Exponential Smoothing Algorithm Research Articles

Measuring user influence in real-time on twitter using behavioural features

Identifying influential users in online social networks, specifically Twitter, has drawn considerable research interest due to their profound influence on real-world events. Existing studies have primarily focused on topological aspects to identify influential users, which necessitate a complete network structure and ignore the behavioural aspects of the users. However, real-world network structure can be challenging to obtain. Thus, this study presents the BehaviourRank Influence (BRI) method, which focuses on evaluating Twitter user influence by analysing behavioural characteristics instead of traditional network structures. This approach acquires data in real-time to derive six behavioural characteristics by employing new metrics to achieve accurate and uniform characterizations. The proposed metrics are compared to baseline metrics from the literature using a user classification prediction model to validate their predictive ability. It also ranked behavioural characteristics by importance using SHAP and Information Gain approaches. To determine overall influence, a unique Rank-based Exponential Smoothing algorithm is proposed. The findings indicate that most features incorporating proposed measures exhibited superior performance compared to features with baseline metrics across all three datasets. The proposed feature sets achieved accuracy scores of 86.67%, 73.47%, and 85.87% in the respective datasets, while the baselined feature sets attained scores of 64.23%, 63.30%, and 66.30%. Moreover, the Rank-Based influence measurements algorithm provides a detailed and adaptable structure for measuring influence, recognising the significance of feature ranks in capturing the evolving nature of user behaviour.

Application of Holt-Winter Exponential Smoothing Method to Design a Drug Inventory Prediction Application in Private Health Units

This research aims to see how to design a drug supply prediction application using the Holt-Winter Exponential Smoothing method. The collection methods used in the research are as follows: observation, interviews. The prototyping system development method includes several important stages in designing research applications. The first stage is communication. After that, the Quick Plan stage. Construction of prototype stages. The final stage, deployment delivery and feedback, is the phase of system use by users. In addition, the team also conducts regular system maintenance to ensure optimal performance. These stages together form an iterative process for developing research applications using the prototyping method. Based on the research results, it was found that the test results for the drugs amoxicillin, cefixime, paracetamol, and CTM showed that the MAPE value was less than 10% for these four drugs, which means that the predictive value has quite high accuracy. So it can be concluded that the Holt Winter Exponential Smoothing algorithm can be well implemented to predict drug supplies.

Can Europe Reach Its Environmental Sustainability Targets by 2030? A Critical Mid-Term Assessment of the Implementation of the 2030 Agenda

The Sustainable Development Goals (SDGs) serve as a pivotal framework globally, addressing environmental concerns. The 2023 Agenda emphasizes the interconnectedness of environmental issues with socio-economic development, recognizing their fundamental role in human prosperity. This research critically evaluates the mid-term progress of EU Member States in achieving the 2030 Agenda’s environmental targets. Using Eurostat data for SDGs 6, 11, 12, 13, 14, and 15, we’ve analyzed trends via the AAA (Holt–Winters) exponential smoothing algorithm. Results highlight progress from 2015–2022 but signal concerns for 2030 targets in several Member States. These findings urge local, national, and EU stakeholders to intensify efforts toward environmental sustainability goals. Corrections are imperative, given the predicted negative trends, emphasizing the need for immediate action to rectify trajectories before it is too late.

Impact of the COVID-19 pandemic on cancer screenings in Portugal

ObjectivesThis study aimed to evaluate the impact of the COVID-19 pandemic on cancer screening in Portugal, and its consequences on cancer morbidity and mortality. MethodsThe pre-pandemic and pandemic periods were compared using publicly available data on performance and health outcomes indicators of the Portuguese NHS, namely the numbers and proportions of eligible individuals who underwent cancer screening (breast, cervical or colorectal). Pre-pandemic data were modelled to project hypothetical scenarios without a pandemic using an exponential smoothing algorithm, and then compared with data collected during the COVID-19 pandemic. A Markov model was developed to estimate years of life lost (YLL) due the reduction in the number of cancer screenings during the pandemic. The MS Excel and the PRISM symbolic model checker software were used. ResultsThere was a decrease in the number of breast (13 %), cervical (15 %) and colorectal (9–11 %) cancers screenings during the first two years of the pandemic. The model projections are 506, 41, and 148 additional deaths, losses of 11, 6, and 4 months of life per patient, and 12.8 thousand, 576, and 4 thousand YLL by the population due to breast, cervical, and colorectal cancer, respectively, over a 25-year time horizon in Portugal. ConclusionsThe disruption in cancer screening may contribute to increase cancer morbidity and mortality, with significant YLL. The long-term implications of the impaired cancer screening should be assessed, and proactive measures put in place to mitigate the increase in cancer morbidity, and mortality associated with the COVID-19 pandemic.

