Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 84 https://internationalpubls.com Mathematical Analysis and Non-Linear Optimization of EV Battery Health Using Fuzzy Logic and Neural Computing Techniques Dr. Sunil Kumar Gupta1, Abhinav Kashyap2, Dr. Siddharthsingh K. Chauhan3, Dr. Vineeta Chauhan4, Dr. Ashish Raj5 1Professor, Department of Electrical and Electronics Engineering, Poornima University, Jaipur, India 2Assistant Professor, Department of Mechanical Engineering, School of Engineering, P P Savani University, Surat, India 3Associate Professor, Institute of Technology, Nirma University, Ahmedabad, Gujarat (India) 4Assistant Professor, Indus University, Ahmedabad, Gujarat (India) 5Associate Professor, Department of Electrical and Electronics Engineering, Poornima University, Jaipur (India) Email: sunil.gupta@poornima.edu.in, abh.ksh20@gmail.com Article History: Received: 05-03-2024 Revised: 22-04-2024 Accepted: 08-05-2024 Abstract: This article is related to a mathematical optimization model of the electric vehicle (EV) battery health management, which is based on fuzzy logics and neural network models. The study achieves a neural network to recognize charging patterns and preceding SOC in addition to the full charge temperature dependent upon the duration and ampere within the Multiple-Stage Constant Current (MCC). The target is SOC of 83%, which is made in 43 minutes upon maintaining the optimal temperature factor (of about 35 degrees). 85°C, representing a 3. At this point we observed 30% higher specific output capacity (SOC) versus standard constant current- constant voltage (CC-CV) method with a very small temperature increase of only 0. 41°C. The project includes several technical specifications, such as 96s2p where the complete battery runs through 192 cells, 40 kWh nominal capacity and 350 V nominal voltage. The flow of work will be database creation and management, the design of the simulation, machine learning model creation, testing and evaluation. The dataset is built from a sample, which includes features like the temperature within the room, the starting temperature of the battery and the time points (t1, t2, t3, t4); these are used for the training the machine learning algorithm. The simulation is followed by determination of the SOC and battery temperature, which are utilized as target features by the model. In Exploratory Data Analysis (EDA) one can highlight all the essential statistics while developing neural network model. Approach incorporated means of data analysis which include distribution, identification, and correlation, and prepared the way for outliers to be handled. The optimization outcomes per 28 degrees display the performance of the joint neural network and fuzzy logic method. The model gives SOC level above 80% with final temperature below 40°C, in which the errors of the voltage and temperature are lower than 2% and 1%, respectively. The fuzzy logic does that it has a parameter choosing method that makes the final battery temperature to go down and thus improves SOC as compared to other parameters method. This paper gives an insight into the use of hybrid optimization via combining three main variables: fuzzy logic, neural networks as well as various criteria of battery health management, the final result is optimization of charging parameters into EV's life. Keywords: Fuzzy Logic, Neural Networks, EV Battery Optimization, State of Charge (SOC), Battery Health Management, Multi-Stage Constant Current (MCC) Charging, Mathematical Modeling, Nonlinear Optimization, Machine Learning, Battery Temperature Control. mailto:sunil.gupta@poornima.edu.in mailto:abh.ksh20@gmail.com Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 85 https://internationalpubls.com 1. INTRODUCTION The EVs possess a fundamental role in the field of green mobility, as they provide an attractive alternative to the reduction of the greenhouse emissions during the combustion to the dependence on the fossil fuels. Nonetheless, there is a huge challenge of whether EVs all over the world can play their expected role in so far as their performance and health are concerned. Batteries are the central factors of the electric vehicles such as their efficiency, durability and security, and these factors build the foundation for a sustainable development of this technology. The principal direction is the management of the battery charging and discharging nonlinear behaviors as this downgrades both the battery state of charge (SOC) and temperature, among other things. These elements are essential for promoting the battery's health and performance being lasting during its service life. Battery charging optimization is a very challenging task riddled with interdependent factors that are insignificant individually