Comparison of Prediction Performance of Lithium Titanate Oxide Battery Discharge Capacity with Machine Learning Methods

doi:10.21203/rs.3.rs-3615930/v1

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Comparison of Prediction Performance of Lithium Titanate Oxide Battery Discharge Capacity with Machine Learning Methods

https://doi.org/10.21203/rs.3.rs-3615930/v1

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Due to the non-linear characteristics of rechargeable batteries, many studies are carried out on battery life, state of charge and health status monitoring systems, and many models are developed using different methods. Within the scope of this study Lithium Titanate Oxide (LTO) battery was discharged at room temperature with different discharge currents. Through the experiments, the discharge capacity, current, voltage and temperature values of the LTO battery were recorded and the min-max scaling method was applied to the obtained discharge experiment data. 70% of the experimental data is reserved as training data and 30% as test data. Models have been developed to estimate the discharge capacity of LTO batteries using machine learning algorithms. Random Forest, K-Nearest Neighbor, Decision Tree and Linear Regression methods were used in the prediction models. By comparing the performance values obtained from the models used, the model that makes the best estimation of the solution of the problem has been determined. In the performance evaluations of machine learning methods Explanatory Coefficient (R²), Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values were used. As a result of the study, it was seen that the Random Forest model gave the most successful result in terms of success rates with a predictive value of % 99,8836.

lithium titanate oxide battery

machine learning

battery discharge capacity estimation

artificial intelligence methods

Batteries, which have a long history, provide many conveniences in our daily lives. There are many types of batteries that are of great importance in many areas such as electronic devices, medical applications, electric vehicles, energy storage and aviation industry. Lithium-based batteries, which have become popular for many reasons such as high energy density, high cell voltage and low weight, have become more and more important day by day according to the needs of developing technology [1, 2]. The reason why lithium batteries are widely used is that the amount of energy they contain per unit volume is higher than other types of batteries and the reserves of the lithium element in nature are in processable amounts. To ensure reliability and efficiency in lithium batteries, accurate prediction of battery performance and health is necessary [3]. Accurate estimation of state of charge (SOC) plays an important role in optimizing battery energy management [4]. SOC is the internal state of the battery reflecting the energy in the battery pack an indication of the current charge. It is defined as the ratio between the remaining capacity and the total usable capacity provided by the battery [2, 5, 6]. Charge/discharge control is very important to ensure efficient, healthy and reliable operation of batteries, to increase their lifespan and to optimize their performance. State of charge estimation is a very important parameter as it provides an idea about the charge/discharge strategies of the battery protects the battery from overcharge/discharge and indicates the remaining available energy in the battery [7, 8]. Since the SOC value cannot be measured directly, various methods have been developed to estimate the state of charge. Unlike model-based SOC prediction methods whose performance relies heavily on the quality of battery models data-driven methods are model-free and easily extensible [9]. Machine learning, one of the artificial intelligence methods, is the scientific study of algorithms and statistical models that can self-learn with data-based decision making and complex pattern detection features and that computer systems use to perform a certain task without being explicitly programmed [15]. The data set obtained for the solution of a problem and the model created with the preferred machine learning method are established to achieve the highest performance in problem solving. For this reason, various machine learning methods have been developed that produce solutions to different types of problems with the highest accuracy [16, 23]. Support Vector Machines, Logistic Regression, Linear Regression, Simple Bayes, K-Nearest Neighbor, Random Forest, Decision Tree etc. are some of them.

The remainder of this article is organized as follows. In the first part literature summaries are given, and a solution proposal is put forward with machine learning algorithms to predict the capacity change in the lithium titanate battery, whose equilibrium potential and dischargeable capacity change with increasing C rates. In the second part summary information is given for the lithium titanate battery and equivalent circuit model, obtaining the discharge experiment data set, and machine learning methods used in estimating battery discharge capacity. In the third part a comparative evaluation of the changes in battery capacity during discharge experiments and the results obtained from preferred machine learning methods is included. In the last section, the results obtained from this study are interpreted.