Modelling Risk for Commodities in Brazil: An Application for Live Cattle Spot and Futures Prices

This study analyses a series of live cattle spot and futures prices from the Boi Gordo Index (BGI) in Brazil. The objective is to develop a model that best portrays this commodity’s behaviour to estimate futures prices more accurately. The database created contains 2010 daily entries in which trade in futures contracts occurs, as well as BGI spot sales in the market, from 1 December 2006 to 30 April 2015. One of the most important reasons why this type of risk needs to be measured is to set loss limits. To identify patterns in price behaviour in order to improve future transaction results, investors must analyse fluctuations in asset values for longer periods. Bibliographic research reveals that no other study has conducted a comprehensive analysis of this commodity using this approach. Cattle ranching is big business in Brazil given that in 2021, this sector moved BRL 913.14 billion (USD 169.29 billion). In that year, agribusiness contributed 26.6% of Brazil’s total gross domestic product. Using the proposed risk modelling technique, economic agents can make the best decision about which options within these investors’ reach produce more effective risk management. The methodology is based on Holt–Winters exponential smoothing algorithm, autoregressive integrated moving-average (ARIMA), ARIMA with exogenous inputs, generalised autoregressive conditionally heteroskedastic and generalised autoregressive moving-average (GARMA) models. More specifically, five different methods are applied that allow a comparison of 12 different models as ways to portray and predict the BGI commodity behaviours. The results show that GARMA with order c(2,1) and without intercept is the best model. Investors equipped with such precise modelling insights stand at an advantageous position in the market, promoting informed investment decisions and optimising returns.

Assessing the security status and future scenarios of the Mediterranean region through the water-energy-food nexus

Over the past decades, the Mediterranean region has faced significant challenges due to the impacts of climate change and ongoing conflicts. This study proposes an assessment of the region's security status and potential future scenarios through the lens of the water-energy-food nexus, utilising indicators that align with the Sustainable Development Goals (SDGs). These indicators include agricultural yields, value-added, and land variations, water and sanitation services, income and inequality, use of renewable energy, carbon footprints, and political stability. To evaluate the situation, this analysis applies Ward's hierarchical clustering algorithm to group countries based on these indicators, examining the average terms and the years 2006 and 2015 for comparative analysis. Additionally, an exponential smoothing algorithm forecasts future trends and generates clusters for the years 2030 and 2050. By computing an index of convergence for each cluster and indicator, this contribution identifies areas of particular interest from a security perspective. The findings of this analysis reveal a growing polarisation within the Mediterranean region, with European countries and Israel forming one distinct group, and African and Eastern countries (excluding Israel) forming another. Notably, recurring disparities exist in variables such as agricultural land, political stability, violence, income per capita, and agricultural value added. Conversely, certain variables, including the Gini coefficient, prevalence of overweight population, and access to drinking water services, show signs of convergence. These results shed light on potential areas of both conflict and cooperation in the Mediterranean region, highlighting the importance of addressing the challenges posed by climate change. By understanding the geopolitical dynamics and identifying key areas of concern, policymakers can develop informed strategies to promote stability and sustainable development in the region.

