emission rate results in the aggravation of climate 

change phenomena. Climate change is considered among the most significant risks 

that threaten human society and all species kinds on Earth. This phenomenon's direct 

and indirect impacts can be seen as increasing the global temperature, diminishing the 

ice area, more droughts seasons, frequent flash floods, and fierce storms (Khan et al., 

2019). However, carbon dioxide gas CO2, which mainly emits fossil-fuel-based energy 

production and transportation, accounts for 78% of GHG emissions (Climate Change 

Indicators: Greenhouse Gases, 2021). Some researchers claim that if the CO2 

emissions rates continue to follow the current manner, the global temperature will 

increase by 6°C by the end of this century (Gallo et al., 2016). However, to keep the 

global temperature growth under 2 °C, not more than 33% of the discovered fossil fuel 

reserves can be consumed by 2050. In addition to its effect on the environment, 

hydrocarbon fuel is a finite energy resource, and it is expected to deplete in the 

coming few decades.   Thus, the transition toward sustainable energy systems has 

become an urgent task to mitigate the severe effects of climate change and 

greenhouse gas (GHG) emissions and secure the energy supply in parallel with 

expanding energy demand (Kalair et al., 2020). 



 

  

 

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As a result, many governments and organizations have agreed on setting some pledges 

and commitments to restore the environment. More integration of renewable energy 

shares in the energy systems is one of the most viable solutions for this problem. 

However, it is impossible to control the production of some clean energy resources 

such as hydro, wind, and solar energy, i.e., variable renewable energy sources (VRES), 

because of their stochastic nature. Hence, the need for energy storage systems (ESS) 

has risen to absorb the extra power generated during the off-peak times and release it 

during the critical periods (Gallo et al., 2016b). 

  

Depending on the working principle and the utilized technology, ESS can be classified 

mainly into five categories: mechanical, electrochemical, chemical, electrical, and 

thermal energy storage. They distinguish from each other by many factors, including 

power and energy densities, charge/discharge time, response time, self-discharge rate, 

storage period, efficiency, lifespan, and capital and maintenance costs (Sufyan et al., 

2019). 

 

Among different kinds of ESS, Battery Energy Storage Systems (BESS) have shown 

many advantages in applications that require fast response and independency of 

geographical demands. They are also successful in supplying power and energy for 

both a fast and short time (Yang et al., 2018).  

  

Lithium-ion batteries (LiBs) are rechargeable batteries that excel in different 

applications such as electronic devices (e.g., mobile phones and laptops), medical 

appliances, and EV sectors. They also showcase great potential to be integrated into 

the electric grid applications, especially as ancillary services providers. Compared to 

other batteries, LiBs feature in providing high energy and power densities regarding 

their size and weight; they are capable for fast charging and can work under a wide 

ambient temperature range; they are almost 100% efficient and have a shallow self-

discharging rate (Akinyele & Rayudu, 2014) 



 

  

 

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Nevertheless, like other batteries, Li-ion batteries experience the aging phenomena. It 

is an inevitable process that happens because of the side effect of chemical reactions 

inside the battery cells. The degradation is a highly complex problem. It depends on 

the variation of many external factors like temperature, depth of discharge (DOD), 

battery loading, charging/discharging current rates, cut-off voltage, etc. These factors 

are interconnected and affect each other. Hence, the determination of the battery life 

is considered a challenging task.  

 

However, scientists have applied different kinds of experiments and tests on various 

LiBs cells to track their aging modality. They aim to a comprehensive understanding of 

battery aging to help manufacturers choose the most suitable materials and structure 

of the battery, develop the cell production processes, and establish a guided design of 

battery systems for various uses (Guo et al., 2021). As a result, the users would have 

more reliable and safer battery systems (Lin et al., 2015).   

 

In contrast, an accurate lifetime prediction model must be included in the battery 

management system (BMS). Therefore, the users would be able to trace the 

degradation behaviors of their batteries, avoid failures by applying maintenance 

processes in advance, and try to exploit their potential capacity efficiently. Thus, 

different estimation approaches have been investigated in both academia and 

industry. The most applied models can be divided into three main types: physical-

based model (PBS), equivalent circuit model (ECM), and data-driven model DDM (Ng et 

al., 2020); however, the focus of this thesis would be on adopting DDM for capacity 

fade estimation.    

 

1.2 Thesis purpose 

he primary purpose of this thesis is to examine the performance of a specific data-

based approach to track and predict the capacity fade of a lithium-ion battery cell. The 



 

  

 

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thesis focuses on the cycle aging effect and neglects the effect of calendar aging on the 

capacity fade. Two systematic sequential laboratory tests have been run on the cell 

under 1C and 5C, respectively. The thesis will utilize the data extracted from the tests 

and perform data engineering, including data cleansing and feature extraction, to 

prepare data to be injected into the prediction model. Long-short term memory 

recurrent neural network (LSTM- RNN) algorithms will be adapted to achieve the 

prediction task. LSTM is a powerful tool in dealing with time series problems. Hence, it 

will be executed on each of the two tests separately.  

 

1.3 Thesis contribution 

The thesis will investigate two main issues related to capacity fade prediction. The first 

one is the feature extraction problem. There is a lack of battery testing datasets, so it is 

crucial to extract as many features as possible from the available datasets to have an 

accurate and practical battery cell model. Second, this thesis tries to predict the 

capacity fade of the battery cell using a novel machine learning approach LSTM (long-

short term memory).  

  

The objectives of this thesis are summarized as follows 

1.    Theoretical review on the aging phenomena and impact factors affecting battery 

performance.  

2.    Create a systematic test technique for Lithium-ion battery  

3.    Monitor the degradation behavior of the lithium-ion cell under constant 

temperature and two different C-rates.  

4.    Employ data engineering on the battery datasets to clean the data and extract the 

most efficient features.  

5.    Build a capacity fade estimation model using Python programming language and 

other related libraries (e.g., Pandas, Numby, Sciketlearn, Matplot, etc.), evaluate the 

outputs' accuracy, and discuss the results. 

  



 

  

 

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The applied approach and the results are limited to the cell level of lithium-ion 

batteries. However, the results cannot be generalized as they are done on only one cell 

in a laboratory environment. 

 

1.4 Structure of the thesis 

The thesis is structured as follows: 

Chapter 1 introduces the background of the subject, explains the motivation and goals 

of the study, and defines the thesis's contribution.  

  

Chapter 2 provides a theoretical overview of the aging phenomena in Li-ion batteries. 

It defines factors that expedite the aging process and relates them to their effect on 

the battery components.  

  

Chapter 3 briefly describes Artificial neural network (ANN) and focuses on (LSTM- RNN) 

theory and functionality.  

  

Chapter 4 is assigned to explain the practical part of this thesis. It will introduce the 

methodology and procedure used to estimate the capacity fade of a Li-ion LTO 

(lithium-titanate-oxide) cell. It illustrates the test procedure done on the cell, the 

feature engineering method, and the model parameters.  

  

Chapter 5 explains the model's results and compares them with the output of the 

experimental process.  

  

Chapter 6 concludes the study, explains its limitations and suggests development for 

future work. 



 

  

 

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2 Overview of li-ion battery ageing  

Lithium-ion (Li-ion) battery aging is a nonlinear and irreversible reaction that occurs 

with time and use inside the battery cell caused by a combination of external and 

internal factors (Xu et al., 2018). Generally, there are two types of aging: calendar 

aging when the battery is in standby mode, i.e., rest or storage mode, and cycle aging 

when the battery is under operation, i.e., charge/discharge mode. The battery 

degrades in different ways and rates under each mode mentioned above. There is a 

wide range of degradation mechanisms; some are triggered instantaneously with the 

early moments of the battery operation, while others can occur later or result from the 

formation of other mechanisms (Edge et al., 2021). In contrast, two leading physical 

indicators of battery aging are capacity fading and resistance increases. Capacity fade 

results from the loss of active material (LAM) of electrodes, loss of cyclable lithium 

(LLI), or the growth of internal resistance (IR). In contrast, the increase in the cell 

resistance downgrades the available power that the battery can discharge.   

 

This chapter defines the components of Lithium-ion batteries and the working 

principle, presents the causes behind battery aging, identifies the concept of calendar 

and cycle aging, and explains the key factors that expedite the degradation.     

 

2.1 Component of LIBs and working principle  

Lithium-ion batteries comprise four main components: cathode, anode, separator, and 

electrolyte.  