1.1. Literature Review

Hüseyin Selçuk POLATÖZ used readily available lithium ion battery data named CS-2 and CX-2 from the University of Maryland CALCE Research Institute which are charged/discharged under different load scenarios. The data were processed with the Neural Net Fitting product of the Matlab program and the data were analyzed with forward propagation and back propagation neural network methods. Battery life estimation has been tried to be carried out with the least margin of error by selecting appropriate parameters. As a result of the studies it has been observed that if the battery data are interpreted correctly and the necessary parameters are selected from the data the error rate in the estimation results is quite low [1]. Xiaosong Hu et al. They examined the types of rechargeable batteries and compared the differences in their technologies [2]. Samarendra Pratap Singh et al. They provide technological summaries of electric vehicles as well as a review of lithium-based battery features. Various aspects of recent research and developments in current/voltage predictions, state of charge (SOC) predictions, capacity predictions, algorithms and models, and Li-ion battery state of charge prediction and health monitoring are summarized [3]. Xinyou Lin et al. They propose a SOC prediction method with adaptive unscented kalman filter (AUKF) based on an accurate equivalent circuit model. Estimating the charge state of the battery pack in electric vehicles is an important factor in ensuring efficient, healthy and reliable operation of the battery, as well as extending its life and optimizing its performance. The accuracy advantage of the equivalent circuit model was determined by comparing and analyzing the voltage response curves of different equivalent circuit models. Then, numerical verification experiments were established based on the AUKF algorithm and constant current discharge test, hybrid pulse test, and durability verification test were carried out. They used the extended kalman filter (EKF) algorithm and unscented kalman filter (UKF) algorithm to effectively evaluate the developed SOC. When the results were compared, it was seen that the AUKF-based method determined the SOC more accurately [4]. Liang Ma et al. They present a new method of performing multi-state prediction of batteries using a data-driven deep learning approach using a long short-term memory (LSTM) neural network. State of charge (SOC), which refers to usable capacity in Ah, and state of energy (SOE), which corresponds to usable energy in Wh, are two important indicators for battery management. The proposed algorithm has been validated with two dynamically driven loops for various operating conditions such as different temperatures, noise interference, and different battery materials. It has been observed that the proposed algorithm obtains more accurate results compared to known algorithms such as support vector regression (SVR), random forest (RF) and simple recurrent neural network (RNN) [5]. Icham Ben Sassi et al. Unlike traditional comparative studies, they make a detailed and critical comparison of the unscented kalman filter (UKF) and the artificial neural network (ANN), taking into account their design requirements and implementation processes. They investigate the accuracy and sensitivity of both methods to erroneous initial SOC values, their tolerance to unpredictable operating conditions, using different load scenarios and V2G (vehicle-to-grid) environment [6]. Raif Bayır et al. They determined the type and charge state of various rechargeable batteries using a cascade neural network. They monitored the electrical status of batteries online with a graphical user interface designed using a visual programming language [7]. Hannan Ma et al. They comprehensively study lithium-ion battery state-of-charge (SOC) estimation and battery management system for electric vehicle applications. One of the reasons for the increasing interest in electric vehicles is that the lithium-based batteries used in their batteries meet the energy and power density demanded from electric vehicle batteries with their advantages such as low weight, fast charging and high energy density. On the other hand, increasing concerns about global environmental problems such as global warming, greenhouse gas and CO₂ emissions, and depletion of fossil fuels also increase the interest in electric vehicles [8]. Fangfang Yang et al. They propose a recurrent neural network to obtain state-of-charge estimation (SOC) from measured current, voltage and temperature signals. Compared to feedforward neural networks, the proposed method leverages knowledge of previous SOC values and measurements and provides better prediction accuracy, is robust to unknown initial SOC values, and can be trained to learn the effect of ambient temperatures [9]. Michael Brunell conducted a study on storing lithium titanate battery cells at 0 volts, a voltage level that damages batteries in commercial battery cell storage. According to this study, the lithium titanate battery cell has demonstrated its ability to withstand low voltage conditions. This capability improves the safety level in transportation and storage and provides a competitive advantage in terms of battery transportation and replacement costs [10]. Chu Wang et al. They examined the change in power capacity of the LTO battery and the aging behavior of the battery by performing discharge experiments on cylindrical steel-shell lithium titanate cells at a rate of 66C (66 times its rated capacity) to obtain aging cycles under high-rate discharge conditions. The data obtained from the study will serve as a reference in developing the health status model for high-power batteries and in selecting cells with high power capacity. When the LTO battery was discharged at 66C for 10 cycles, the battery's capacity decreased to 80% of its initial capacity. It is predicted that the main cause of battery aging as a result of high-speed discharge cycles is that the ionic mobility in the battery deteriorates and the polarization resistance increases due to excessive discharge [11]. Ana-Irina Stroe et al. They conducted experiments for different temperatures and different C ratio ratios in a laboratory environment to observe the effect of C ratio and