Comparison of Triple Exponential Smoothing and Support Vector Regression Algorithms in Predicting Drug Usage at Puskesmas

Comparison of Triple Exponential Smoothing and Support Vector Regression Algorithms in Predicting Drug Usage at Puskesmas

Penerapan Algoritma Adaptive Response Rate Exponential Smoothing Terhadap Business Intelligence System

PT. XYZ is one of the companies in the field of furniture sales by offering its flagship product, namely spring bed. The company's business continues to grow every year, of course, the company must be able to complete its work quickly and precisely. One of the main problems of the company is that the increase in company sales is still not able to cover the company's expenses and sometimes the company still suffers losses. This happens because companies often make mistakes in purchasing product inventory stock. Not all types of spring beds sell well, so sometimes purchases are made of the type of spring bed that is not selling well, which results in stock accumulation and instability of the company's cash inflow and outflow. In this study, a Business Intelligence System was built, which is a form of information technology implementation to store, collect and analyze data into knowledge so that it can be used as prediction results. The prediction algorithm used in this research is the Adaptive Response Rate Exponential algorithm. The expected goal of this research is to build a Business Intelligence System that can calculate product sales predictions in the following month using the Adaptive Response Rate Exponential Smoothing (ARRES) algorithm. Based on the results of the MAPE test, it can be concluded that the percentage of prediction accuracy from the ARRES algorithm on the sales transaction data of PT. XYZ is 53.33% which is categorized as quite accurate and the percentage of prediction error from the ARRES method is 46.67% which is categorized as reasonable

Dynamic robust analysis of IoV link delay in cellular Telematics and smart edge networking base on deep reinforcement learning

Applications for the Internet of Vehicles (IoV) are progressing from more fundamental ones like those for traffic efficiency, road safety, and information services to more sophisticated ones like autonomous driving and intelligent mobility that have a variety of connectivity requirements. Therefore, IoV communication systems must overcome various obstacles in order to enable a variety of IoV applications. Attacks on TSP servers are the major target of telematics attack threat events. This article analyses data security monitoring from the vehicle end to the TSP platform, as well as gathering and analysing the status and intelligence of linked vehicles, in order to develop a Telematics TSP server attack monitoring system. Experiments show that the error detection rate of the benchmark algorithms decreases significantly as the error rate of vehicle speed data increases, with the exponential smoothing algorithm showing the largest decrease in the error detection rate. However, the proposed combined model is very close to the error detection rate of the benchmark algorithm at the later stages when the error rate is high, with an error detection rate of more than 80%.It provides great assistance for anomaly detection and data recovery, especially in researching key technologies for remote information processing data security and reliability, greatly improving their performance.

Direct-Drive Electro-Hydraulic Servo Valve Performance Characteristics Prediction Based on Big Data and Neural Networks.

Direct-drive electro-hydraulic servo valves play a key role in aerospace control systems, and their operational stability and safety reliability are crucial to the safety, stability, and efficiency of the entire control system. Based on the prediction of the performance change of the servo valve and the resulting judgement and prediction of its life, this can effectively avoid serious accidents and economic losses caused by failure due to performance degradation in the work. On the basis of existing research, factors such as opening, oil contamination, and pressure difference are used as prerequisites for the operation of direct-drive electro-hydraulic servo valves. In addition to the current research on pressure gain and leakage, the performance parameters of servo valves, such as overlap, threshold, and symmetry, are also expanded and selected as research objects, combined with pressure design servo valve performance degradation experiments for testing instruments such as flow and position sensors, and data are obtained on changes in various performance parameters. The experimental data are analyzed and a prediction model is built to predict the performance parameters of the servo valve by combining the existing popular neural networks, and the prediction error is calculated to verify the accuracy and validity of the model. The experimental results indicate that as the working time progresses, the degree of erosion and wear on the valve core and valve sleeve of the servo valve increases. Overall, it has been observed that the performance parameters of the servo valve show a slow trend of change under different working conditions, and the rate of change is generally higher under high pollution (level 9) conditions than under other conditions. The prediction results indicate that the predicted values of various performance parameters of the servo valve by the prediction model are lower than 0.2% compared to the experimental test set data. By comparing the two dimensions of the accuracy and prediction trend, this model meets industrial needs and outperforms deep learning algorithm models such as the exponential smoothing algorithm and ARIMA model. The experiments and results of this study provide theoretical support for the life prediction model of servo valves based on neural networks and machine learning in artificial intelligence, and provide a reference for the development of direct-drive electro-hydraulic servo valves in aerospace and other industrial fields for use and failure standards.

