Optimization of Sand Battery Systems for Renewable Energy Storage Using Artificial Neural Networks

Optimization of Sand Battery Systems for Renewable Energy Storage Using Artificial Neural Networks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimization of Sand Battery Systems for Renewable Energy Storage Using Artificial Neural Networks Kriti Vaid, Anil Soharu, Naveen BP This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8298202/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract As renewable energy systems become increasingly intertwined globally, the need for low-cost, large-scale, and environmentally benign long-duration energy storage technologies has intensified. Silica-rich materials found in deserts have led to the implication that sand-based thermal energy storage (TES) systems should be developed in advance. Due to unavoidable heat-transfer limitations, nonuniform thermal distribution, and scepticism about the intelligent optimisation framework, system performance still operates within its limits. In this paper, we present a framework for optimizing sand battery systems using Artificial Neural Networks to improve operational efficiency. We developed a numerical thermodynamic model that simulates temperature dynamics within a silica sand bed as a function of key input parameters , including charging temperature (300–700°C), charge/discharge rate (5–25°C·min⁻¹), and coupling material type. A multilayer ANN trained on a dataset of 500 simulated scenarios generated using Latin Hypercube Sampling. As a result, the ANN demonstrated high predictive ability (MAE = 1.72%; RMSE = 2.31%; R² = 0.963). Afterward, a Genetic Algorithm (GA) was used to find operating conditions with the highest efficiency. We then derive a decision-tree model that classifies storage performance based on efficiency, retention time, energy loss rate, and cost. The Mean Performance Index (MPI) achieved was 84.1%, suggesting a high degree of overall fitness of sand-based TES for long-term storage. The combined ANN–GA–Decision-tree framework is a promising tool for improving the performance of sand batteries, paving the way for computerized, intelligent optimization and supporting economies of scale for low-cost renewable energy storage technology. Sand battery Thermal energy storage Artificial Neural Networks Renewable energy optimisation Genetic Algorithm Heat transfer modelling Figures Figure 1 Figure 2 Figure 3 1. Introduction Transitioning to renewable energy on the timescales required is now one of the signature technological and environmental challenges of the 21st century. In a bid to reduce high-GHG-emitting fossil fuels, amid rising energy security concerns, and in line with commitments to global climate targets, countries around the world are deploying more solar photovoltaic (PV) and wind energy in power grids. While these renewable energy sources are highly beneficial to the environment and the economy, they have an inherent intermittent nature that is highly dependent on weather (Carmichael 2017 ). Solar power patterns are affected by changes in cloud cover. However, solar irradiance, and therefore energy production, has a diurnal cycle as well as seasonal variability. At the same time, wind energy is subject to unpredictable atmospheric patterns. The intermittent nature of these sources leads to inevitable supply-demand mismatches that limit the stability and reliability of today's power systems. With the rise in renewable penetration, flexible, scalable long-duration energy storage solutions are urgently needed. Traditional electrochemical battery technologies—primarily lithium-ion, lead–acid, sodium–sulfur, and next-generation solid-state batteries—have been established as sustainable options for short-term grid-scale, electric mobility, and consumer electronics applications. However, its commercial use at a large scale is impeded by problems including degradation during cycling, thermal instability, material scarcity in large quantities , and high capital costs. The price fluctuations of lithium and cobalt — necessary materials for high-performance batteries — also impose significant environmental and geopolitical constraints due to the concentration of global supply chains. Moreover , of course, big batteries also pose recycling problems and long-term environmental risks. The limitations of these storage methods have compelled investigators and policymakers to seek alternative, more environmentally friendly energy storage technologies that use readily available materials, have a low environmental impact, and provide a long service life. Thermal energy storage (TES) offers strong potential as an alternative to electrochemical batteries, with applications in the grid and at an industrial scale. TES technologies, which store excess energy as heat and release it when needed, are natural long-duration storage systems. While many TES media have been proposed, such as molten salts, water, concrete, phase-change materials (PCMs), and ceramic composites, sand has recently drawn attention due to its unique combination of wide availability, low cost, thermal stability, and safety. Silica Rich Sand is abundant in nature, has no toxicological characteristics, is chemically inert, is thermally stable (> 800°C ), and thus is a potential material for high temperature sensible heat storage. Compared to molten salts, sand does not exhibit freezing–melting restrictions or corrosive behaviour, and compared to PCMs, it does not require encapsulation or complex phase management (Vaid