temperature change on the battery surface on the charge state estimation of lithium titanate oxide-based battery cell [12]. Qiuting Wang et al. They conducted experiments under constant current and dynamic operating conditions (UDDS) using three types of lithium titanate batteries. Regarding the condition estimation of lithium titanate batteries used in rail transportation vehicles, they studied the model-oriented condition estimation method on a short time scale, and the analysis of aging mechanisms based on the condition estimation result on a long time scale. The results show that the maximum voltage error of the designed battery model and prediction method is less than 2% [13]. Hamit Erdal et al. The company designed hybrid models using the principal component analysis method to determine the variables affecting the failure problem, and artificial neural networks and support vector machines from machine learning techniques for failure prediction, and examined the feasibility of failure prediction [14]. Batta Mahesh has provided a brief review of machine learning applications and a study on the future prospects of machine learning applications [15]. Vladimir Nasteski provides an overview of the basic structure and workings of various machine learning algorithms [16]. In this study by Leo Breiman, theoretical information was given about the basic structure and functioning of random forest regression [17]. Yi Li et al. They propose random forest regression, a machine learning technique for online battery capacity prediction. The proposed random forest regression is based on signals such as current, voltage and time measured during battery operation. The developed method was applied and validated on lithium nickel manganese cobalt oxide batteries with different aging patterns. Experimental results show that the proposed technique can evaluate the health states of different batteries under various cycling conditions, with an average error of less than 1.3% and a low computational requirement [18]. Manjot S. Sidhu et al. They propose an improved SOC prediction for lithium-ion battery using a hybrid machine learning technique that combines random forest regression and gaussian filter. The proposed approach includes a two-stage process consisting of random forest regression and gaussian filter. After obtaining the SOC value with random forest regression based on voltage, current and previous SOC sample data, a gaussian filter was used to reduce the variability caused by random forest regression and obtain high accuracy results [19]. Chuanjiang Li et al. They propose random forest regression to estimate the state of charge of a lithium-ion battery. They also use a backpropagation neural network to compare the performance of the proposed model. In the training of the model, battery current, battery voltage, battery temperature and other correlation factors obtained from the constant and dynamic discharge processes of the battery were determined as input data. The SOC value of the lithium-ion battery is determined as the output data of the model. Experimental results show that the proposed method can effectively predict battery SOC and has a higher prediction accuracy than the BP neural network prediction method [20]. Banu Saçlı et al. Investigated the inherent dielectric property difference between different types of kidney stones (calcium oxalate, cystine, and struvite) to enable rapid and accurate classification of kidney stones using a machine learning algorithm. They present a new approach that enables classification of kidney stones based on microwave dielectric properties with a high accuracy of 98.17% using the k-nearest neighbors (k-NN) machine learning algorithm [21]. Yaochi Tang et al. Studied a supervised machine learning model based on wind turbine noise signals and the k-nearest neighbors (k-NN) algorithm for a diagnostic method that will help detect the initial damage to wind turbine blades as early as possible [22]. Nitin Kumar Chauhan et al. They conducted a comparative study between different machine learning approaches such as SVM, PCA, LDA, decision trees, NN, naive bayes, etc., and examined the differences between traditional machine learning and deep learning by examining CNN, RNN deep learning methods [23]. Yanming Yang presents the application of multivariate linear regression model in the problem of aviation material consumption, using the data of three key monitoring indicators of aircraft tire consumption for the forecast model of aviation material consumption through multivariate linear regression. It establishes the multivariate linear regression prediction model of aircraft tire consumption and proves that the prediction model has some theoretical and practical values through various model testing methods, reflecting wide application [24]. Ismail El Kafazi et al. They conducted a study to analyze the change in energy production and predict energy production using polynomial curve fitting and linear regression methods. The results show that the polynomial curve fitting model provides the highest R² and therefore the polynomial curve fitting model is more suitable for predicting energy generation applications [25]. Songül ÇINAROĞLU created a multiple regression model consisting of machine learning regression methods to estimate per capita health expenditure. The performance results of lasso regression, random tree regression and support vector machine regression obtained when different hyperparameter values were determined were compared. The results show that the random tree regression method better predicts per capita health expenditure [26]. Nicole H. Augustin et al. Recommends quantile quantile plots for generalized linear models. These plots are closer to a straight line, making them much more useful for model checking [27]. Subhra Sankar Dhar developed a multivariate version of the Q-Q chart. He developed some statistical tests on Q-Q graphs and conducted a study on their asymptotic properties [28]. R. Wayne Oldford introduces a new and improved qqplot to aid in the interpretation of qqplots (quantile-quantile plots) by leveraging widely used computational and imaging capabilities. It introduces the self-calibrating qqplot graph by demonstrating it on various synthetic and real examples [29].