but take critical nature when influencing each other, including current levels, temperature, and SOC. CC-CV (constant current - constant voltage) device electricity management methods that are current in the market have many disadvantages that may result in underperforming batteries and a reduction of their life. Hence, this motivates the engineers to come up with the modern algorithms that will able to solve the complicated dynamics of battery recharging. Here, the fuzzy logic and neural network-type mathematical optimization are deployed in order to deal with the defined water shortage challenges. Thus, it accomplishes the goal using the hydrocarbon compounds to store energy non- chemically by employing the computational techniques to increase the efficiency and accuracy of the systems that manage electric vehicles’ battery health. The non-uniform character of the batteries behavior most especially during discharging and charging increases the complication in terms of algorithm and hence the necessitation of sophisticated optimization. Batteries do not charge uniformly: charging of the same battery at the same current under different conditions can progress at various rates [1-14]. Table 1: Analysis of Related Works [1-17] Authors Year Main Findings Methodological Limitations Wenxia et al. 2016 Developed a greedy method to address the location problem within an acceptable timeframe. Considered only a few factors for station location. Alipour et al. 2017 Created a stochastic schedule but disregarded price sensitivity. Limited scope of analysis to price insensitivity, potentially increasing distribution system losses. Bayram et al. 2016 Found correlation between charging demands and solar output at a university campus. - Galiveeti et al. 2018 Added DG units to a CS-integrated system to reduce network power loss. Focused on adding DGs before finding optimal CS locations, which is not always feasible. Pallonetto et al. 2016 Chose optimal CS location considering high solar panel penetration. Only one charging station was considered; driver behavior was not accounted for. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 86 https://internationalpubls.com Miralinaghi et al. 2016 Aimed to reduce total ownership cost (TOC) considering driving distance and recharging time. Did not incorporate the option of skipping trips in the final solution. Huang et al. 2015 Scheduled PHEV charging at night to reduce operational costs. High night-time load could be problematic; study did not consider varied workplace locations for charging. Alharbi et al. 2014 Analyzed the impact of home charging on the distribution grid. Relied on specific charging times, which may not hold in real scenarios. Shuai et al. 2016 Reviewed smart grid scheduling for lowering PHEV charging costs. - Gheorghe Badea et al. 2019 Planned an EV charging station in a remote area using solar energy. - M. Zeman et al. 2016 Studied solar energy for charging EVs in the Netherlands. Due to low solar insolation, required a higher- rated PV array than the converter. Thenmozhi G et al. 2020 Proposed a solar-powered electric vehicle. - Jamuna K et al. 2021 Described charging of electric vehicles in office parking using PV cells. - Seyezhai et al. 2019 Analyzed high-quality DC-DC converters for battery charging. - Shambhavi Bade et al. 2020 Used a sliding mode controlled SEPIC converter for optimal operation of a PV panel. - Qi Liu et al. 2016 Proposed alternatives for the photovoltaic architecture of charging stations. - Siddiq Khateeb et al. 2018 Discussed the global infrastructure for solar PV-EV charging. - These conditions include initial temperature, ambient temperature, and the current, among others, which are applied at different stages of the charging process. This non-linearity stands out most in that they do not have any straight line relationship with the SOC and temperature which makes it difficult to model and control. Linear optimization methods, such as techniques that involve fuzzy logic or neural networks, are usually the best-fit because of their ability to accommodate the complexities [14- 18]. They can build the correlation among the several elements using the modified predictions and management system of control tools. Fuzzy logic is regarded as the world of handling uncertainties and inaccuracy that BMS in the state of charge is characterized with. Linguistic variables and the matrix of rules are established to imitate the style of decision making of a human. It allows the invention of adaptive and bendy systems governing the range of parameters of the battery. Although the neural networks are the most accurate machines for detection and prediction of patterns, they are Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 87 