Depending on the required characteristics of the battery, materials and compounds 

used for manufacturing the cell components are varied. The cathode is the positive 

electrode usually made of metal oxide active material coated into an aluminum foil 

that acts as a current collector. The most used commercial cathode compound is 

lithium cobalt oxide (LiCoO2). However, usually commercial batteries are named after 

the lithium donator material in the cathode (Zubi et al., 2018). In contrast, the anode, 



 

  

 

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i.e., the negative electrode, is manufactured of active carbonaceous material such as, 

e.g., graphite, lithium titanate (LTO), or silicon (Si) coated into copper current collector 

foil (Kabir & Demirocak, 2017). Lithium electrons placed in the cathode are released 

through an external path to be stored in the anode structure during charging 

operation. In the meantime, a process called intercalation happens when Lithium ions 

(Li+) pass among the electrolyte and through the separator to join lithium electrons 

into the graphite layers of the anode. In the discharge phase, electrons and lithium 

ions move back to the cathode through the same path they utilized in the charging 

process. 

 

 

Figure 1 A schematic of a lithium-ion battery and its components (L. Guo et al., 2021) 

 

The electrolyte is a solvent located between cathode and anode to be the medium that 

allows the shuttling of lithium ions between the two electrodes. The electrolyte is 

usually comprised of material dissolved in salt, and it usually is not involved in the 

chemical reaction when charging /discharging the battery cell (Song et al., 2021).  

 

In contrast, the separator, a semipermeable and electronic insulating membrane, plays 

an essential role in cell safety by preventing short-circuiting cathode and anode. It has 

big enough holes that permit Li+ to pass back and forth. Figure 1 shows the 

components of one LTO cell (L. Guo et al., 2021). 

 



 

  

 

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2.2 Ageing types 

LiBs undergo the effect of aging under both operating and non-operating conditions. 

Calendar aging occurs when the battery degrades under a non-operation state, while 

cycle aging is caused by operating the battery (Zubi et al., 2018). Both aging types 

affect each other; the rate and the causes of any type affect the rates and the causes 

of the other type.   Although calendar aging rates are slower than cycle aging, it is 

deemed the most influential type of battery degradation, specifically in some 

applications when batteries spend less time operating than rest, such as in EV batteries 

(Sui et al., 2021). Calendar aging is mainly driven by external factors such as 

temperature and the battery's state of charge (Soc). Storing the battery at high 

temperature and SoC rates expresses the SEI layer's formation, growth, or rebuilding 

on the anode side.  

 

On the other hand, cycle aging is a more complex type than calendar aging due to 

various factors that influence its occurrence. However, cycle aging is mainly catalyzed 

by lithium plating of the anode. It is proved that operating the battery with elevated 

charge rates, and low temperatures accelerate the lithium plating rates (Redondo-

Iglesias et al., 2018). 

 

2.3 External ageing factors of Li-ion batteries 

Understanding the external factors that trigger and evolve Li-ion battery capacity and 

power deterioration is vital to slow down the aging rate and allow the maximum usage 

of their capacity. This section discusses how factors like temperature, SOC, C-rate, etc. 

influence the battery aging rate during storage and operation. 

 

2.3.1 Impact of temperature 

Abnormal ambient temperature values have a detrimental effect on the functionality, 

safety, and age of the Li-ion battery. However, the impacts of low temperatures are 



 

  

 

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different from those of high-temperature values. In general, the impacts of the 

temperature manifest more clearly in cell failure than in the reduction of its cycle life. 

Figure 2a) shows that the cell works ideally in temperatures between 10°C and 60°C. 

Operating the cell beyond this range leads to a sharp decline in the number of 

available cycles (Kabir & Demirocak, 2017).   Figure 2b) (Xu et al., 2018) presents the 

aging calendar rate of five battery cells stored at different temperatures at 50% SoC.  

 

         

a)                                                                                  b) 

Figure 2. a) Expected cell cycle life under varied operating temperatures. b)  Calendar 

aging at 50% Soc under different temperatures. 

 

Operating or storing the battery under high-temperature values leads to incremental 

parasite reactions on the anode, the cathode, and the electrolyte (Amine et al., 2005). 

The SEI layer will increase on the anode side, causing a loss in the lithium inventory 

(LLI) and a rise in internal cell resistance. In contrast, metal dissolution from the 

cathode and electrolyte solution decomposition will occur, leading to loss of active 

material (LAM) and LLI (Li et al., 2019). In the worst scenario, the battery can be 

threatened by thermal runaway risk (Finegan et al., 2015). It can be noticed clearly 

that high-temperature factors trigger all degradation modes; thus, the battery will lose 

power and capacity when cycling or resting at elevated temperatures.   

  

Nevertheless, low temperature affects the performance and the age of the battery. On 

the one hand, the performance declines as the transportation rate of Li+ becomes 



 

  

 

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slower, the conductivity of the electrolyte weakens, and the diffusion rate of the 

lithium-ion diminishes (Jaguemont et al., 2016). On the other hand, lithium plating on 

the anode may happen along with LLI when charging the battery under high C-rate and 

low temperatures. This phenomenon's continuity may lead to the growth of lithium 

dendrites, which may pierce the separator, causing a short circuit inside the cell. In 

contrast, all other aging mechanisms mentioned above are hindered or not influential. 

However, Storing the battery at low temperatures does not have a remarkable effect 

on the aging rate (Li et al., 2019), while cycling the battery at low temperatures results 

in an irreversible loss of capacity and power (Jaguemont et al., 2016). 

 

2.3.2 Impact of high/low state of charge (SoC) 

Both high and low SoC may cause severe damage to both electrodes. When the cell is 

overcharged, the cathode becomes fully delithiated, and all active lithium ions migrate 

to the anode causing the over lithiation problem. As a subsequent implication, the 

cathode structure undergoes irreversible damage. A reduction in the active material, 

decomposition of electrolyte, rising internal resistance, dissolution of transition metal 

ions, and substantial increase in cell temperature are further consequences (He et al., 

2011) and (Li et al., 2019). Also, the cell may experience a thermal runway when 

overcharging it with a high C-rate (Ohsaki et al., 2005).  

At over-discharging conditions, an unusual increase of anode potential arises, leading 

to a dissolution of the current collector. When recharging the cell, after the above 

process, copper dendrites can grow, which may short circuit the cell. This will result in 

a loss of available capacity and power, and the effect will amplify when accompanied 

by high C-rate charging conditions (Sun et al., 2022).    

  

It is recommended to operate the battery at a specific range between 20% and 90 and 

store it at around 50% (Kabir & Demirocak, 2017). Figure 3 illustrates that the battery 

stored at 100% SoC experienced a higher degradation rate than those stored at 60 % 

SoC.  



 

  

 

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Figure 3 Calendar aging at 25 oC for different SoC (Xu et al., 2018) 

 

2.3.3 Impact of high C-rate 

Cycling the battery with rapid C-rates has a similar influence on the cell of the 

overcharge/over-discharge. High charging/discharging current is always accompanied 

by heat waste, which raises the internal cell temperature, thereby accelerating aging 

rates. This factor becomes more influential with some material of cell components. For 

instance, organic electrolytes have low heat capacity; hence, their temperature will 

increase rapidly when a high current flows through (Chandrasekaran, 2014). In 

addition, Lithium plating can be initialized on the graphite anodes as they cannot 

absorb the massive amount of Li ions when transferred at high rates (Keil & Jossen, 

2016). Also, electrodes may experience partial overcharge/over-discharge behavior as 

lithium ions accumulate on specific parts of the anode or the cathode. 

  

(Dubarry et al., 2011) studied the impact of charging different battery cells under 

different C-rates on the capacity fade and ascribed the proportions of different 

degradation modes over battery lifespan. Figure 4 reveals that in the first 500 cycles, 

the cells degrade linearly under five different C-rates. The authors suggest that LLI 

mode drives the cells' aging in this stage because of some side reactions that permit 

the formation of SEI layer on the surface of the electrodes. After 500 cycles, LAM is 

claimed to be the responsible mode for accelerating capacity degeneration.   

 



 

  

 

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Figure 4 Specific battery cell aging under different C-rates at fixed room temperature. 

(Dubarry et al., 2011) 

 

2.3.4 Impact of mechanical stresses 

Along with its life, from the manufacturing phase to recycling, Li-ion batteries 

experience mechanical tension or pressure, including volume increasing of electrodes, 

gas evolution in some battery packs, and an undesired load during operation. 