There are different methods in the literature to determine the charge/discharge status of lithium-based batteries, which deviate from the equilibrium potential and whose dischargeable capacity changes under dynamic conditions and increasing C rates. For the validity of a model developed depending on the needs and usage priorities, the necessary experimental studies must be carried out and the method must be investigated. There are many different artificial intelligence methods in the literature. In this study, it is aimed to obtain the charge/discharge status values of the lithium-titanate battery in the most accurate way and with the least error by using the machine learning method, which is one of the artificial intelligence methods. For this purpose, the lithium-titanate battery was discharged with different discharge currents and a discharge data set was obtained. The performance of machine learning models was tested using the discharge data set, the model results were compared and the discharge capacity of the battery was tried to be estimated. When the results are examined, it is seen that the Random Forest model, designed to estimate the discharge capacity of the lithium-titanate battery, predicts the battery discharge capacity with a high accuracy of 99.8836%. The battery discharge data recorded as a result of the discharge experiments of the lithium-titanate battery can be used in different artificial intelligence techniques, and the performance results of different artificial intelligence methods can be compared in estimating the battery charge/discharge state. Depending on the prediction performances of machine learning models, it can be decided which of the artificial intelligence methods is more successful in practice and this study can be expanded in this way.

In this study, lithium-titanate battery was discharged with different discharge currents. Using the obtained data set, the discharge capacity of the lithium titanate oxide battery will be estimated using different machine learning methods and the performance results of the used machine learning methods will be compared.

2.1. Lithium Titanate Oxide Batteries

Different battery parameters such as battery voltage, charge/discharge efficiency, energy density, operating temperature, safety, volume, weight, etc. affect consumers' battery preferences. Lithium Titanate Oxide (Li₄Ti₅O₁₂) is a chemistry that is gaining traction in various markets, unlike the multitude of lithium-ion battery technologies available on the market. Figure 2.1 shows the structure of the LTO cell. In the LTO battery, unlike the traditional lithium ion battery structure, lithium titanate oxide nano material is used instead of graphite in the anode electrode. It is commonly known as Lithium titanate (LTO) or nano material (nLTO). There are different manufacturers such as Leclanche, Altairnano, Microvast and Toshiba, which can produce lithium titanate powder with different chemistries for use in LTO battery cells [10].

Lithium titanate batteries have both longer cycle life and calendar life than commercially available rechargeable battery technologies such as traditional lithium-ion, nickel-metal hydride (NiMH) batteries and nickel cadmium (NiCd) batteries. The energy storage ability of any rechargeable battery will decrease as a result of repeated charge/discharge cycles. When the battery cell is discharged at increasing C levels, an imbalance or deficiency occurs between the anode and cathode materials that enter into a chemical reaction in the battery as a result of overdischarge of the battery. This imbalance in the battery disrupts the ionic mobility of the battery and as a result, the discharge capacity of the battery decreases [11]. A battery's "cycle life" is the number of times it can be charged and discharged without significant reduction in energy storage capacity. Lithium titanate battery is called a zero strain material. The zero strain state means that the material used in battery chemistry does not substantially change shape as a lithium ion moves in and out of the material during charge/discharge processes. Graphite, the most common material in traditional lithium-ion batteries, expands and contracts by up to 8% with each charge/discharge cycle. This continuous change in volume leads to a shorter cycle and calendar life compared to lithium titanate anodes. Due to their zero strain properties, even after 25,000 cycles, LTO cells retain more than 80% of their original charge capacity [30].

One of the main advantages of a lithium titanate battery is its fast charge and discharge rate. Charging rate is the rate at which battery energy is renewed. Discharge rate is the rate at which the energy stored in the battery is transferred. Thanks to the optimization of the materials used in the negative electrodes of lithium titanate battery cells, LTO batteries can charge and discharge quickly. Fast charging/discharging capacity is important for electric vehicles and public transport buses [30].

Figure 2.2 shows the operating voltage and charge state change during the charge/discharge processes of the LTO battery at room temperature. The intersection of the charge, discharge and average curves indicates that the LTO cell has a stable operating voltage.

LTO (Lithium Titanate Oxide) battery offers fast charging, high charge/discharge rate, high safety, high performance and long lifespan. Low cell voltage and high cost are the disadvantages of this battery. It can be used to create power supplies, electric vehicles, solar energy storage and smart grids.

2.2. Equivalent Circuit Model for Lithium Titanate Battery

Different types of equivalent circuit models are available to meet the different needs required by applications. Criteria such as model accuracy, calculation complexity, ease of applicability, etc. are decisive in determining the battery model. Traditionally, the first-order RC parallel network model is used to determine the polarization state of lithium-based batteries that deviate from the equilibrium potential under dynamic conditions. Using the first-order RC parallel network model as the basic model for the lithium titanate battery in this study is also useful in terms of comparison with other different battery models mentioned in the literature [13].

The lithium titanate battery equivalent circuit model in Fig. 2.3 consists of U_ocv (open circuit voltage), R₀ (ohmic internal resistance) and RC parallel network.