https://internationalpubls.com also prone to biases and errors. They are able to study what was hidden in the historical data and locate emerging strategies as a new method of non-traditional analytical approaches. Through combining the two we can develop an adaptive charging optimization system that can be used to set the charger parameters dynamically to maximize battery performance whiles enhancing the battery’s life [15-24]. Mobilization of EVs seems to be entirely dependent on efficient storage of energy. That is delivered by the advanced battery system. The indicated system should be handled effectively such that one gets a powerful battery life, efficiency and a smooth performance. Without battery management system, which are in charge of charge and release power, safety and battery’s lifespan prolongation, battery cannot work properly. Such engineering methods are liable to utilize the mathematics modeling and advanced algorithms which are the basic factors for improvement in EVs (electric vehicles) [24-32]. Battery Charging Non Linear Dynamics : The State of Charge (SOC) is a critical parameter in battery technology, indicating the current energy level of the battery compared to its total capacity. It is typically expressed as a percentage: SOC(𝑡) = SOC⁡(𝑡 − 1) + Δ𝑡 × 𝑙(𝑡) 𝐶 × 3600 (1) Here, 𝐼(𝑡) represents the current, 𝐶 is the total capacity, and Δ𝑡 is the time increment, showing how 𝑆𝑂𝐶 evolves as the battery charges. The charging strategy is pivotal, particularly in how the current is modified over time to optimize both charging speed and battery health. A multi-stage current profile (MCC) can be effectively modeled as a piecewise function, adjusting the current at different phases of the charging cycle: 𝐼(𝑡) = { 𝐼1 if 0 ≤ 𝑡 ≤ 𝑡1 𝐼2 if 𝑡1 < 𝑡 ≤ 𝑡2 𝐼3 if 𝑡2 < 𝑡 ≤ 𝑡3 𝐼4 if 𝑡3 < 𝑡 ≤ 𝑡4 (2) Voltage dynamics are crucial as they affect both the charging speed and the longevity of the battery. Managing voltage carefully to avoid exceeding the battery's voltage limit, which can cause damage, is essential. Battery temperature significantly impacts both the efficiency and lifespan of the battery. Excessive heat generation during charging can lead to thermal runaway, a dangerous condition. The heat generation model and cooling rate are expressed as: 𝑄(𝑡) = 𝐼(𝑡)2 × 𝑅⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(3) 𝑑𝑇 𝑑𝑡 = 𝑄(𝑡) − ℎ × (𝑇(𝑡) − 𝑇𝑚+) 𝑚 × 𝑐𝑝 ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(4) Here, 𝑄(𝑡) represents the heat generated, 𝑅 is the internal resistance, ℎ is the heat transfer coefficient, 𝑇env is the ambient temperature, 𝑚 is the battery's mass, and 𝑐𝑝 is the specific heat capacity. Neural networks are utilized to predict the 𝑆𝑂𝐶 and temperature at the end of the charging process. The inputs to these networks include initial conditions, environmental factors, and historical data from the charging process. These models learn from the data to make accurate predictions about the future state of the battery: Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 88 https://internationalpubls.com SOĈ(𝑡4) = 𝑓NN(𝑇0, 𝑇rooma , 𝑡1, 𝑡2, 𝑡3, 𝑡4)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(5) �̂�(𝑡4) = 𝑔NN(𝑇0, 𝑇roamu , 𝑡1, 𝑡2, 𝑡3, 𝑡4)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(6) Optimization Techniques The primary objective is to minimize the total charging time while ensuring that the 𝑆𝑂𝐶 reaches a desired level without the temperature exceeding a specific threshold. This involves complex constraints and requires advanced optimization algorithms: ⁡min∑   4 𝑖−1   𝑡𝑖 ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(7) SOC(𝑡4) ≥ 83% 𝑇(𝑡4) ≤ 35.85∘C Fuzzy logic is employed to handle uncertainty and variability in battery charging. It adjusts the charging parameters in real-time based on fuzzy rules, which can better manage the nuances of battery behavior under different conditions: 𝑡new ,𝑖 = Fuzzy Adjust (𝑡𝑖, ΔSOC, Δ𝑇) (8) Gradient descent, stochastic gradient descent, and simulated annealing are techniques used to find optimal charging schedules. These methods adjust the parameters iteratively to minimize errors between predicted and actual outcomes: 𝑡𝑖+1 = 𝑡𝑖 − 𝜆 ∂ Eirtorsact 𝑖𝑡𝑖 ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(9) ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑇(𝑡) = 𝑇0 × 𝑒−𝑘𝑡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(10) ⁡⁡⁡⁡⁡⁡⁡⁡ Neural networks are employed to predict the 𝑆𝑂𝐶 and temperature at the end of the charging process. The inputs to these networks include initial conditions, environmental factors, and historical data from the charging process. The networks learn from this data to make accurate predictions about the battery's state at any future point. SOĈ(𝑡4) = 𝑓NN(𝑇0, 𝑇room , 𝑡1, 𝑡2, 𝑡3, 𝑡4) �̂�(𝑡4) = 𝑔NN(𝑇0, 𝑇room , 𝑡1, 𝑡2, 