Electrodes’ sides near the separator are mostly affected by these factors causing them 

to crack or fracture. At high fracture or cracking rates, the electrodes’ structures fail 

and cause severe cell degradation (Li et al., 2019). 

  

The cause-consequence relation is presented in Figure 5 below, summarizing the 

contributions of some aging factors to the power and capacity loss of the battery. In 

practice, a battery management system (BMS) is assigned to control and mitigate the 

effect of aging factors on large-scale battery applications. BMS, e.g., develops suitable 

charging protocols, manages cell temperature, and prevents over-charging/ 

discharging conditions. 

 



 

  

 

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Figure 5 Cause-effect relation of some aging factors on battery degradation, adopted 

from (Li et al., 2019). 

 

2.4 Description of common aging mechanisms   

Each of the four main components of the lithium cell wears out in different ways and 

rates. Accordingly, each battery cell degrades uniquely. Some degradation mechanisms 

influence only one of these components, while some mechanisms have an associated 

broad effect on many cell components. Figure 6 summarizes the most common 

mechanisms that impact the battery components. This chapter will explain and classify 

the most influencing degradation mechanisms according to their effect on the cell 

components. In context, the cause-effect relation between the most critical aging 

mechanisms and capacity fade or power loss will be presented. However, the influence 

of the external factors, e.g., temperature and SoC during cyclic and calendar aging, will 

be linked with the corresponding aging mechanism.   

 

Consequences

Capacity 
loss

Power
fade



 

  

 

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Figure 6 Schematic of component-wise mechanism of li-ion batteries 

 

 

2.4.1 Solid electrolyte interphase (SEI) layer  

A layer initiates due to chemical reactions in the contact area between the electrolyte 

liquid and the conductors on the anode surface. This reaction leads to a breakdown of 

the reductive electrolyte and causes a reduction in Li-ions. The output particles of this 

reaction will gather on the negative electrode surface, forming the SEI layer. Although 

it may affect the cathode, SEI is primarily considered an anode degradation 

mechanism. It starts directly on the cell's first charge when li ions travel from cathode 

to anode among the electrolytes, and it will keep growing even if the cell is in storage 

mode (Edge et al., 2021). SEI has dual effects on battery performance; during the initial 

stage of its formation, cells lose around 10% of the lithium inventory because of the 

rapid loss of the electrolyte and the reduction in li-ions. However, the positive effect of 

SEI is to allow the passage of Li+ in/out of the electrodes while blocking the passage of 

electrons and electrolyte particles, preventing further corrosion and reduction of 

electrolytes and electrons. (Vetter et al., 2005). The thickness of the SEI layer could 

grow if a new anode surface exposes to electrolyte or the solvent molecules diffuse 

inside a formed SEI layer. 



 

  

 

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Figure 7  Schematic of SEI layer formation (Edge et al., 2021) 

 

SEI formation and growth are claimed to be the leading cause of lithium-ion battery 

degradation. Elevated temperature expedites the diffusion rate of lithium ions 

resulting in the development of the SEI layer. Moreover, cycling the cell with a high C-

rate leads to particle cracking and the formation of new SEI layers (Kabir & Demirocak, 

2017). The formation and growth of SEI cause an irreversible loss of capacity and 

increase the cell's internal resistance. Some types of anode material do not experience 

the SEI process under normal conditions, such as Lithium titanate anode (LTO) 

(Chahbaz et al., 2021).    

 

2.4.2 Lithium plating 

Lithium plating is a parasitic reaction that occurs on the graphite anode during the 

charging process forming a spiky, granular, and/or mossy metallic Li+ on its surface (X. 

Lin et al., 2021). It happens in two forms; thermodynamic and kinetic plating. 

Thermodynamic plating happens when the NE is fully lithiated and has no space for Li-

ion to be absorbed. Kinetic plating occurs when the cell is charged with a high C-rate 

triggering more side reactions from the primary intercalation reaction (Edge et al., 

2021).   However, the metallic lithium can be restorable or not restorable. The 

restorable portion indicates the deposited lithium with an electrical contact with the 



 

  

 

23 

 

anode surface. It can be restored during the relaxation or discharging phase after the 

lithium plating by a lithium stripping process, which leads to the reinjection of these 

lithium metals into the anode. In contrast, irreversible lithium reacts with electrolyte 

and form a secondary SEI layer or lithium film. The latter is a composite of dead lithium 

with no electrical contact with the anode. The effect of irreversible lithium is seen as 

an increase in internal resistance, decline of the energy density, and acceleration of 

capacity fade (X. Lin et al., 2021).    

  

Generally, lithium plating is ascribed to three main enablers: (i) unsafe operating 

environments, (ii) cell manufacturing flaws, and (iii) Cell aging (X. G. Yang et al., 2018). 

These factors are further detailed in table 1. 

 

 

Table 1 Factors enhance Lithium plating (X. G. Yang et al., 2018) 

 

Lithium plating is a potential safety risk as it could tear the separator, causing a 

hazardous short circuit between anode and cathode, which could lead to a thermal 

runaway and an instant failure of the cell. It also causes the loss of lithium ions and 

consumption of electrolyte solvent leading to capacity fade and restricting the fast-

charging capability (X. Lin et al., 2021). 

  

Lithium plating can be detected during cell operation by studying the voltage curve 

when discharging or resting the cell after the charging process. A plateau in voltage 



 

  

 

24 

 

value shows because of the stripping phenomena when the deposited Li metal return 

to its typical case (Figure) (X. G. Yang et al., 2018). 

 

 

Figure 8 Voltage plateau during relaxation phase (X. G. Yang et al., 2018) 

 

The lithium plating mechanism obstructs further development and adaptation of 

lithium-ion batteries. In some applications, batteries are demanded to fulfill some 

requirements such as the capability of fast charging, charging at low temperatures, 

high level of safety, long lifespan, and self-recovery ability. Unfortunately, all these 

requirements enable Lithium plating in the battery (X. Lin et al., 2021b).      

 

2.4.3 Particle fracture 

Operating the cell leads to expanding and diminishing electrodes' volume in response 

to the intercalation/ deintercalation process. The continuity of this process, along with 

specific intrinsic factors including "(particle size, morphology, element composition, 

structure, pre-existing defects, and mechanical properties) and extrinsic factors (C-

rate, cutoff voltage, cycling time, and thermal treatment)" drives particle fractures in 

the electrodes. However, a solid-state electrolyte (SSE) in solid-state batteries (SSBs) is 

also susceptible to examining particle fracture phenomenon (P. Li et al., 2020). It can 



 

  

 

25 

 

be described as tiny cracks spread on the electrodes and the solid electrolyte body and 

is considered one of the essential contributors that cause capacity fade and 

consequently accelerate the battery degradation. It is usually located near the 

separator's electrodes' side because of the high stress caused by the high local current 

densities (Hendricks et al., 2015).  

  

 The particles crack in two ways; intergranular fractures, where the fracture occurs in 

the borders between the primary particles, and intragranular fractures, which affect 

the material's primary particles. The formation and growth rate of each of these types 

depends on the electrodes' structure and materials and the operation conditions of 

the battery (P. Li et al., 2020).  

  

These cracks expose new surfaces of active materials to react with electrolytes forming 

new SEI layers. In contrast, some cracks can produce idle areas of active materials that 

cannot react with other parts of the electrode and /or with electrolytes. Hence, 

impactful amounts of active materials and lithium inventory (when isolated parts 

contain Li+) will be lost as a result (Birkl et al., 2017). Moreover, the advent of these 

cracks is responsible for the instability of the electrodes' structure, which will cause 

the cracks to continue forming until the electrodes collapse (J. Guo et al., 2021).   

 

 

2.4.4 Transition metal dissolution (TMD)   

his mechanism mainly influences the Mn-based cathodes (e.g., The spinel lithium 

manganese oxides (LMO)), and it is accelerated when operating the cell under high SoC 

or at elevated temperatures. Although other transition-metal-oxides-based cathodes 

such as lithium-nickel-cobalt-mixed-oxides can examine this degradation mechanism it 

is usually neglected as it occurs only under extreme operation conditions (J. Guo et al., 

2021).  