The initial SOC (State of Charge) value is an important parameter for estimating the state of charge and the current power capacity of the battery. The battery model can be expressed by Eq. 2.1. Here C_Q indicates the battery nominal capacity and I₀ indicates the battery discharge current [13].

\(SOC=SOC\left({t}_{0}\right)–\frac{1}{{C}_{Q}}\underset{{t}_{0}}{\overset{t}{\int }}{I}_{0}\left(t\right)d\left(t\right)\)

(2.1)

U_p (polarization voltage of the battery) can be expressed by Eq. 2.2.

\(\begin{array}{c}{U}_{p}\left(t\right)={U}_{p}{I}_{0}\left(t\right)\cdot [1-{\text{e}}^{-(t-{t}_{0})/\left(\tau \right)}],{t}_{0}<t<{t}_{1}\\ {U}_{p}\left(t\right)={U}_{p}\left({t}_{1}\right)\cdot \left[{\text{e}}^{-(t-{t}_{0})/\left(\tau \right)}\right],{t}_{1}<t<{t}_{2}\end{array}\)

(2.2)

Here, τ (time constant) is the time constant of the polarization voltage generation process and is defined as R_p*C_p.

U_o(t) (battery terminal voltage) can be expressed by Eq. 2.3.

\({U}_{0}\left(t\right)={U}_{OCV}\left(t\right)–{U}_{p}\left(t\right)–{R}_{0}{I}_{0}\left(t\right)\)

(2.3)

T_o determine the dynamic properties of the LTO (lithium titanate oxide) battery in different situations, U_OCV, R_o and C_p model parameters can be expressed as in Eq. 2.4.

\(\begin{array}{c}{U}_{OCV}\left[SOC\right(t\left)\right]{\mid }_{T={T}_{1}}={a}_{1}SOC\left(t\right)+{a}_{2}\\ {R}_{0}\left[SOC\right(t\left)\right]{\mid }_{T={T}_{1}}={b}_{1}SOC\left(t\right)+{b}_{2}\\ {C}_{p}\left[SOC\right(t\left)\right]{\mid }_{T={T}_{1}}={c}_{1}SOC\left(t\right)+{c}_{2}\end{array}\)

(2.4)

The coefficient values a₁,a₂,b₁,b₂ and c₁,c₂ can be obtained by linear interpolation based on the parameters of the characteristic points in the battery charge/discharge experiments.

2.3. Obtaining Experimental Data

The block diagram of the experimental setup established to obtain experimental data of the LTO battery and conduct charge-discharge experiments is as shown in Fig. 2.4.

Figure 2.4. Experimental Setup Block Diagram

In the experimental setup, battery discharge current, battery voltage, discharged capacity from the battery and battery temperature data were measured. These data are transferred to the computer environment via a programmable DC electronic power supply. The discharge capacity of the lithium-based battery will be estimated by running different machine learning models with the obtained battery data.

The picture of the implemented experimental setup is given in Fig. 2.5.

TDK-Lambda brand programmable power supply was used to charge the battery. With this power supply, the battery was charged with a constant charging current value of 1000 mA and the power supply was adjusted to stop the charging process at 2.8 Volts and 10mA. Gw İnstek 300 brand dc current probe was used to measure the discharge current value of the battery. With this current probe, battery current data is transferred to the programmable dc electronic load device. A K type thermocouple was used to measure the temperature values of the battery. Battery temperature data was transferred to the programmable dc electronic load device via a K-type thermocouple. Gw İnstek Pel 3111 brand programmable dc electronic load was used for the discharge process of the battery. By means of this electronic load, the battery was discharged at different current values and 1.5 volt battery voltage was set as the discharge termination voltage. Battery data was transferred to the computer environment with the multi-interface of the programmable dc electronic load device.

Through the established experimental setup, the min-max scaling method was applied to the discharge test data of the lithium-titanate battery. By scaling the values in the data set, the data to be used in machine learning models are scaled with a common scale in the range of 0–1, which is a more regular and easily understandable range, without distorting the differences between them. Thus, data values that are different from each other are represented in the range of 0–1, reducing the processing time of machine learning models and enabling the models to produce more accurate predictions.

Equation 2.5 is used for the Min-Max scaling method [14].

\({X}_{new}=({X}_{old}–{X}_{min})/({X}_{max}-{X}_{min})\)

(2.5)

In this equality; X_new : represents the new x data scaled in the data range, X_old : represents the previous value of any x data in the data range, X_min : represents the smallest x value in the data range, X_max : represents the largest x value in the data range. The technical specifications of the LTO battery used in this study are as in Table 2.1.