et al., 2021 ). Just a few examples of early prototypes and pilot-scale implementations of "sand batteries" report storing heat at 600–700°C for several days. The systems use resistive or inductive heaters to generate thermal energy from excess electricity, which is stored in a silica sand bed within an insulated steel vessel. Another area of promising adaptability is heat extraction via air movement, heat exchangers, or thermal oil loops, allowing the concept to be used for district heating, industrial processes, greenhouse heating, and, perhaps later, even a power-generation cycle coupling. Sand-based batteries provide low-cost conversion capacity, extended operational longevity, and a low environmental footprint, making them a desirable option for seasonal-scale energy storage and grid decarbonisation applications. Nonetheless, important scientific and engineering issues remain to be overcome in the optimisation of sand battery systems. Granular media have low thermal diffusivity, so sand takes a long time to absorb heat, and shallow layers of sand exhibit different temperature distributions. Suppose the system's heating is not uniform. In that case, the overall efficiency can be reduced, and thermal losses through the container's boundaries will increase. In addition to grain size distribution, porosity, mineral composition, and water content, grain size also affects the thermal behaviour of sand. Identification of materials and modelling of their coupling (aluminium, copper, steel, etc.) regulates the direct transfer of heat. However, the choice involves trade-offs among thermal conductivity, structural stability, and cost. Finding the best operating conditions, including charging temperature, charge rate, insulation thickness, material, and discharge patterns, requires complex modelling of nonlinear thermal and physical behaviours (Vaid et al., 2020 ). To meet these challenges, the health field has new capabilities enabled by artificial intelligence (AI). Machine learning models (MLMs), especially artificial neural networks (ANNs), have shown extraordinary ability to capture complex, nonlinear, and multivariate relationships in many energy systems. ANNs were used for state-of-charge prediction in batteries, renewable generation prediction, optimising microgrid performance, and thermal behaviour analysis in heat storage systems. As they learn from simulation or experimental data and generalise across varied operating conditions, they are best suited for modelling sand TES, where traditional analytical equations cannot accurately capture nonlinear temperature gradients and multi-parameter associations. In addition, using ANNs in conjunction with optimisation algorithms such as Genetic Algorithms (GAs) can considerably improve performance by determining suitable configurations for practical energy storage. On the other hand, although there has been significant advancement in the optimisation of energy storage, ANN-based modelling and ANN–GA hybrid optimisation frameworks have not been applied to sand battery systems in the prevailing body of research. This opens a clear door for the development of sand TES technologies and their potential use. The novelty of this study is that it attempts to fill that research gap by developing a coherent modelling methodology based on numerical thermodynamic simulation, ANN prediction, GA optimisation, and decision-tree interpretability. A key objective is to optimize sand battery performance to increase charging efficiency, thermal homogeneity, and functional integrity across a wide range of thermal, material, and geometric parameters. Closing these gaps improves system performance and yields an actionable framework that serves a diverse set of stakeholders involved in renewable energy deployment, such as operators, engineers, and policymakers. 2. Literature Review 2.1 Sand-Based Thermal Energy Storage (TES) In this TES method, called sand-based TES, thermal energy is stored as sensible heat by raising the temperature of a solid medium [8]. Sand is one of those candidates due to its high abundance and stability, as described by Carmichael in 2017. Recent commercial prototypes indicate commercial readiness, with heated sand at 500–700°C as a potential heat storage system with exceptionally long life (after being heated with excess renewable electricity) (Kilic et al., 2024 ). Sand is a promising, non-toxic, low-cost material that could serve as a sustainable substitute, at least for electrochemical storage (especially at grid and industrial scales). 2.2 Thermophysical Properties of Sand As per Table 1 , Silica sand rich in quartz has an SiO₂ content of 70–90%, a high melting temperature (> 1600°C), low thermal expansion, and chemical inertness (Prasad et al., 2019 ). This can negatively affect clinker performance or cause gas release at high temperatures (Radwan & Humphrey, 2024). Size (optimal, 0.2–1 mm) achieves good porosity and heat-transfer efficiency. A higher quartz content increases thermal conductivity, thereby facilitating the effective heat transfer (Chung & Chen, 2022 ). Table 1 Composition of sand and its behaviours towards sand batteries. Component Percentage Behaviour towards sand batteries Quartz (SiO₂) 70–90% Excellent thermal stability, high melting point, and chemically inert. Ideal for heat storage. Feldspar (KAlSi₃O₈ – NaAlSi₃O₈ – CaAl₂Si₂O₈) 5–15% Decent thermal properties can undergo phase changes or break down at very high temperatures. Gypsum (CaSO₄·2H₂O) 1–5% Decomposes at relatively low temperatures (~ 