Enhancing Sales Forecasting Accuracy Through Optimized Holt-Winters Exponential Smoothing with Modified Improved Particle Swarm Optimization

The Holt-Winters Exponential Smoothing method utilizes three smoothing parameters, namely alpha (α), beta (β), and gamma (γ), which have a significant impact on the accuracy of the forecasting process. One of the main challenges in the Holt-Winters Exponential Smoothing method is to find the best combination of the smoothing parameters, α, β, and γ, to achieve optimal forecasting accuracy. In this research, the MIPSO optimization method is used to find the optimal combination of values for α, β, and γ. The sales data used in the study covers the period from January 2021 to May 2023. The research results indicate the best accuracy achieved by combining the Holt-Winters Exponential Smoothing algorithm with the MIPSO optimization algorithm during the data period from January 2021 to May 2023, with a MAPE value of 9.1717%. Therefore, the use of the MIPSO algorithm helps discover the optimal combination of α, β, and γ parameters for forecasting.

A new predictive approach for the MAC layer misbehavior in IEEE 802.11 networks

Purpose Ad hoc mobile networks are commonplace in every aspect of our everyday life. They become essential in many industries and have uses in logistics, science and the military. However, because they operate mostly in open spaces, they are exposed to a variety of dangers. The purpose of this study is to introduce a novel method for detecting the MAC layer misbehavior. Design/methodology/approach The proposed novel approach is based on exponential smoothing for throughput prediction to address this MAC layer misbehavior. The real and expected throughput are processed using an exponential smoothing algorithm to identify this attack, and if these metrics exhibit a trending pattern, an alarm is then sent. Findings The effect of the IEEE 802.11 MAC layer misbehavior on throughput was examined using the NS-2 network simulator, as well as the approval of our novel strategy. The authors have found that a smoothing factor value that is near to 0 provides a very accurate throughput forecast that takes into consideration the recent history of the updated values of the real value. As for the smoothing factor values that are near to 1, they are used to identify MAC layer misbehavior. Originality/value According to the authors’ modest knowledge, this new scheme has not been proposed in the state of the art for the detection of greedy behavior in mobile ad hoc networks.

Sales forecasting of marketing using adaptive response rate single exponential smoothing algorithm

Micro, small and medium enterprises (UMKM) is one of the important aspects to support the improvement of the economy in Indonesia. Zee Mart’s business is one of the UMKM shop in Pematang Siantar City with sales and purchase transaction activities for supplies. The purpose of this study is to predict the sales of Zee Mart store goods in the coming month using the adaptive response rate single exponential smoothing (ARRSES) method. ARRSES is a method with the advantage of having two parameters, alpha and beta, where alpha will change every period when the data pattern changes. The dataset obtained will be pre-processed through data selection, cleaning, and transformation. The best beta is determined based on the level of accuracy calculated using the mean absolute percentage error (MAPE). Model development using the ARRSES method will produce forecasting percentages and errors for each product using MAPE. The number of sales data is 23,092 before preprocessing and 23,021 after pre-processing, with the total quantity of goods sold being 149,764 of 1,492 products. The results obtained using sales data 23,021 show the lowest MAPE value of 9.85 at the best beta of 0.6 with the highest accuracy of 90.15% and the model is implemented into a web interface.

Dynamic Prediction of Performance Degradation Characteristics of Direct-Drive Electro-Hydraulic Servo Valves

Direct-drive electro-hydraulic servo valves are widely used in the aerospace industry, in the military, and in remote sensing control, but there is little research and discussion on their performance degradation and service life prediction. Based on previous research, erosion wear is the primary physical failure form of direct-drive electro-hydraulic servo valves, and parameters such as opening, oil contamination, and pressure difference are used as influencing factors of direct-drive electro-hydraulic servo valves. Pressure gain and leakage are used as performance degradation indicators of servo valves, and multiple types of sensors are used for data monitoring. Experimental benches are arranged and verified through experiments. Based on the data and laws obtained from the experiments, the exponential smoothing algorithm and the ARIMA model algorithm were used to establish a prediction model for the servo valve, and the dynamic prediction of the performance indexes was carried out. The error calculation and analysis of the prediction results and the experimental results were then carried out using the Copula function and other mathematical knowledge to verify the accuracy and applicability of this prediction model. This study provides theoretical support and practical guidance for applying and designing direct-drive electro-hydraulic servo valves in industrial applications such as aerospace, sensor experiments, and remote sensing control.