Table 2.1

Technical Data of the Battery Used
Item	General Parameter		Remark
Rated Capacity	Typical	500mAh	Standard discharge (1.0C ) after Standard charge
Nominal Voltage	2.4V		Mean Operation Voltage
Standard charge	Constant Current 500mA (1C) end Voltage 2.8V 10mA cut-off		Charge time : Approx 1.5h
Standard discharge	Constant current 500mA (1C) end voltage 1.5V		Max. Continuous Discharge Current 10A
Fast charge	Constant Current 1000mA (2C) end Voltage 2.8V 10mA cut-off		Charge time : Approx 0.8h
Temperature Range	Charge : 0 ~ 45℃ Discharge : -20 ~ 70℃		60 ± 25%R.H. Bare Cell

2.4. Machine Learning Methods Used in Evaluation

Machine learning is the scientific study of the algorithms, statistical models that computer systems use to perform a specific task without being explicitly programmed. It is a branch of artificial intelligence that focuses on the development of algorithms and statistical models that can learn from and make predictions on data. Machine learning is used to teach machines how to use data more efficiently and to extract information from data using computational methods [15]. Machine learning algorithms are responsible for finding patterns in the data set and creating mathematical models of them. These models are then evaluated based on their predictive capacity for measures of variance in the data itself [16]. Machine learning has various application areas such as data mining, image processing, predictive analytics, handwriting and speech recognition, robotics and computer games, natural language processing, brain-machine interface, information technology, statistics, probability, artificial intelligence, neurobiology [15, 16].

In this study, machine learning methods described below were used.

Random Forest: Random forest (RF) regression is a supervised learning algorithm and was proposed by Leo Breiman [17]. It is a collection of decision trees trained using the method commonly known as bagging, which can perform both regression and classification tasks through the use of multiple decision trees. The purpose of the bagging method is to combine multiple decision trees in determining the final output rather than relying on individual decision trees. A better result is achieved with a combination of learning models by performing random row sampling and feature sampling from the dataset, which creates sample datasets for each model [31]. Figure 2.6 shows the working principle of RF regression.

RF regression produces many decision trees for regression and its output is calculated by averaging the outputs of all decision trees [18, 19]. A random sample is selected from the entire dataset using the bagging method. By creating a regression tree, the data that are not selected and left out of the bag are used as the test set [20]. A decision tree is a model that does not have any prior tree structure, and the structure of the tree depends on the complexity of the training data in the learning phase. The decision tree consists of two nodes: the decision node and the leaf node. Each sample of training data is evaluated by decision nodes and transferred to different nodes depending on the value of the sample's features. RF regression produces regression trees using training data X given by X = x₁, x₂, x_3…x_n. This method produces k outputs T₁(x), T₂(x), ......, T_k(x) corresponding to each tree. The final result is calculated by averaging all tree predictions with Eq. 2.6 [19] .

RF(X) = \(\frac{1}{k}\)*\(\sum _{k=1}^{k}\left({T}_{k}\left(X\right)\right)\)

(2.6)

K-Nearest Neighbor: The K-nearest neighbor algorithm is a simple, supervised machine learning algorithm that can be used to solve both classification and regression problems [15, 31]. It is a machine learning method in which the class (learning set) of the data point to be subject to classification and its nearest neighbor (element) are determined and classified according to the k value (number of nearest neighbours). It is a machine learning method that classifies the data to be classified according to its close relationship with previous data. The k-nearest neighbor algorithm works by categorizing data by associating inputs with similar outputs. In a sense, the algorithm searches for similar examples in the training set when it encounters unknown data [21]. K-nearest neighbor algorithm is widely used in different fields such as fault diagnosis, power system protection and medical detection. It is easy to implement and understand [22]. It has the major disadvantage of slowing down significantly as the size of data in use grows.
Decision Tree: A graph that represents choices and their consequences in the form of a tree. Nodes in the graph represent an event or choice, and edges of the graph represent decision rules or conditions. Every tree consists of nodes and branches. Each node represents attributes in a group to be classified, and each branch represents a value the node can take [15]. Decision trees are used to classify classes by sorting them according to their parameter values. This method is suitable for small data sets but causes delay for large data sets [23].
Linear Regression: A type of supervised machine learning algorithm that calculates the linear relationship between a dependent variable and one or more independent features. When the number of independent features is one, it is known as univariate linear regression, and when there is more than one feature, it is known as multivariate linear regression [31]. Multivariate linear regression is created by generalizing linear regression by considering multiple independent variables and limiting the number of dependent variables to one [24]. The purpose of the algorithm is to find the best linear equation that can predict the value of the dependent variable based on the independent variables. The equation provides a straight line representing the relationship between the dependent and independent variables. The slope of the line indicates how much the dependent variable changes for a unit change in the independent variable(s). Linear regression is widely used in estimating energy production [25].