150–200°C) and releases water vapour, which is unsuitable for stable heat storage. Carbonates (Calcite - CaCO₃, Dolomite - CaMg(CO₃)₂) 1–5% Decompose at 600–900°C, releasing CO₂ — problematic for high-temperature storage. Clay minerals (Kaolinite, Illite, Montmorillonite) < 5% Poor thermal conductivity can expand with heat and moisture. Not ideal. Heavy minerals (Magnetite, Zircon, Ilmenite, etc.) Trace–1% Some, such as Magnetite, have strong thermal storage potential. Others vary. 2.3 Operational Principles of Sand Batteries Sand battery technology works on sensible heat storage, where energy is stored as thermal energy in a solid, granular medium, typically silica-rich sand. A sensible heat storage system typically comprises an insulated steel or concrete box filled with sand, electrical heating elements, and an air duct, heat exchanger, or thermal oil circuit to extract the heat. The charging process converts excess electrical energy generated by renewable sources (solar PV or wind) into thermal energy via resistive or inductive heating. This heat is transferred into the sand bed, increasing the temperature from ambient levels to about 600–800°C due to system design and material limitations. As depicted in Fig. 1 , heat transfer in sand occurs principally by conduction and by some convection in the air between the particles. Due to sand's relatively low thermal diffusivity, the heating process leads to nonuniform temperature gradients, with the hottest regions forming around the heating elements. The process of heat diffusion towards the periphery of the bed takes time. However, homogenisation can take days (in extreme cases). Characterization of thermal storage capacity by mass / specific heat capacity and in terms of the allowable temperature range of sand. To improve heat storage, quartz-dominant silica sands are often used because they exhibit stable thermophysical properties at elevated temperatures (Poulose T et al., 2022 ). In the discharging stage, the thermal energy stored in the storage system is removed and used, for example, for district heating, industrial drying, greenhouse heating, or combined with a thermodynamic cycle for electricity production. The process of heat extraction involves air, water, or thermal oil flowing through tubes or ducts embedded in the sand, extracting heat from the sand, and transporting it to the end application. The success of this part depends on the heat exchanger design, flow rate, and thermal gradient. Instead, sand battery systems provide a high-power, low-cost, long-duration storage option. However, performance is highly dependent on the choice of materials, heating strategy, insulation, and geometry, all of which require sophisticated modelling and optimisation tools. 2.4 Challenges in Sand TES Systems While promising, sand-based TES systems still face several technical challenges that limit their efficiency and use at larger scales. Granular sand exhibits low thermal diffusivity, which slows the charging process as a large temperature gradient forms across the storage bed. This manner of thermal distribution limits the storage capacity allotted. It produces localized heating where there are more heating elements than are being utilized. Moreover, long-term storage behaviour, and hence seasonal operation (Vaid et al., 2020 ), is heavily influenced by thermal losses through the walls of the storage container (e.g., insulation imperfections) and by ambient temperature variation. The heat–transfer behaviour becomes more complicated because sand is a natural material. Its heterogeneity is mainly caused by variations in grain size, mineral composition, and moisture content within a single series. At the same time, thermal decomposition or gas generation at high temperatures further complicates this. Mechanical settling and compaction over several cycles can modify porosity, which, in turn, can affect airflow during heat extraction. Further, the absence of predictive control techniques results in static optimisation of charging and discharging processes, leading to inefficient operation. These challenges highlight an important direction for future system modelling: the need for more sophisticated tools, including machine learning and hybrid numerical–data-driven frameworks, to represent system behaviour and support optimisation and control accurately. 2.5 AI for Energy Storage Modelling Artificial neural networks (ANNs) have been used for forecasting overall lithium-ion battery state-of-charge (Islam et al., 2015 ), thermal system performance (Jha et al., 2017 ), and microgrid performance (Khorsand & Mohammadi-Ivatloo, 2018). Their ability to model nonlinear behaviour is a good fit for sand TES optimisation. The performance of hybrid ANN–GA systems is generally better in renewable energy applications (Mohammad et al., 2018 ). 