  



 

  

 

26 

 

The dissolution of Mn-based cathode particles in the electrolyte release water and 

hydrofluoric acid (HF). Mn dissolution affects cell aging in three directions. First, the 

formed HF keeps the dissolution of TM and Li+ on the cathode's surface, promoting 

the consumption of the active materials and contributing to a substantial loss of 

capacity. Second, the dissolved ion of magnesium will reach the anode and accumulate 

either on its surface or/and on the formed SEI layer. This would increase the thickness 

of the SEI layer, reduce the electrolyte amount and promote self-discharge of carbon-

based anodes. Third, some electrically inert particles, e.g., MnF2 and MnCO3, will 

precipitate on the cathode, causing a continuous increase in its impedance (Kabir & 

Demirocak, 2017). 

 

2.4.5 Cathode electrolyte interphase (CEI) 

his layer forms as a response to a complex chemical surface reaction between the 

cathode and the electrolyte when operating the cell under high voltage values. These 

operation conditions, along with high temperature, ease the electrolyte 

decomposition. This will generate particles such as HF that enhance the cathode 

deterioration and accumulate the ingredients that form the CEI. Usually, the thickness 

of the CEI layer is less than that of the SEI layer and does not affect the whole surface 

of the cathode. However, CEI continues to grow in parallel to the cycling process of the 

cell, which finally may cause an irreversible loss of capacity (Xiong et al., 2020). 

 

2.4.6 Binder decomposition   

Utilizing the battery under elevated temperature is the key influencer of this failure. 

The decomposition of the binder and the dissolution of the current collector will cause 

instability in the cathode compounds. Cathode instability happens because of the rise 

in the internal resistance that is triggered by the loss of contacts in the electrode 

(Xiong et al., 2020). 



 

  

 

27 

 

3 Artificial neural networks 

Artificial neural network (ANN), also referred to as neural network (NN), is a branch of 

artificial intelligence that simulates the structure and function of the nervous system in 

the human brain using computational models. In essence, ANNs are applied to model 

nonlinear functions to obtain outputs with an acceptable level of accuracy. 

Structurally, the basic neural network consists of an input layer, a hidden layer, and an 

output layer. Sometimes input layer is considered a virtual layer. There could be more 

than one hidden layer in a more complex structure where the network is called a deep 

learning network. All layers are interconnected, so neurons in a particular layer are 

connected to neurons in the next layer. The connection lines between nodes work 

similarly to the synapses in the human brain as they transfer the information through 

the model layers. The input layer collects the data and feeds them to the hidden layer, 

where the information is handled, and the relationship between the input and the 

targeted output is built. The output layer receives the information from the hidden 

layer(s) and interprets them to be the result of the system (Abiodun et al., 2018).  

  

ANN is mainly classified into feedforward neural networks (FFNN) and feed backward 

or backpropagation neural networks (FBNN). In FFNN, the data transmit in one 

direction and do not include feedback connection like in FBNN. There are different 

forms of NN under these two classes. Examples of FFNN are multi-layer perceptron 

and radial basis function networks. In contrast, Bayesian regularized neural network 

and self and recurrent neural network (RNN) are examples of FBNN. Describing all 

types of ANN is beyond the scope of this thesis, and the focus will be on the recurrent 

neural network (RNN), which will be discussed in the following paragraph (Abiodun et 

al., 2018). 

 

RNN is a feed backward neural network that uses loop features in its structure to 

handle historical observations among data. RNN can memorize sequences of data and 

handle them accordingly. Thus, it is broadly employed to solve time series problems, 



 

  

 

28 

 

where prior values affect the posterior outcomes. The basic structure of RNN is 

presented in figure 9. RNNs can be seen in three different forms, many-to-many, one-

to-many, and many-to-one. Many-to-many means the model gets a sequence of inputs 

and results in a sequence of outputs. A one-to-many network takes a single input and 

produces a sequence of outputs. Many-to-one is the opposite of the previous type; the 

network requires a sequence of inputs and yields one output (Kaur et al. 2019). 

 

 

Figure 9  Structure of simple RNN (Dataasprint, 2020) 

 

In contrast, basic forms of RNN could experience vanishing or exploding gradient 

problems, making training and getting desired results challenging. The vanishing 

gradient problem appears when the model gets stuck between specific values and 

loses optimal solutions during the long training phase. As a result, the parameters 

could not update, and the network becomes useless. Therefore, in 1997 Hochreiter & 

Schmidhuber have developed a model called LSTM to overcome this flaw of RNN 

(Chung et al. 2014). 

 



 

  

 

29 

 

3.1 LSTM    

ong-short-term memory (LSTM) is a versatile and commonly used recurrent neural 

network in solving a host of machine learning and deep learning tasks. LSTM can look 

back for lengthy time steps, making it the ideal choice for this task compared to 

traditional neural. Because of this merit, this thesis adopted LSTM for capacity 

degradation estimation, as the capacity of a battery cell degrades with time under 

various long- and short-term conditions (van Houdt et al., 2020). 

  

Compared with other RNN (recurrent neural network) types, LSTM excels in two 

points. Firstly, its ability to mitigate the exploding and vanishing gradient problem. 

Secondly, it can learn the information from the data more effectively by looking back 

at the long dependencies. LSTM algorithm could contain one or more of the LSTM 

units. Each LSTM unit has three gates of the same shape. These gates can memorize 

the data according to their importance. So that the data with high importance will be 

kept, while the others will be forgotten. This process aims to pass the most wanted 

information along the sequence to achieve an accurate prediction (van Houdt et al., 

2020). 

  

 LSTM unit structure is shown figure 10. the subscript t refers to the current state of 

each vector. In our application t denotes the cycle number. At each t moment, there 

are three inputs should be passed to each LSTM-RNN unit: 

• Xt is the input vector of the current timeframe. 

• ht-1 is the output value from the previous step, 

• Ct-1 is the cell state pf the previous step. 

 

Meanwhile, the LSTM-RNN produce two outputs: the output value ht and cell state Ct 

at present time t. It can be noticed from the figure that LSTM cell is compromised from 

four main components that will be explained in the following paragraph (Chen et al. 

2020).  



 

  

 

30 

 
 

 

 

Figure 10 The architecture of LSTM unit (P.Venugopal et al. 2021) 

 

Forget gate: his is the first step in LSTM. This gate decides which data are passed to 

the next unit and which are thrown away. It compares the current input Xt and the 

previous output ht-1 by passing them to the Sigmoid function (σ).  

The output of the Sigmoid function ft varies between zero and one. Hence, the result 

that gets a value closer to one will be passed. The forget gate works as follows: 

ft = σ (Wf . [ ht-1 , Xt] + bf)           (1) 

Wf  and  bf stand for the weight matrix and the bias of forget gate, respectively. 

 

Input gate and input node: The cell state will be updated in this stage. First, the 

current input Xt and the previous state ht-1 feed into a sigmoid layer called “input 

gate” and the tanh function called “input node” separately. The output tanh function 

(C̃t), which fluctuates between -1 and 1, will be multiplied by the output of the sigmoid 

function it, resulting in a new vector of candidates injected into the cell state. Equation 

(2) denotes the output of the tanh function, while equation 3 calculates the outputs of 

the sigmoid function. 

 

C̃t =  tanh (Wg. [ ht-1 , Xt] + bg )                (2) 

it = σ (Wi. [ ht-1 , Xt] + bi )                        (3) 



 

  

 

31 

 

Wi  and  bi denotes for the weight matrix and the bias of input gate, respectively. 

 

Cell State: he function of this component is to transfer the relevant data across all time 

steps. The transferred data depends on the output of the forget and the input gates.  

The equation below shows how Ct is calculated.  

 

Ct = ft * Ct-1 + it *C̃t                                  (4) 

 

Output gate: It determines the output of the unit(ht). Similar to forget gate, current 

input Xt and the previous state ht-1 are passed to a sigmoid function, while the newest 

cell state will be passed to the tanh function. Then the output from these functions will 

be multiplied to determine the output. 

  

Ot = σ (Wo. [ ht-1 , Xt] + bo )                    (5) 

                               ht = tanh (Ct) * Ot                                    (6) 

Wo and bo denote the weight matrix and the bias of output gate, respectively. 

 



 

  

 

32 

 

4 Modelling of Li-ion LTO cell capacity fade 

4.1 Methodology 

The practical aspects of the study include designing and implementing battery cell 

tests, gathering and preparing data, and constructing and evaluating the model. After 

completing the test on the cell, the data has been extracted and prepared using some 

feature extraction and data manipulation techniques. The data are then split into 

training and testing sets. Training sets will help the model learn the hidden 

dependencies between features and capacity fade patterns, whereas testing sets will 

be used to validate the model. Subsequently, the results will be evaluated using some 

evaluation metrics. Figure 11 shows the framework and the flowchart of the capacity 

fade prediction. 