Multi-Attention Feature Fusion Network for Accurate Estimation of Finger Kinematics From Surface Electromyographic Signals

Simultaneous and proportional control (SPC) based on surface electromyographic (sEMG) signals has led to a broad range of applications. However, due to the limitation in the generalization and stability of current machine learning algorithms, these methods can only estimate less than 15 simultaneuous and proportional (SP) categories of finger movement. In this article, a novel deep learning algorithm, named multiattention feature fusion network (MAFN), is proposed to estimate comprehensive finger movement (up to 28 categories SP movements) from sEMG signals. MAFN is based on the multihead attention mechanism, which adaptively extracts essential features for analyzing the joint angles from the extracted sEMG features. Furthermore, a real-time exponential smoothing algorithm is designed for further improvement of the prediction stability. MAFN was evaluated on 28 finger movements of 38 subjects in the Ninapro_db2 dataset, and benchmarked with the state-of-the-art methods, such as temporal convolutional network (TCN) and long short term memory network (LSTM). The results demonstrated that the average Pearson correlation coefficient, root mean squared error of MAFN (0.84 ± 0.03,0.09 ± 0.01) were significantly higher than those of TCN (0.52 ± 0.06, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> < 0.001;0.16 ± 0.02, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> < 0.001) and LSTM (0.62 ± 0.06, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> < 0.001;0.13 ± 0.01, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> < 0.001). These improvements led to more stable and accurate movement predictions. Additionally, the time delay and power consumption of MAFN when applied to sEMG signals on a portable device are only 83.4 ms and 3 W, which implies prospective commercial applications.

Nowcasting of Weather Parameters Impacting Solar PV Output Using Grey System Model

Objectives: To nowcast the weather parameters having a direct impact on the power output of the solar PV installations, with high prediction accuracy and a limited quantity of past data. Methods: In this study, the GM (1,1) model with Fourier series of error residuals has been proposed and used for forecasting the weather parameters namely Ambient temperature, Solar Photo Voltaic Module temperature, and Solar Irradiation. Real-time data has been used for showing the suitability of the proposed model to nowcast the weather parameters. The existing models like Autoregression and Double Exponential Smoothing are applied to the same data to prove the superiority of the GM (1,1) model with Fourier series of error residuals. Findings: It is found that the GM (1,1) model with Fourier series of error residuals is an apt model for nowcasting the weather parameters. The accuracy of the predicted result of this model on the real-time data ascertains the appropriateness of this model for nowcasting. The precision of the prediction accuracy of GM (1,1) with the Fourier series of error residuals model is verified by comparing it with other time series prediction models such as Autoregression and Double Exponential Smoothing algorithms. Novelty: Using GM (1,1) with the Fourier series of error residuals model for nowcasting the weather data is novel when compared with the existing algorithms because for nowcasting the weather parameters with accuracy, many of the existing algorithms require a huge volume of past data and involve complex computation. On the other hand, GM (1,1) with the Fourier series of error residuals model requires only a limited measure of past data and involves simple computation. Moreover, the accuracy of prediction is significantly higher than the other models. Keywords: Grey Theory; Renewable Energy; PV Installation; Auto Regression; Double Exponential Smoothing

Cascading auto-regressive exponential smoothing of image sequences for reducing turbulence induced motion

Atmospheric turbulence can significantly degrade images taken over a long horizontal path near the ground. This can hinder the identification of objects in a scene. We consequently introduce the Cascading Auto-Regressive Exponential Smoothing (CARES) algorithm, which is a fast real-time algorithm that suppresses the effects of atmospheric turbulence in image sequences. CARES is a spatial/temporal filtering algorithm that decomposes the image into a Laplacian Image Pyramid (LIP). Each component of the LIP represents the image smoothed to a specific length scale, which is then temporally filtered using an Auto-Regressive Exponential Smoothing (ARES) filter. The ARES filters have a cut-off frequency that are adjusted in such a way for each LIP component to define a critical velocity. Objects in the scene moving below the critical velocity pass through the CARES filter with little distortion or delay. We assess the performance of CARES using turbulent imaging data. We find that CARES improves image quality using a variety of image quality metrics. We use a simple CARES simulation to show that the salient features of a moving object lag behind by one pixel or less.