2.6 Research Gap Despite sand-based thermal energy storage (TES) emerging in recent years as a cost-competitive and sustainable alternative to conventional electrochemical systems, significant knowledge gaps remain. Although studies have examined material characterisation, insulation enhancement through simulations and prototype demonstrations, comprehensive modelling of the nonlinear thermal behaviour of sand beds remains scarce. Currently available analyses are based on simplified conduction models that omit the coupled effects of grain structure, thermal gradients, heating rates, and coupling materials. Additionally, few predictive machine-learning models exist that can generalise across varying operational conditions and provide performance evaluation on the go (Vaid et al., 2020 ). Although artificial neural networks have been widely used in battery management and thermal system optimisation, their application in sandTES remains under-researched. There have also been no optimisation frameworks that use AI alongside evolutionary algorithms to find optimal charging schedules, operating temperatures, or material configurations (Kober T et al., 2020 ). A third gap is the lack of interpretable decision-support tools (e.g., decision trees) that can convert complex system behaviour into meaningful operational actions. Together, these gaps highlight a need for integrated, data-driven solutions that can synergise numerical modelling, AI prediction, and optimisation to improve the design, control, and deployment of sand-based TES at scale. 3. Methodology 3.1 System Configuration The investigated sand-based thermal energy storage (TES) system consists of a perfectly insulated cylindrical steel vessel filled with quartz sand with a particle size of 100 µm. Silica-rich sand (grain size between 0.4 and 0.6 mm) offers advantageous thermophysical properties, such as a high melting temperature, chemical inertness, and stable thermal conductivity, and was therefore chosen. Resistive heating is used for thermal charging by embedding heating elements within the sand bed and an internal heat exchanger (e.g., metal tubes or channels) for thermal extraction during discharge. To distinguish the variation in heat-transfer performance due to significant differences in thermal conductivity, three possible coupling materials (aluminium, copper, and stainless steel) were studied. Being a supreme conductor, copper is used as a reference. At the same time, aluminium and stainless steel are usable alternative materials for price-sensitive applications (Omar A et al. 2019 ). The simulated operational environment resembles that typical of renewable-energy applications, where excess electricity from a photovoltaic or wind system is used to charge the vehicles. This system configuration, hence, takes both practical design considerations and general constraints adopted in large-scale thermal energy storage applications into account. 3.2 Thermodynamic Simulation Model A transient thermodynamic model was also developed to simulate heat transfer in the sand bed under different charging scenarios. It uses the classical transient heat conduction equation with effective thermal conductivity and adequate volumetric heat capacity to account for the effects of solid grains and interstitial air in granular media. Due to sand's low thermal diffusivity , the temporal and spatial evolution of temperature must be well modeled to develop an understanding of charging dynamics. The governing partial differential equation was solved using boundary and initial conditions defined by the location of the heating element, the thickness of the thermal insulation, and the interaction with the ambient. The simulations were performed at charge temperatures from 300 to 700°C and charge rates from 5 to 25°C·min⁻¹ as defined in Table 2 . Table 2 Key input parameters for numerical model. Charging Temperature 300°C to 700°C Charge/Discharge Rates 5°C/min to 25°C/min Coupling Material Types Aluminium, copper, stainless steel We define these ranges based on likely and extreme operational scenarios for high-temperature TES systems. Furthermore, the respective thermal properties of the coupling materials were assigned to assess their effect on heat propagation. Outputs from the model included temperature evolution maps, radial temperature profiles, steady-state profiles, and thermal efficiency. These outputs constituted the initial dataset for downstream machine-learning analysis and optimisation (Radwan O, Humphrey J 2024). 3.3 ANN Dataset Preparation A 500-scenario dataset exhibiting various charging conditions was generated using Latin Hypercube Sampling (LHS) to ensure adequate, representative training data for the artificial neural network (ANN). In high-dimensional engineering simulations, LHS is preferred , as it provides more homogeneous coverage of the parameter space while minimising correlation among sampled variables. There are three input parameters for each simulation scenario (charging temperature, charge rate, and type of coupling material), and four output parameters reflecting the system's efficiency, temperature rise rate, thermal loss indicators, and retention behaviour. Thus, the dataset captures the nonlinear relationships between the input variables and the sand bed's thermal response. The collected data were normalised and subsequently split into three unique subsets: 70% for training and 15% each for validation and testing. So that the rad pattern for the ANN will learn the underlying patterns but keep generalisation for unseen data (Smith MT et al. 2020). Thus, the dataset provides an appropriate basis for an informative ML-driven model that can improve physics-based simulations. 