 

 

Figure 11 Framework of capacity fade estimation 

 

Python programming language is used for coding in this study. However, other open-

source libraries are employed as well. Pandas (a library designed to manipulate and 

analyze data) and Numby (a library that uses high-level mathematical functions for 

handling arrays and matrices) are operated for data preprocessing (Pandas, 2008) and 



 

  

 

33 

 

(NumPy, 2006). Scikit-learn (a library that contains a complete set of functions for 

machine learning problems and provides tools for measurement and evaluation tasks) 

is involved in data scaling, model construction, and performance assessment (Scikit-

Learn, 2007). TensorFlow and Keras (libraries that focus on deep learning tasks) are 

used for building the model (TensorFlow, 2015) and (Keras, 2015). Plotting and 

visualization are carried out using Seaborn and Matplotlib (plotting libraries for python 

programming language) (Seaborn, 2012) and (Matplotlib, 2003). 

 

4.2 Test arrangement and procedures  

The battery cell was tested under two different C-rates at a fixed ambient temperature 

value of 25 oC. First, the cell is subjected to a cycling test under 1 C-rate. After 

completing 700 cycles, it was then rested and exposed to a cycling test under 5 C-rate 

for 700 cycles. The primary purpose of these tests is to identify the degradation 

characteristics of the cell when it is operated at two different C-rates.  

 

Product name LTO battery cell 

Nominal capacity ≈ 3.09 Ah 

Nominal voltage 2.4 V 

Work Voltage (min-max) 1.7 v- 2.9 v 

Dimension W63 × D14 × H97 mm 

Max charging current 10 C 

Max discharging current 10 C 

 

Table 2 Specification of the battery cell 

 

This experiment is conducted with a used cell. Therefore, the maximum capacity 

reached during the first cycle will be considered the nominal voltage, while all other 



 

  

 

34 

 

values will be adopted from the factory data sheet. The specifications of the tested cell 

are shown in table 2 above.  

  

 During the first stage of the test, the cell was fully charged and discharged at 1 C-rate. 

Charging and discharging time lasted around 1 hour for each. The cell was rested for 

30 minutes after each charging or discharging phase. The test has been conducted due 

to the following procedure:  

1.    Charging the cell from 0 % to 100% SoC under 1 C-rate using Constant Current 

Constant Voltage (CCCV). CCCV values are set to current= 2.9 A and voltage= 2.65 V.  

The charging process ended either when the cell reached the upper voltage limit of 

2.65 v or is fully charged.  

2.    Resting for 30 minutes to achieve stability. 

3.    Discharging the cell completely using Constant Current (CC) technique with a 

current equal to 2.9A. The discharge phase is stopped by the cell is fully discharged or 

reached the lower voltage limit at 1.7 V. 

4.    Resting for 30 minutes. 

5.    Repeating the above process for 100 cycles.  

6.    Applying Hybrid Pulse Power Characterization (HPPC) test profile on the cell to 

estimate cell DC resistance and its adjoining parameters. 

7.    The tests have been terminated after completing 700 cycles under 1 C-rate. 

  

The cell maximum capacity then degrades from 3.09 to 3.05 Ah.  3.05 Ah is considered 

the nominal capacity for this stage of the test. As in the first stage, the temperature 

was fixed at 25 oC. However, the cell was fully charged/discharged at a 5 C-rate using 

the following steps:   

1.    Charging the cell from 0 % to 100% SoC under 5 C-rate using CCCV. The charging 

current is set to 14.5 A while the voltage value stays at 2.65 V.  

The charging process ended either when the cell reached the upper voltage limit of 2.8 

v or when it was fully charged. 



 

  

 

35 

 

2.    Resting for 30 minutes. 

3.    Discharging the cell completely using Constant Current (CC) technique with a 

current equal to 14.5 A. The discharge phase was stopped when the cell fully 

discharged or reached the lower voltage limit at 1.7 V. 

4.    Resting for 30 minutes  

5.    Repeating the above process 20 times.  

6.    Charging and discharging the cell under 1 C conditions.  

7.    Applying the HPPC test. 

8.    Repeating the above sequence until reaching 700 complete cycles under 5 C-rate. 

  

The equipment used in this experiment includes WEISS, Neware Battery Cell testing 

equipment, and a computer. Technik climate test chamber was used to sustain the 

ambient temperature around the cell. Neware Battery Cell Testing Equipment 

(BTS8000 model) was used to cycle the cell. Neware was connected to PC, where test 

parameters were controlled, and the results were recorded. The data were recorded 

every second during the test. Figure 12 below shows the configuration of the test 

equipment. 

 

 

Figure 12 Equipment used for cell testing 

Negative terminalPositive terminal

LTO cell

Neware BTS8000 cell testing 

equipment: 4 channels, 5V 

and 300A

Thermal chamber: -10 

ᵒC to +90 o C

Control station and data 

server



 

  

 

36 

 

 

4.3 Data preprocessing  

here were two sets of data gathered from the test; the first set is the results of the 1C 

cycling test, while the second set is the output of 5C. The original 1C set contains 

3355347 samples and 12 columns, while the 5C sets contained 4150048 samples and 

12 columns. Each sample in both tests represents the recorded values for one second. 

The most valuable parameters obtained from the tests are voltage (V), 

charging/discharging current(mA), capacity (mAh), energy (mWh), cycle number, 

status (Rest, CCCV charge, CC charge, CC discharge). 

  

To train the model, only charging data under the CCCV protocol are used. There are 

two fundamental reasons for this. First, the cell has been through repeated and 

symmetrical charging/discharging patterns, so any effect of the charging phase on 

capacity will be seen during the discharging phase and vice versa. Therefore, it is 

unnecessary to include data from both phases. Second, using only CCCV charging data 

reduces the compute power required for training the model, which has been 

considered an obstacle due to the limited computing power resources. Thus, all data 

related to the discharging phase, HPPC test phase, and rest phase are excluded from 

the set of data injected into the model. Moreover, only data related to each cycle's 

maximum capacity has been selected to further reduce the needed computation 

power for training the model. This reduced the data samples for 1C and 5C to 703 and 

699 samples, respectively. Figure 13 shows the capacity fade for each cycle for 1C and 

5C, respectively. The steep decline or rise in 1C test figures corresponds to the capacity 

values following the HPPC test phase, while spikes in values for the 5 C-rate test 

represent the values when cycling under 1 C-rate. 

 

 

 

 



 

  

 

37 

 

 

a) 

 
b) 
 

Figure 13 Capacity degradation over cycle for a) 1C test b) 5C test 

 

4.5 Feature extraction and selection 

t is a process where new sets of features are extracted from the original data to 

capture more insights from the dataset. Therefore, due to the limitations of the 

battery data parameters, it is essential to extract some features relevant to capacity 

degradation (Zhang et al., 2017). In this work, some features have been obtained from 

analyzing voltage and energy values over time for both 1C and 5C tests. It is noticed 

that at the last testing cycles, the voltage reaches the upper cut-off value faster than in 

the first cycles. Figures 14a and 14b show a decline in the time required to reach from 

one voltage to another as the number of cycles increases for both tests. This behavior 

can be noticed clearly at the final stage of the curve when the cell voltage approaches 

the upper cut-off voltage of 2.65 v.  

a)

b)



 

  

 

38 

 

(Li et al., 2021) investigated this phenomenon and considered it as an indicator of 

capacity degeneration. 

a) 

 

 
b) 
 

Figure 14 The cell voltage during CCCV phase for a) 1C test and b) 5C test at different 

degradation levels. 

 

In the same way, the amount of energy stored in the cell during the charging phase 

varies over cycles. As the cell degrades, its ability to store energy reduces, and loss in 



 

  

 

39 

 

its energy occurs faster than in initial cycles. Herein, this is considered an indicator of 

capacity fade phenomena. As such, the change in the stored energy amount over 

cycles is extracted as a feature. Figure 15 shows the pattern of the energy stored in the 

cell over different cycles for 1C and 5C testing systems.   

a) 

 

 
b) 

Figure 15 The cell energy during CCCV phase for a) 1C test and b) 5C test at different 

degradation levels. 

 
Thus, this study extracted features from voltage and energy variables. Equation 7 was 

used to measure the transit time between Vi and Vi+1. 

DT= |tv2-tv1|                                                       (7) 

DT stands for the change in time for specific voltage intervals, tv1 is the time at v1, and 

tv2 is the time at v2. In this way, the voltage data is divided into six ranges for each 

cycle, with the time passed for each interval considered a feature.   