𝑡3, 𝑡4) (11) The final step involves implementing these models in a simulation environment or directly in the BMS hardware. The models are evaluated based on their accuracy in predicting 𝑆𝑂𝐶 and temperature, their impact on battery health, and their effectiveness in optimizing charging times. The integration of neural networks and fuzzy logic into the battery charging process represents a significant advancement in battery management technology, allowing for more sophisticated and responsive control strategies that can adapt to the needs of modern electric vehicles. Overview of Fuzzy Logic and Neural Network Techniques Fuzzy logic (Fuzzy logic), which is getting a lot of attention now, was introduced by Lotfi Zadeh in the 1960s under the name of an approach that allows investigating and solving reasoning issues that are approximate. In the application of fuzzy logic for battery management, the principle involves the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 89 https://internationalpubls.com fuzziness and unpredictability of battery characteristics to improve battery function. For example, the idea of three-layer membership is replaced by a more gradual interpretation based on degrees of membership that justifies the scale of warm or cold that is needed. The ability to adapt is what particularly describes this operation allowing the controlled charging rate as well as maintaining the temperature of the battery which is very vital for an efficient charge. Neural networks, which are basically models inspired by the human brain, include of layers which are connected through nodes (neurons). Such networks own a remarkable ability to learn from data gradually, and this process continues until the networks achieve the best performance. In battery management, neural networks can be programmed to be able to forecast and the state of the charge and temperature using historical charging data as a reference. While neural networks make it possible to realize patterns in the data, these patterns in turn provide accurate predictions that are the key for improving charging process. The merging of fuzzy logic and neural network provides an effective machinery for handling the intricate non-linearity characteristic of the storage batteries powering EVs. Implementation of Fuzzy Logic and Neural Network in Battery Optimization The principles of fuzzy logic and neural networks are involved in the EV battery optimization through the stages of sensor inputs, fuzzy system identification, and online execution. The first step is to get together a total dataset containing some factors like the initial temperature of battery, room temperature, charging speed, and charging stages. These data sets make up a foundation for the training of neural network model. After the data collection is accomplished, the next stage is to clean up the data, done by correction of inconsistencies or outliers. The precise work of data preprocessing serves to cut down the error rate of the neural network model. Standardization and outlier processing are tools we use in order to clean and prepare the data for the training phase. The neural network is the last stage and this one is then trained with the help of the preprocessed data having an object of learning the complex connection that exists between the inputting parameters and the targeting variables (SOC and Final Battery Temperature). While that, fuzzy logic controller managing of charging process is put-together as well. The fuzzy logic controller uses a set of rules that is based on the decision criteria of experts to determine the optimal charging parameters. This is a calculated algorithm which is responsible to maximize the SOC while keeping the battery temperature under the safe limit threshold. The fuzzy logic controller harmonizes with the neural net performance and adjusts the charging regime based on the real-time predictions of neural network. The combination of weakening and neural networks makes the system to be an adaptive null optimal process however. As a result, it keeps on tracking the battery's state and making adjustments on the charging parameters, the system guarantees that the battery operates efficiently and safely. Moreover, this technology will elevate the power and last ability of battery pack as well as guaranteeing a very good trustworthy of the EV. 2. PROPOSED METHODOLOGY This research proposes an advanced methodology for optimizing the charging process of electric vehicle (EV) batteries using neural networks and fuzzy logic. By integrating these computational Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 90 https://internationalpubls.com techniques, the research aims to improve the accuracy of predicting and managing the state of charge (SOC) and temperature, key factors in enhancing battery efficiency and longevity. The primary objective is to develop a robust model that: 1. Accurately predicts SOC and temperature at various stages of the charging cycle. 