The working process of machine learning methods is shown in Fig. 2.7. The process starts with processing and training the data. After the model evaluation and selection is made, the parameter settings of the selected model are adjusted and finally the model predictions are tested.

The effectiveness and performance of the method used will be determined according to the accuracy of the prediction obtained from machine learning models.

In the performance evaluations of machine learning methods, Explanatory Coefficient (R²), Mean Squared Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values were used. Among these performance measures, R² is the accuracy rate decision coefficient of the model, and a high value of this coefficient indicates that the prediction relationship is good. MSE, RMSE and MAE are error measures, and their convergence to zero indicates that the model performance is with the least error and the model shows high prediction performance. For example, if the RMSE value is equal to zero, it means that the designed model has a good performance [26]. Various error metrics given in Table 2.2 were used to compare the machine learning models used in this study.

Table 2.2

Error metrics used in performance evaluation of machine learning prediction models
Name	Formula
Mean Square Error (MSE)	MSE =\(\frac{1}{N}*\sum _{İ=1}^{N}{\left({xi}_{rv}-{xi}_{ev}\right)}^{2}\)
Root Mean Square Error (RMSE)	RMSE =\(\sqrt{\frac{1}{N}*\sum _{İ=1}^{N}{\left({xi}_{rv}-{xi}_{ev}\right)}^{2}}\)
Mean Absolute Error (MAE)	MAE =\(∣\frac{1}{N}*\sum _{İ=1}^{N}{\left({xi}_{rv}-{xi}_{ev}\right)}^{2}∣\)

The difference between the actual values in a data set and the estimated values of the data is the error value. Mean square error is a value found by taking the sum of the squares of the error values occurring in a data set and dividing the result by the total number of samples in the data set. MSE provides information on how much the predicted value differs from the actual value and is a measure of accuracy performance.

In these equations;

N : total number of samples in the data range, xi_rv : real value of any x data in the data range,

MSE : mean square error, xi_ev : estimated value of any x data in the data range,

RMSE : root mean error, MAE : mean absolute error, represent.

A Q-Q plot was used to visualize how well the best-performing Random Forest model predictions in terms of error metrics (MSE, RMSE, MAE) and R² value fit the actual values. Q-Q plot [27] is a graphical method used to determine whether two data samples come from the same population [28, 32]. It shows the comparison of theoretical quantile values of a probability distribution with its actual values and is used to evaluate how well the probability distribution fits the normal distribution or how close it is to another distribution [28, 29]. These graphs show how well the model predictions fit the actual values and how close the error distributions are to a normal distribution [28]. Such Q-Q plots are often used to test the assumption of normality or to visualize how well predictions fit actual values [29]. If the points are tightly distributed along the line, the model's predictions are in good agreement with the actual values. When the points move away from the line, it means that the estimates tend to deviate from the actual values.

During discharge experiments with increasing C rates, the changes in the dischargeable and usable capacity of the LTO battery are seen in Fig. 3.1.

Discharge experiments performed at low-level discharge current rates between 1C and 5C show that more than 99% of the battery's usable capacity can be discharged. In discharge experiments performed at moderate discharge current rates between 6C and 10C, it is seen that 96% of the battery's usable capacity can be discharged. In discharge experiments conducted at high level discharge current rates between 11C and 15C, it is seen that 83% of the battery's usable capacity can be discharged and the battery's usable capacity is exhausted in a very short time. Excessive discharge of the battery affects the ionic mobility balance between the anode and cathode materials, which chemically react at the positive and negative poles of the battery, and limits the capacity that can be discharged from the battery.

In tests performed with machine learning models R², MSE, RMSE and MAE values were taken as basis in evaluating model performance. The results obtained from the models studied to estimate the discharge capacity of the LTO battery are shown in Table 3.1. The situation where the R² value approaches 1 and the MSE value approaches 0 is the parameter used to determine the most successful of the machine learning models used in this study.

Table 3.1

Comparison of Machine Learning Methods Results
Evaluation Criteria	MSE	RMSE	MAE	R²	Accuracy
Random Forest	0,000092	0,009616	0,004285	0,998836	0,998836
K-Nearest Neighbor	0,000105	0,010237	0,003924	0,998681	0,998681
Decision Tree	0,000201	0,014186	0,005563	0,997467	0,997467
Linear Regression	0,011611	0,107753	0,088806	0,853870	0,853870

When Table 3.1 is examined ;

It is seen that the Random Forest model is the best performing model compared to other models in terms of both R² value and error metrics (MSE, RMSE, MAE). The correct prediction rate of 0.998836 shows that the model has a high ability to make correct classification.