  



 

  

 

40 

 

Likewise, the energy produced during the same previous voltage ranges was extracted 

to include them in the dataset. The amount of energy stored in a specific range can be 

calculated as follow. 

    ES = |Ev2-Ev1|                                                     (8) 

Where ES represent the energy stored in the cell during a specific voltage range 

between v1 and v2, Ev2 represents the energy at the end of voltage range v2, and Ev1 

represents the energy at the beginning of the same voltage range v1.  Table 3 presents 

the extracted features. 

  

Time-based 
features 

Description Energy-based 
Features 

Description 

F1 
Time the cell needed to 
transit from 2 to 2.2 volts 

F7 
Energy stored during 
voltage range 2 to 2.2v 

F2 
Time the cell needed to 
transit from 2.2 to 2.4 volts  

F8 
Energy stored during 
voltage range 2 to 2.4 volts 

F3 
Time the cell needed to 
transit from 2.4 to 2.5volts  

F9 
Energy stored during 
voltage range 2.4 to 2.5 v 

F4 
Time the cell needed to 
transit from 2 to 2.5volts  

F10 
Energy stored during 
voltage range 2 to 2.5 v 

F5 
Time the cell needed to 
transit from 2.5 to 2.6 volts 

F11 
Energy stored during 
voltage range 2.5 to 2.6 v 

F6 
Time the cell needed to 
transit from 2.6 to 2.7 volts 

F12 
Energy stored during 
voltage range 2.6 to 2.7 v 

 

Table 3 The extracted features 

 

After extracting the features, it is necessary to choose only features that score high 

correlation values with the capacity using a specific filtering method. Herein, the 

Pearson correlation method was employed. It is commonly used for numerical 

parameters to measure the linear relationships between them (Williams et al., 2020). 

Values between 1 and -1 are assigned, with 0 indicating no correlation, 1 indicating 

total positive correlation, and -1 indicating a total negative correlation. In other words, 

positive values over 0.8 mean that the variables have a substantial direct relationship, 

while negative values of less than -0.8 imply a strong inverse relationship (Berman, 



 

  

 

41 

 

2016). However, in this study, thresholds between (-)0.5 and (-)0.95 have been set to 

filter the features. Therefore, any feature that scored value out of the threshold range 

with capacity is removed from the datasets. Similarly, either feature will be deleted if it 

scores a value out of the threshold range with another feature. The correlation has 

been applied only to the training set to overcome overfitting and underfitting 

problems. Figure 16 below shows the correlation maps for both tests after filtering the 

original sets with the specified thresholds.  

 

            

                           a) 1C        b) 5C  

Figure 16 Correlation map for both test 

 

 

4.6 Implementation of the LSTM 

After finishing data pre-processing and feature extractions, the datasets become ready 

to be trained and tested on the model. Nevertheless, the data needs to be 

transformed into a standard scale since LSTM is a scale-sensitive. Thus, the min-max 

normalization method in equation 9 has been applied to scale data into the range [0,1] 

(Witten et al., 2016). 

𝑦𝑖 =
𝑥𝑖−min⁡(𝑥)

max(𝑥)−min⁡(𝑥)
                                           (9) 

 



 

  

 

42 

 

Where 𝑦𝑖 corresponds to 𝑥𝑖 value after scaling, and max(𝑥) and min(𝑥) represent the 

maximum and the minimum observations in the dataset, respectively.   

 

The model was constructed with one input layer, one hidden layer of 40 LSTM units, 

followed by one dense output layer. Linear function was used as an activation 

function. Adam optimizer was applied, while mean squared error was employed as a 

loss function. The model was trained on 70 percent of the scaled data. The remainder 

of the data was assigned for the testing part. LSTM algorithm requires three-dimension 

data. Hence, before injecting the data, they have been modified to 3-dimensional 

arrays representing features, samples, and timestep of 30 cycles as dimensions. 

Afterward, Model fitting was done for 50 training epochs with a batch size of 20 to 

estimate the next capacity value based on values of 30 previous cycles. The model 

parameters are summarized in table 4 below. 

 

Parameter  Value 

No. of hidden layers  1 layer  

No. of LSTM units 40   

Data split  70 % for training, 30% for testing  

Epoch 50 

Batch size 20 

Loss method MSE, MAE 

Metric MAE, RMSE, R2 

Optimizer Adam 

Activation function  Linear 

 

Table 4 LSTM model parameters 



 

  

 

43 

 

5 Results and discussion 

This LSTM-RNN model follows an online capacity face estimation method; hence the 

previous values of the capacity were always available to be included as input. Two loss 

functions were implied to minimize the error of the model; mean square error (MSE), 

which is the most common loss function used for regression problems, and mean 

absolute error (MAE). Figure 17 shows the convergence curves of these two functions 

over the epochs for both tests. From all graphs, it can be seen how the model learned 

from both the train set and test set, where the error reduced significantly to lower 

values.   

      

   

                                      a)           b) 

Figure 17 Loss function of a) 1C test, b) 5C test 

 

The model showed good skills in tracking and estimating the capacity fade pattern for 

both tests. Three criteria were implemented to measure the prediction performance. 

Root mean squared error (RMSE), mean absolute error (MAE), and goodness-of-fit (R 

2). Values change between zero and infinity for the two first metrics, where zero is the 



 

  

 

44 

 

idle result. Instead, R2 output alters within 0 and 1, where 1 is the perfect value. The 

following formulas mathematically define the metrics mentioned above. 

 

𝑅𝑀𝑆𝐸 = √
1

𝑚
∑ (𝑦𝑖
𝑚
𝑖=1 − 𝑦̂𝑖)⁡2⁡⁡⁡⁡                                               (10) 

𝑀𝐴𝐸 = √
1

𝑚
∑ |𝑦𝑖
𝑚
𝑖=1 − 𝑦̂𝑖|⁡⁡⁡⁡                                                     (11) 

𝑅2 = 1 − ∑ (𝑦𝑖
𝑚
𝑖=1 − 𝑦̂𝑖)⁡

2/∑ (𝑦𝑖
𝑚
𝑖=1 − 𝑦̅𝑖)⁡

2⁡                           (12) 

 

𝑦̂𝑖 , 𝑦𝑖 , 𝑦̅𝑖  represent the estimated value, the actual value, and the average value, 

respectively. While  𝑚 refers to the total number of samples.  

 

RMSE is the prediction error's standard deviation, which calculates how data are 

distributed around the regression line. MAE measures the average of the absolute 

difference between actual capacity and predicted capacity. In contrast, R2 defines the 

precision of the model (Chen et al., 2020).   

 

 

1C test 5C test 

Training set Testing sets Training set Testing sets 

MAE 1.99 1.713 2.637 2.483 

RMSE 2.57 2.186 4.814 4.265 

R2 0.91 0.285 0.777 0.766 

 

Table 5 comparison of model results for both tests. 

 

The same parameters in table 4 are applied for training the models of both tests. In 

table 5, a comparison between the results of both tests for the training and testing set 

is shown. For the 1 C-rate cycling test, the model scored 1.99 for MAE and 2.57 for 



 

  

 

45 

 

RMSE; these values indicate a narrow estimation error range. The model has 

performed well also in the testing set considering MAE and RMSE values. R2 scores are 

dissimilar with 0.91 and 0.285 for training and testing sets, respectively. These values 

show 91% similarities between the predicted and actual values for training sets and 

only 28.5% for testing sets. On the contrary, for the 5C model, R2 results are almost 

similar for the test set and train set, while the values of MSE and MAE are slightly 

higher than for the 1C test. Figure 16 presents the prediction performance of the 

model for both tests. 

a) 

 

 
b) 

Figure 18 prediction performance for a) 1C model & b) 5C model 



 

  

 

46 

 

6 Conclusion  

The adoption of Lithium-ion batteries as energy storage is hindered by various factors, 

precisely the complexity and the nonlinearity nature of their deterioration behavior. 

Hence, efforts have been dedicated to first developing these batteries and making 

them last longer by tolerating different critical operation factors. Second, building 

models that replicate the functionality of these batteries, estimating the degradation 

rate and the end of life in advance to overcome the failures and perform the 

maintenance duties in advance.   

  

This study reviewed the most common mechanisms and factors that initiate and 

enhance the degradation phenomena of Lithium-ion batteries during storage and 

operation states. It also related the discussed mechanisms to factors that impact them. 