2. Dynamically adjusts charging parameters to maximize battery health and performance. 3. Outperforms traditional constant current-constant voltage (CC-CV) methods in terms of efficiency and battery health conservation. Methodological Framework Database Creation and Management The initial phase involves creating a comprehensive dataset that captures various parameters influencing battery behavior. This dataset will include: • Battery Initial Temperature (𝑇0) : Influences the rate of charging and efficiency. • Room Temperature (𝑇room ) : Environmental factor affecting charging dynamics. • Charging Durations (𝑡1, 𝑡2, 𝑡3, 𝑡4) :Specific time intervals for charging stages. • Final SOC(SOCfinal ) ) The target state of charge post-charging. • Final Battery Temperature (𝑇fimal ) : Reflects thermal management effectiveness. Equations used to derive initial data: SOC(𝑡) = SOC(𝑡 − 1) + Δ𝑡 × 𝐼(𝑡) 𝐶 × 3600⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(12) 𝑇(𝑡) = 𝑇(𝑡 − 1) + Δ𝑇⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(13) Where Δ𝑇 represents the temperature change influenced by internal and external factors, and 𝐼(𝑡) is the current at time 𝑡. An extensive EDA will be conducted to understand data patterns and distributions. This includes: • Calculating statistical metrics such as mean, median, and standard deviation. • Analyzing correlations between 𝑆𝑂𝐶, temperature, and time intervals. Corr⁡(𝑋, 𝑌) = Cov⁡(𝑋,𝑌) 𝜎𝑋𝜎𝑌 (14) Where Corr is the correlation coefficient, Cov is the covariance, and 𝜎 represents the standard deviation. A neural network model will be trained to predict SOC and temperature based on input features. The model architecture will include: • Input Layer: Accepts raw data as input. • Hidden Layers: Multiple layers to process data non-linearly. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 91 https://internationalpubls.com • Output Layer: Produces predicted SOC and temperature. 𝑦=𝑓(𝑊⋅𝑥+𝑏) Where 𝑦y is the output, 𝑓f is the activation function, 𝑊W and 𝑏b are the weights and biases, and 𝑥x is the input. Fuzzy Logic Integration To handle uncertainties and fine-tune the charging process, a fuzzy logic controller will be implemented. This controller will adjust charging parameters in real-time based on: • If-Then rules derived from the expert knowledge. Membership functions defining the linguistic variables. To handle uncertainties and fine-tune the charging process, a fuzzy logic controller will be implemented. This controller will adjust charging parameters in real-time based on: • If-Then rules derived from expert knowledge. • Membership functions defining the linguistic variables. 𝜇High SOC (𝑥) = { 0 if 𝑥 < 80% 𝑥−60% 100%−00% if 80% ≤ 𝑥 ≤ 100% 1 if 𝑥 > 100% (15) Where 𝜇High𝑆𝑂𝐶 defines the degree of membership to the "High 𝑆𝑂𝐶 " fuzzy set. Optimization and Testing The optimized parameters from both neural network predictions and fuzzy logic adjustments will be tested through: • Simulations using varied environmental and operational conditions. • Real-time implementation in a controlled environment to validate model predictions against actual outcomes. Error SOC =∣ Predicted SOC - Actual SOC ∣ (16) Error ⁡𝑇 =∣ Predicted Temperature - Actual Temperature ∣ (17) The final step involves evaluating the model's performance and iteratively refining the system based on: • Performance metrics such as Mean Square--1 Error (MSE) for predictions. • Feedback from the testing phase to improve model accuracy and reliability. MSE = 1 𝑛 ∑  𝑛 𝑖−1 ( Predicted 𝑖 − Actual 𝑖) 2 (18) Where 𝑛 is the number of observations. This methodology leverages advanced machine learning and fuzzy logic to manage the complexities of battery charging in electric vehicles, aiming to optimize both performance and longevity through a systematic, data-driven approach. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 92 https://internationalpubls.com 3. RESULT ANALYSIS This research analyzes the usage of neural networks and fuzzy logic for conditions during the charging process of EV batteries which aims at optimizing the overall outcome. GOE's results - which shows improvements in capacity and temperature management - obviously proves the method's effectiveness, making batteries last longer and run much better. The research scored a highly remarkable SOC of about 83% in the less than 45 minutes charging duration. This represents a 3. So the high efficiency of OTLP was proven by a 38% increase in contrast to the conventional constant current-constant voltage (CC-CV) approach. The fundamental factor that not only increases the charging method efficiency but also significantly shrinks the total charging time (which is very important for the user convenience and battery health) lies in this charge enhancement technology. Thermal management is absolutely necessary for ensuring the functioning of the cells of battery. The research method adopted optimally the battery temperature of almost 35 that was controlled. 