Uncertainty in the Back-Calculation of Geometric Parameters of Vertical Curves Obtained with UAV

In existing roads, the geometrical parameters of the alignment are the primary input for safety or geometrical improvement studies. However, the as-built drawings are not always available to obtain geometrical parameters, whereby they must be back-calculated from surveying data. The procedures to back-calculate geometrical parameters of existing roads and fit profile data use parametric methods such as polynomials or explicit functions and nonparametric methods such as splines or smoothers. In smoother-based methods, a usual computing decision is to consider a fixed spacing, one smoothing algorithm, and one set of smoothing parameters to obtain a single set of curvature, deflection, and length (KAL) parameters of vertical curves. Therefore, different values of KAL parameters will be obtained depending on the choice of spacing, smoothing algorithm, and smoothing parameters. This paper aims to study the relative effect in the variability of KAL parameters of a vertical curve, introduced by several spacing combinations, smoothers, and parameters, using data obtained with an unmanned aerial vehicle (UAV). Elevation and slope data were obtained from a digital elevation model every 2, 5, and 10 m. The slope-horizontal distance diagrams were smoothed using single, double, and triple exponential smoothing for different levels, trends, and season parameters. The KAL parameters were back-calculated for each slope-horizontal distance diagram, and the variability analysis was undertaken with boosting regression, multiple analysis of variance, and k-nearest neighbor algorithm and tested using receiver operating characteristics (ROC) curves. Results show that the smoothing algorithm and parameters choice affected mainly the K parameter and that the single exponential smoothing algorithm is more suitable than double and triple exponential smoothing algorithms to estimate the KAL parameters.

Sustainable Supply Chain Management of Electric Grid Power Consumption Load for Smart Cities Based on Second-order Exponential Smoothing Algorithm

Electric grid power consumption load is one of the fundamental areas that need to be faced to provide a sustainable and green ecosystem in smart cities. Consumption load as well as supply and availability of electricity to suppliers and customers is a major issue to be faced to have a balanced smart city power grid infrastructure. Balancing in this case is assumed as a well-designed supply chain management system to be applied in the Smart City (SC) of Athens, Greece. Core of such a system is the knowledge of electric power consumption load per weekly basis of a year, that is the granularity of the proposed system is one week of the system’s operation. In this paper, focus is given on the electric load forecast component of an Energy Management System (EMS) such as the Independent Power Transmission Operator (ITPO) of Greece. Concretely, stochastic data of electric energy consumption load are used to predict the demand or offering of electric power in the future. This is achieved by incorporating a machine learning second-order exponential smoothing algorithm. Such an algorithm is able to speculate near or far in the future power consumption load thus providing a promising parameter to predict smart city needs for electric power in the future. Adopted system is evaluated by the evaluation metric of Normalized Root Mean Square Error (NRMSE), which assures that the system can be used for future predictions of electric power consumption load in smart cities.

Mathematical Modelling and Simulation of Second Life Battery Pack with Heterogeneous State of Health

The service life of Lithium-ion batteries disposed from electric vehicles, with an approximate remaining capacity of 75–80%, can be prolonged with their adoption in less demanding second life applications such as buildings. A photovoltaic energy generation system integrated with a second life battery energy storage device is modelled mathematically to assess the design’s technical characteristics. The reviewed studies in the literature assume, during the modelling process, that the second life battery packs are homogeneous in terms of their initial state of health and do not consider the module-to-module variations associated with the state of health differences. This study, therefore, conducts mathematical modelling of second life battery packs with homogenous and heterogeneous state of health in module level using second-order equivalent circuit model (ECM). The developed second-order ECM is validated against experimental data performed in the lab on 3Ah NCM batteries. The degradation parameters are also investigated using the battery cell’s first life degradation data and exponential triple smoothing (ETS) algorithm. The second-order ECM is integrated with the energy generation system to evaluate and compare the performance of the homogenous and heterogeneous battery packs during the year. Results of this study revealed that in heterogeneous packs, a lower electrical current and higher SOC is observed in modules with lower state of health due to their higher ohmic resistance and lower capacity, compared to the other modules for the specific battery pack configuration used in this study. The methodology presented in this study can be used for mathematical modelling of second life battery packs with heterogenous state of health of cells and modules, the simulation results of which can be employed for obtaining the optimum energy management strategy in battery management systems.