  

In the practical part, this thesis applies organized tests in a successful version of these 

batteries called Lithium titanate cell LTO to estimate its degradation rate using LSTM-

RNN machine learning model. Each test completed around 700 cycles that were 

interspersed with rest periods and HPPC tests. 

  

Under the 1C test, the cell degrades around 1.5 % from the nominal value of 3090 mAh 

to the last recorded maximum value of 3050 mAh. The last maximum recorded value 

under the 1C test is considered the nominal value of the 5 C test. Accordingly, the cell 

lost only 0.7% of its capacity under the 5 C test. In sum, the cell degrades almost 2.2% 

over around 1400 completed cycles.   

  

The model may be enhanced by extracting geometrics features from the 

measurements’ curves and by including internal temperature and internal resistance 

values.  



 

  

 

47 

 

Nevertheless, the model results cannot be generalized and are limited to this thesis 

experiment for many reasons. Firstly, the experiment has been done on only one cell, 

so the degradation rates of the first test influence the rates of the second one.  

Secondly, the experiments were done to accelerate the degeneration of the cell. 

Hence they do not replicate the real-world applications of batteries. Finally, although 

the model succeeded in tracking the general trends of capacity fade, the model 

experienced a lack of ability to predict precisely when it comes to the details. LSTM-

RNN model that is used here was a simple one with only one hidden layer, and its 

hyperparameters were not tuned to the perfect values. Hence, the model could 

perform better when increasing the hidden layers, and the hyperparameters are 

optimized. Also, the data used to train the model was insufficient, and there was also a 

low correlation between features and capacity values. Thus, to achieve better results, 

one can work on optimizing the model parameters, adding more experimental data, 

reducing the filtering thresholds, and extracting features that are more relevant to 

capacity fade. The previous limitations points can be considered for future research to 

get better and more practical results from the model. Also, to get a clearer view of 

LSTM model performance, it can be compared with another machine learning model 

performance such as Support Vector Machine (SVM).      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 

  

 

48 

 

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Appendices 

Appendix 1. Python programming code  

 

1. Importing Libraries and Data 

In [1]: 

import numpy as np 

import pandas as pd 

import matplotlib.pyplot as plt 

import seaborn as sns  

In [2]: 

#Import data 

df= pd.read_csv ('final_df.csv') 

print('data shape is', df.shape) 

print(df.info()) # shows some information about the data 

df.head() 

In [3]: 

df['Time'] = pd.to_datetime(df['Absolute Time']) # convert the 'Absolute Time' column type from obje

ct to datetime 

print(df.info()) 

 

In [4]: 

#pd.set_option('display.max_rows', 5000) # show 5000 samples  

a= df[df.Status == 'CCCV_Chg'] # choose the only 'CCCV_Chg' data  

a= a[a['Cur(mA)'] != 0]        # Remove current values equal to zero 

a= a[a['C-rate'] == 1]         # Choose only the tesst values unde 1C 

a['Voltage(V)'] = (round(a['Voltage(V)'], 1))  """ round the voltage to one decimal value, to get more

                                                                                            similar records between cycles""" 

a=a.reset_index(drop=True) # reset index and drop the old one 

a=a.drop(columns=["Step","Status","Absolute Time"]) # drop unuseful columns 

a.head(5000) 

 

In [5]: 

g=a.groupby('Voltage(V)').count() # count the data amount based on the recorded voltage values 

g.sort_values("Voltage(V)", ascending = True).head(5000) 

 

2. Features Extraction 

In [6]: 

v1 = a.where(a['Voltage(V)'] == 2) # extract data that recorded at voltage = 2 volt 

v2 = a.where(a['Voltage(V)'] == 2.2) 

v3 = a.where(a['Voltage(V)'] == 2.4) 



 

  

 

58 

 

v4 = a.where(a['Voltage(V)'] == 2.5) 

v5 = a.where(a['Voltage(V)'] == 2.6) 

v6 = a.where(a['Voltage(V)'] == 2.7) 

 

 

v1=v1.dropna() # Drop non-number records 

v2=v2.dropna() 

v3=v3.dropna() 

v4=v4.dropna() 

v5=v5.dropna() 

v6=v6.dropna() 

 

v1.shape,v2.shape,v3.shape,v4.shape,v5.shape,v6.shape #shape of each datasets 

 

In [7]: 

x1=v1.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0) """ Group the data by cycle

 and choose the first recorded data when V=2v""" 

x2=v2.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0)  # V=2.2  

x3=v3.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0)  # V=2.4 

x4=v4.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0)  # V=2.5 

x5=v5.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0)  # V=2.6 

x6=v6.groupby(['Cycle'])[["Voltage(V)","Time","Energy(mWh)"]].nth(0)  # V=2.7 

 

x1.shape,x2.shape,x3.shape,x4.shape,x5.shape,x6.shape 

 

2.1 DT1(F1) & ES1(F7) (2v-2.2v) 

In [8]: 

result = pd.concat([x1, x2], axis=1, join="inner") 

print(result.shape) 

result.head() 

 

In [9]: 

# change in time dt1 

start=result.iloc[:,1:2] 

end= result.iloc[:,4:5] 

dt1=(end - start) 

dt1['Time']= dt1['Time'].astype('timedelta64[s]') 

dt1=dt1.dropna() 

print(dt1.head()) 

 

#change in energy de1  

start=result.iloc[:,2:3] 

end= result.iloc[:,5:] 



 

  

 

59 

 

de1=(end - start) 

de1=de1.dropna() 

print(de1.head()) 

 

In [10]: 

# change in time dt1 

start=result.iloc[:,1:2] 

end= result.iloc[:,4:5] 

dt1=(end - start) 

dt1['Time']= dt1['Time'].astype('timedelta64[s]') 

dt1=dt1.dropna() 

print(dt1.head()) 

 

#change in energy de1  

start=result.iloc[:,2:3] 

end= result.iloc[:,5:] 

de1=(end - start) 

de1=de1.dropna() 

print(de1.head()) 

 

In [11]: 

#Plot  

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

ax1.scatter(result.index ,dt1['Time'],  label='Time(s)',c='g',alpha=1,linewidth=1) #voltage 

ax2.scatter(result.index , de1['Energy(mWh)'],c='r', label='Energy(mwh)', alpha=1,linewidth=1)  # 

energy 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2v-2.2v)",size = 20) 

ax1.legend(loc=(0.01,0.9)); ax2.legend(loc=(0.01,0.95)) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

 

#ax1.set_xticks(np.arange(779, 1500, 50)); 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

2.2 DT2(F2) & ES2(F8) (2.2v-2.4v) 

In [12]: 

result1 = pd.concat([x2, x3], axis=1, join="inner") 

print(result1.shape) 

result1.head() 



 

  

 

60 

 

 

In [13]: 

# dt2 

start=result1.iloc[:,1:2] 

end= result1.iloc[:,4:5] 

dt2=(end - start) 

dt2['Time']= dt2['Time'].astype('timedelta64[s]') 

dt2=dt2.dropna() 

print(dt2.head()) 

 

#de2 

start=result1.iloc[:,2:3] 

end= result1.iloc[:,5:] 

de2=(end - start) 

de2=de2.dropna() 

print(de2.head()) 

 

In [14]: 

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

 

ax1.scatter(result1.index ,dt2['Time'],  label='Time(s)',c='g') # dt2 

ax2.scatter(result1.index , de2['Energy(mWh)'],c='r', label='Energy(mwh)')  # de2 

 

ax1.legend(loc=(0.01,0.9)); 

ax2.legend(loc=(0.01,0.95)) 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2.2v-2.4v)",size = 20) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

#fig.savefig('dv1/dt, de1/dt.png', dpi=600) 

 

 

2.3 DT3(F3) & ES3(F9) (2.4v-2.5v) 

In [15]: 

result2 = pd.concat([x3, x4], axis=1, join="inner") 

print(result2.shape) 

result2.head() 

 



 

  

 

61 

 

 

In [16]: 

# dt3 

start=result2.iloc[:,1:2] 

end= result2.iloc[:,4:5] 

dt3=(end - start) 

dt3['Time']= dt3['Time'].astype('timedelta64[s]') 

dt3=dt3.dropna() 

print(dt3.head()) 

 

#de3 

start=result2.iloc[:,2:3] 

end= result2.iloc[:,5:] 

de3=(end - start) 

de3=de3.dropna() 

print(de3.head()) 

 

In [17]: 