85°C, just marginally--but at least--a slight temperature increase of 0. Traditional methods for centralized power generation are outperformed by solar prowess at 41°C. Adequate thermal management can help maintain the optimal temperature, enabling greater cycle life and safety from risks that may cause the overheating. The fact that the machine learning algorithm that predicted the operation cycles and battery temperature by taking into account different durations of charging and the level of current supplied was deemed as the key. The neural network provided the machine with a capability of learning historical data and recognizing patterns toward achieving more accurate and adaptive control which generated more precise and accurate decisions. The acceptance of fuzzy logic consideration meant that the process of managing the charging algorithm got smarter and at some point, not using the standard but relying on flexible approach. Using rules that are not hard-wired, fuzzy logic supplied with a way to freely adjust current consumed for charging by adapting to charge based on the status of the battery, thus increasing the charging efficiency by ensuring that temperature is maintained under safe regulations. Table 2: Battery Specifications and Technical Parameters Technical Index Value Number of battery cells 192 Battery configuration 96s2p Nominal capacity 40 kWh Nominal voltage 350 V Number of battery modules 24 Battery cell size: Width 261 mm Battery cell size: Length 216 mm Battery cell size: Thickness 7.9 mm Maximum power 46 kW Average power 40 kW Battery temperature tolerance 45°C to 60°C Charging time (10% to 80%) 43 minutes Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 93 https://internationalpubls.com Table 3: Database Creation and Management Sample Data Battery Initial Temp (°C) Room Temp (°C) t1 (s) t2 (s) t3 (s) t4 (s) Final Battery SOC (%) Final Battery Temp (°C) 25.66 28.12 1989.83 2484.47 2542.12 2576.31 0.85 317.30 29.56 30.14 2423.81 2577.48 2579.01 2579.66 0.88 310.02 30.12 32.78 1146.96 1646.36 1827.81 2462.77 0.78 310.98 Table 4: Exploratory Data Analysis (EDA) Summary Parameter Count Mean Standard Deviation Minimum 25th Percentile Median 75th Percentile Maximum Battery Initial Temp. 149 28.58 2.04 25.06 26.85 28.69 30.25 31.90 Room Temp. 149 28.31 2.06 25.03 26.30 28.19 30.15 31.91 t1 149 1300 757 0.88 647 1257 1922 2573 t2 149 1926 567 198 1571 2063 2393 2579 t3 149 2251 355 917 2096 2391 2527 2580 t4 149 2413 219 1721 2367 2518 2562 2580 Final SOC 149 77.78 0.09 48.66 72.06 79.80 84.38 89.43 Final Battery Temp 149 37.65 3.44 31.33 35.65 37.46 38.67 51.57 Table 2: Battery Specifications and Technical Parameters provided a snapshot of the battery's technical specifications such as number of cells, configuration, nominal capacity, and voltage. Such detailed specifications are crucial for understanding the baseline performance and capabilities of the battery system under study. Table 3: Initial Conditions and Battery Parameters involved detailed recordings of initial temperatures, room temperatures, and specific time intervals (t1 to t4), which were essential for running the simulations and feeding into the machine learning models. plaintext Table 4: EDA Summary Statistics provided insights into the mean, standard deviation, and other statistical measures of the collected data, which was foundational for the initial setup of the neural network models. Plaintext. Table 5 to 7: Optimization and Prediction Outcomes highlighted the results from the optimization algorithms, showing predicted versus actual SOC and temperatures, showcasing the precision and effectiveness of the combined neural network and fuzzy logic approach. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 94 https://internationalpubls.com Figure 1: Design of Fuzzy Inference Systems Figure 2: Analysis on Behavior of Parameters with Respect to Temperature Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 95 https://internationalpubls.com Figure 3: Comparison Between Predicted and Actual Value Figure 4: Analysis of Correlation Heat map Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 96 https://internationalpubls.com Figure 5: Analysis of Battery Temperature Figure 6: Analysis of Predicted V/s Simulated Temperature Figure 7. Analysis of Predicted V/s Simulated SOC Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 97 https://internationalpubls.com Figure 8: Analysis of Battery Temperature with respect to Time The following tables illustrate the results from the optimization process using a combination of neural network and fuzzy logic at an ambient temperature of 28°C. Detailed outcomes for each battery initial temperature setting are provided below: Table 5: Battery Initial Temperature = 28°C Parameter t1 (s) t2 (s) t3 (s) t4 (s) Predicted Final SOC (%) Simulated Final SOC (%) SOC Error (%) Predicted Final Temp (°C) Simulated Final Temp (°C) Temp Error (%) Minimum Temperature (°C) 2011.88 2226.44 2230.75 2242.59 81.56 80.44 1.12 35.86 35.86 0.02 Maximum SOC (%) 2114.65 2274.17 2287.36 2578.50 83.92 84.76 0.84 36.13 35.98 0.41 Fuzzy Logic 2063.26 2228.37 2228.64 2265.96 82.74 81.07 1.67 35.99 35.89 0.29 Table 6: Battery Initial Temp = 30°C Parameter t1 (s) t2 (s) t3 (s) t4 (s) Predicted Final SOC (%) Simulated Final SOC (%) SOC Error (%) Predicted Final Temp (°C) Simulated Final Temp (°C) Temp Error (%) Minimum Temperature (°C) 2002.33 2226.90 2236.72 2366.84 81.84 81.31 0.53 35.80 35.86 0.16 Maximum SOC (%) 2113.85 2253.35 2255.27 2578.86 83.44 84.25 0.81 36.12 35.95 0.46 Fuzzy Logic 2058.09 2237.66 2238.99 2574.71 82.64 83.46 0.82 35.96 35.91 0.14 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 98 https://internationalpubls.com Table 7: Battery Initial Temp = 32°C Parameter t1 (s) t2 (s) t3 (s) t4 (s) Predicted Final SOC (%) Simulated Final SOC (%) SOC Error (%) Predicted Final Temp (°C) Simulated Final Temp (°C) Temp Error (%) Minimum Temperature (°C) 2083.44 2225.97 2228.84 2239.54 82.67 80.97 1.70 36.10 36.42 0.88 Maximum SOC (%) 2114.79 2228.06 2267.70 2578.45 84.08 84.12 0.04 36.51 36.48 0.09 Fuzzy Logic 2099.12 2230.86 2231.22 2327.76 83.38 81.83 1.55 36.31 36.44 0.37 Hence, these tables are exemplary at presenting the outcomes of the study as well supporting academic talks on the methodological novelties presented in the paper by the main idea of integrating deep neural networks and fuzzy logic for optimal discharging of the battery. The application of neural networks and game theory in SOC and battery temperature management showed very powerful performance during battery charging which was beyond the scope of traditional methods. Such an innovative methodology, on the other hand, provides a smarter charging mechanism, ensured through the safer path, and serves to prolong the battery lifespan, which is a crucial factor for EV technology sustainability. The degree of precision in predictions and flexibility in charging-change adaptations is another feature that illustrates the significance of advanced computational methods in present battery management systems. The results of the study have achieved the result of a combined fuzzy logic and neural network application, being the best method for the improvement of battery charging of electric vehicles. The outcomes of experiment revealed that the system was able to reach a SOC value of 83% in a charging time of 45 min and the battery temperature was maintained at optimum level of approximately 35 degrees. 85°C. This represents a 3. Much higher scalability is observed as the multiplexing efficiency improved by 38% when compared with the conventional 2CC-CV method, with temperatures just rising by 0. 41°C. The above comparison would allow to emphasize the significant differences between the newly developed technique from traditional charging strategies. 4. CONCLUSION In this research Paper, the application of fuzzy logic and neural network-based mathematical optimization demonstrates that this solution is promising for addressing the non-stationary behavior of EV batteries. Research into these technologies shows their capability in achieving higher battery capacity, faster charging speeds, and incremental improvements in battery health. As electric driving increases, the role of high-quality battery management systems will become more critical. By applying fuzzy logic and neural networks to current systems, battery challenges in transportation can be more effectively resolved. The flexibility in setting power values based on current data enables more accurate battery decarbonization, reducing charging times and improving battery conditions. Intelligent logic control by the fuzzy controller prioritizes reasonable charging speeds and temperatures, preventing overheating that could damage battery functionality in the long term. This study has significant implications, warranting further research in EV battery management. The Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2s (2024) 99 https://internationalpubls.com integration of fuzzy logic and neural networks introduces new ways to enhance battery recharging efficiency. 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