The K-Nearest Neighbor model has slightly higher error metrics than the random forest model, but its R² value is still quite high and it performs very close to the Random Forest model.

The Decision Tree model has higher error values and a slightly lower R² value than the Random Forest and K-Nearest Neighbor models. This means that the Decision Tree model captures slightly less of the variance in the data set.

Linear Regression model, error metrics (especially MSE) are quite high compared to other models. The R² value of 0.853870 is quite low compared to other models. This means that the linear regression model captures 85% of the variance in the data set, indicating that the model is less suitable for this data set compared to others.

When we examine the Q-Q graph of Random Forest and K-Nearest Neighbor Models shown in Fig. 3.2, it is seen that the models comply with the normal distribution and the end points are far from the normal distribution due to outliers. This shows that both models capture the data set quite well.

To check whether there is overfitting in the machine learning models used, the model predictions made with the training and test data specified in Table 3.2 can be compared.

Table 3.2

Overfitting Control of Machine Learning Methods
Models	TRAINING			TEST
Models	MSE	R²	Accuracy	MSE	RMSE	MAE	R²	Accuracy
Random Forest	1.264583e-05	0.999839	0.999839	0.000092	0.009616	0.004285	0.999836	0.999836
KNN	6.190308e-05	0.999212	0.999212	0.000105	0.010233	0.003921	0.998682	0.998682
Decision Tree	1.757578e-07	0.999998	0.999998	0.000201	0.014186	0.005563	0.997467	0.997467
Linear Reg.	1.150412e-02	0.853500	0.853500	0.011611	0.107753	0.088806	0.853870	0.853870

When we look at the performance metrics on the training and test data set, we see that there is no significant difference between the training and test results for Random Forest, KNN, Decision Tree and Linear Regression methods. This shows that the models do not engage in excessive learning and repetition (overfitting).

From the graph in Fig. 3.3, it can be said that the error distribution of the random forest model is good. The points are generally tightly aligned around the line, indicating that the model predictions are closer to the actual values.

Random Forest gave the best results with accuracy rates of 99.8836% and K-Nearest Neighbor 99.8681%. The Linear Regression method shows a worse performance compared to other models, with an accuracy rate of 85.3870%. Experimental results show that Random Forest and K-Nearest Neighbor methods have the highest R² and lowest MSE, MAE rates.

In order to determine the applicability of a theoretically designed method, the necessary experimental studies must be carried out and the designed method must be investigated. Which method to choose depends on your application's needs and priorities. Other factors such as forecast time, size of the model, or understandability of the model also influence model selection. This study can be expanded by comparing the performance results of different artificial intelligence methods in battery discharge prediction by using the battery discharge data recorded as a result of the discharge experiments of the lithium-titanate battery.

In this study, the relationship between the current, voltage and temperature data of the lithium titanate battery and the discharge capacity of the battery was examined. The lithium-titanate battery was discharged with different discharge currents, and from the recorded data, the current, voltage and temperature data of the battery were determined as the input parameters of the machine learning models. The discharge capacity of the battery is determined as the output parameter in machine learning models. The performance of machine learning models was tested using the discharge data set, the model results were compared and the discharge capacity of the battery was tried to be estimated.

When the results are examined, it is seen that the Random Forest model, designed to predict the discharge capacity of the lithium titanate battery with machine learning methods, predicts the battery discharge capacity with a high accuracy of 99.8836%. Linear Regression method shows the worst performance with an accuracy rate of 85.3870%.

Author Contribution

All authors contributed to the concept and design of the study. Material preparation, data collection and analysis were carried out by [Ilyas ANDIK], [Fatma Yasemin ARSLAN] and [Ali UYSAL]. The first draft of the article was written by [Ilyas ANDIK], and all authors commented on previous versions of the article. All authors read and approved the final manuscript.IA: Wrote the main manuscript text. AU: Project management and supervision. IA and FYA: visualization and research, conceptualization. All authors reviewed the article.

Acknowledgements

The authors express their sincere gratitude to the editor and independent reviewers who provided valuable comments and suggestions to this article and declare that there is no conflict of interest regarding the publication of this article.

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Comparison of Prediction Performance of Lithium Titanate Oxide Battery Discharge Capacity with Machine Learning Methods

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Abstract

Figures

1. Introduction

1.1. Literature Review

2. Material and Method

2.1. Lithium Titanate Oxide Batteries

2.2. Equivalent Circuit Model for Lithium Titanate Battery

2.3. Obtaining Experimental Data

2.4. Machine Learning Methods Used in Evaluation

3. Research Results

4. Conclusion

Declarations

Author Contribution

Acknowledgements

References

Additional Declarations

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