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

 

ax1.scatter(result2.index ,dt3['Time'],  label='Time(s)',c='g') # dt2 

ax2.scatter(result2.index , de3['Energy(mWh)'],c='r', label='Energy(mwh)')  # de2 

 

ax1.legend(loc=(0.01,0.9)); 

ax2.legend(loc=(0.01,0.95)) 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2.4v-2.5v)",size = 20) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

 

2.4 DT4(F4) & ES4(F10) (2v-2.7v) 

In [18]: 

result3 = pd.concat([x1, x4], axis=1, join="inner") 

print(result3.shape) 

result3.head() 

 

In [19]: 

# dt4 



 

  

 

62 

 

start=result3.iloc[:,1:2] 

end= result3.iloc[:,4:5] 

dt4=(end - start) 

dt4['Time']= dt4['Time'].astype('timedelta64[s]') 

dt4=dt4.dropna() 

print(dt4.head()) 

 

#de4 

start=result3.iloc[:,2:3] 

end= result3.iloc[:,5:] 

de4=(end - start) 

de4=de4.dropna() 

print(de4.head()) 

 

In [19]: 

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

 

ax1.scatter(result3.index ,dt4['Time'],c='g',  label='Time(s)') # dt2 

ax2.scatter(result3.index , de4['Energy(mWh)'],c='r', label='Energy(mwh)')  # de2 

 

ax1.legend(loc=(0.01,0.9)); 

ax2.legend(loc=(0.01,0.95)) 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2v-2.5v)",size = 20) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

2.5 DT5(F5) & ES5(F11) (2.5v-2.6v) 

In [20]: 

result4 = pd.concat([x4, x5], axis=1, join="inner") 

print(result4.shape) 

result4.head() 

 

In [21]: 

# dt5 

start=result4.iloc[:,1:2] 

end= result4.iloc[:,4:5] 

dt5=(end - start) 

dt5['Time']= dt5['Time'].astype('timedelta64[s]') 



 

  

 

63 

 

dt5=dt5.dropna() 

print(dt5.head()) 

 

#de5 

start=result4.iloc[:,2:3] 

end= result4.iloc[:,5:] 

de5=(end - start) 

de5=de5.dropna() 

print(de5.head()) 

In [22]: 

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

 

ax1.scatter(result4.index ,dt5['Time'],c='g',  label='Time(s)') # dt2 

ax2.scatter(result4.index , de5['Energy(mWh)'],c='r', label='Energy(mwh)')  # de2 

 

ax1.legend(loc=(0.01,0.9)); 

ax2.legend(loc=(0.01,0.95)) 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2.5v-2.6v)",size = 20) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

2.6 DT6(F6) & ES6(F12) (2.6v-2.7v) 

In [23]: 

result5 = pd.concat([x5, x6], axis=1, join="inner") 

print(result5.shape) 

result5.head() 

 

In [24]: 

# dt6 

start=result5.iloc[:,1:2] 

end= result5.iloc[:,4:5] 

dt6=(end - start) 

dt6['Time']= dt6['Time'].astype('timedelta64[s]') 

dt6=dt6.dropna() 

print(dt6.head()) 

 

#de6 

start=result5.iloc[:,2:3] 



 

  

 

64 

 

end= result5.iloc[:,5:] 

de6=(end - start) 

de6=de6.dropna() 

print(de6.head()) 

 

In [25]: 

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twinx() 

 

ax1.scatter(result5.index ,dt6['Time'],c='g',  label='Time(s)') # dt2 

ax2.scatter(result5.index , de6['Energy(mWh)'],c='r', label='Energy(mwh)')  # de2 

 

ax1.legend(loc=(0.01,0.9)); 

ax2.legend(loc=(0.01,0.95)) 

 

plt.title("Time and enenrgy variation over cycle for charging vlaues (2.5v-2.6v)",size = 20) 

ax1.set_xlabel('Cycle',size=(15)) 

ax1.set_ylabel('Time(s)',size=(15)) 

ax2.set_ylabel('Energy(mwh)',size=(15)) 

 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

2.7 Final Dataframe 

In [26]: 

#print the shape of each feature 

print('dt1 shape=',dt1.shape,'; dt2 shape=',(dt2.shape),'; dt3 shape=',(dt3.shape),'; dt4 shape=',(dt4.

shape) ,'; dt5 shape=',(dt5.shape),'; dt6 shape=',(dt6.shape)) 

 

print('de1 shape=',de1.shape,'; de2 shape=',(de2.shape),'; de3 shape=',(de3.shape),'; de4 shape=',(d

e4.shape)  ,'; de5 shape=',(de5.shape),'; de6 shape=',(de6.shape)) 

 

In [27]: 

#combine all features in one dataset 

Dv= pd.concat([dt1,dt2,dt3,dt4,dt5,dt6,de1,de2,de3,de4,de5,de6], axis=1, join="inner")  

Dv.columns = ['F1', 'F2','F3','F4','F5', 'F6','F7','F8','F9','F10','F11','F12'] 

print(Dv.shape[0]) 

Dv 

 

In [28]: 

#Extract the maximum recorded capcity for each cycle 

b=a 



 

  

 

65 

 

b['CapaCity(mAh)'] = round(b['CapaCity(mAh)'], 3)  

b=b.groupby('Cycle')['CapaCity(mAh)'].max() 

print(b.shape[0]) 

b.head() 

 

In [29]: 

#combine b and DV 

DV= pd.concat([b,Dv], axis=1, join="inner") 

DV.head() 

 

3. Plots 

3.1 Ploting the maximum capacity per cycle for CCCV charging phase 

In [30]: 

#1.prepare the data 

df1=df[df['C-rate'] == 1] 

df1=df1[df1.Status == 'CCCV_Chg'] 

df1=df1.groupby(['Cycle'])[["Voltage(V)","Energy(mWh)",'CapaCity(mAh)']].max()  # V=2 

df1=df1.reset_index(drop=True) 

 

print(df1.shape) 

print(df1.tail()) 

 

In [31]: 

df1.head() 

 

In [32]: 

#2.plotting part 

%matplotlib inline 

fig= plt.figure(figsize=(18,6)) 

sns.lineplot(x=df1.index, y=df1['CapaCity(mAh)'], color='orange',legend=False) 

plt.scatter(df1.index,df1['CapaCity(mAh)'], c='blue',s=15,) 

plt.title("Capacity evolution over cycles",size = 20) 

plt.xlabel("Cycle",size = 10) 

plt.ion() 

plt.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

3.2 Ploting the variation in time and energy at different voltage ranges 

In [33]: 

#1. prepare the data 

df2=df[df.Status == 'CCCV_Chg'] 

df2=df2[df2['C-rate'] == 1] 

df2=df2[df2['Cur(mA)'] != 0] 



 

  

 

66 

 

df2=df2.reset_index(drop=True) 

print(df2.shape) 

df2.head() 

 

In [34]: 

# 2. voltage ploting  

%matplotlib inline 

 

fig, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twiny();ax3=ax2.twiny(); 

 

ax1.plot(df2.index[:3852],df2.iloc[0:3852,6:7],c='g',label='C1') 

ax2.plot(df2.index[785285:785795],df2.iloc[785285:785795,6:7],c='r', label='C250')  

ax3.plot(df2.index[994536:995047],df2.iloc[994536:995047,6:7],c='b', label='C700', linewidth=1) 

 

ax1.legend(loc=(0.92,0));ax2.legend(loc=(0.92,0.04));ax3.legend(loc=(0.92,0.08)) 

#ax1.set_xticks(np.arange(0, 4000, 250)) 

ax2.set_xticks([]) 

ax3.set_xticks([]) 

 

ax1.set_xlabel('Time(s)',size=(20)) 

ax1.set_ylabel('Voltage(v)',size=(20)) 

ax1.grid(color = 'pink', linestyle = '--', linewidth = 0.5) 

 

In [35]: 

#3. Energy ploting 

 

%matplotlib inline 

 

fig1, ax1 = plt.subplots(figsize=(18,8)) 

ax2 = ax1.twiny();ax3=ax2.twiny(); 

 

ax1.plot(df2.index[:3851],df2.iloc[0:3851,8:9],c='g',label='C1') 

ax2.plot(df2.index[785285:785794],df2.iloc[785285:785794,8:9],c='r', label='C250')  

ax3.plot(df2.index[994536:995046],df2.iloc[994536:995046,8:9],c='b', label='C700', linewidth=1) 

 

ax1.legend(loc=(0.92,0));ax2.legend(loc=(0.