3.4 ANN Architecture Also developed was a multilayer feedforward ANN used to map input operational parameters to the system's efficiency empirically. As per Table 3 , the selected architecture has an input layer, which corresponds to the three input quantities, namely, charging temperature, charge rate, and coupling material; the first hidden layer, which contains 10 neurons; a second hidden layer with seven neurons; and an output layer, which consists of 1 neuron, namely, overall system efficiency (Vani E et al. 2024 ). The hidden layers used a sigmoid activation function to capture more nonlinear behaviour, and the output layer used a linear activation function. Table 3 Artificial neural network architecture structure. Input Layer 3 neurons (charging temperature, charge rate, coupling material) Hidden Layers 2 layers with 10 and 7 neurons, respectively, using the sigmoid activation function Output Layers 1 neuron representing system efficiency Backpropagation with a gradient-descent algorithm was used for training, and learning was assessed using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R²). The ANN's prediction accuracy was very high; on a test dataset, MAE = 1.72%, RMSE = 2.31%, and R² = 0.963, as tabulated in Table 4 . These results validate that the ANN generalises well over a wide range of operating conditions and indicate that it can be used as a surrogate model for optimisation and for real-time prediction. The ANN is therefore a computationally efficient substitute for multiple numerical simulations, resulting in reduced computation time whilst maintaining accuracy. Table 4 Performance model values MAE 1.72% RMSE 2.31% R² 0.963 3.5 Genetic Algorithm Optimisation To determine the optimal operational configurations that maximize efficiency in a sand battery, a Genetic Algorithm (GA) was coupled with the ANN model. Using methods analogous to natural selection, the GA explores the multidimensional parameter space to find high-performing solutions. Each candidate solution in this implementation corresponds to a distinct set of charging temperature, charge rate, and coupling material. The ANN output, representing the predicted efficiency, served as the GA fitness function, resulting in a much more efficient optimisation process than performing thermodynamic simulations in a loop. Optimisation was performed with a population of 50 candidate solutions, a crossover fraction of 0.8, a mutation rate of 0.01, and up to 100 generations as defined in Table 5 . In the GA, candidate solutions were iteratively evolved via crossover and mutation to a best-fitting parameter set. The integrated ANN–GA hybrid framework combines machine learning and evolutionary optimisation to explore a complex design space efficiently. Table 5 Genetic Algorithm parameters. Population Size 50 Crossover Fraction 0.8 Mutation Rate 0.01 Maximum Generations 100 3.6 Decision-Tree Model The ANN and GA offer predictive accuracy and practical optimisation, but at the expense of interpretability. To counter this disadvantage, we created a decision-tree model grounded in operational performance measures, enabling classification of operational scenarios. The tree included variables for charging efficiency, thermal retention time, loss rate, operating temperature, and cost per unit of energy. The internal nodes represent decision rules derived from the dataset, thresholds that split scenarios so that high- and low-performing scenarios can be readily identified. Quantitative evaluation of system performance across a range of operational states is included in the model's Mean Index (M.I.), Performance Index (PI), and aggregated Mean Performance Index (MPI) outputs. Thus, the decision-tree model provides an interpretable diagnostic tool that aids operators in decision-making, helps tune parameters under active conditions, and provides interpretability and guidance for the ANN–GA framework. 4. Results This section presents simulation outcomes, ANN predictive performance, GA optimisation effects, and decision-tree derived performance indices. 4.1 Thermal Charging Behaviour Thermal charging simulations reveal the short-term behavior of the sand bed at different heat-input rates over a given time period. Temperature profiles within the sand battery for charging rates of 1.0×, 1.2×, and 1.5× are shown in Fig. 2 . At baseline (1.0×), the temperature rises slowly over time, consistent with a typical conduction-limited response in a granular material. The bed temperature reaches around 600°C after 10 hours of charging, with various thermal gradients across the core and the external regions. When the charging rate reaches 1.2×, the initial temperature increases rapidly, and the sand can reach nearly 620°C in the same time. This behaviour corresponds to higher bed heat flux and a lower delay between the heating element and the adjacent beds. At a rate of 1.5×, the maximum, the thermal ramp is the steepest, reaching 648°C after 10 hours. Again, as in the previous conditions, the curve levels off as the system approaches thermal equilibrium. That asymptotic behaviour reflects the intrinsic limits of sand's thermal diffusivity: heat transfer slows and slows as the temperature gradient decreases. The ability of higher charge rates to increase energy absorption in the early periods, while producing diminishing returns in the late periods, is consistent with these findings. In actual system operation, this means that efficiency can be improved with an adaptive charging strategy — for example, if a high flux is used but the thermal gradient is slight, the system may not operate as expected, so the heat input is successively tapered. Simulations show: Baseline (1.0×): Temperature rises gradually from 500°C to approximately 600°C after 10 h. 1.2× rate: Faster thermal penetration, reaching ~ 620°C in the same duration. 1.5× rate: Highest thermal intensity, achieving ~ 648°C. These curves exhibit an asymptotic tendency toward thermal equilibrium, consistent with conduction-limited thermal transport in granular media (Prasad et al., 2019 ; Radwan & Humphrey, 2023 ). 4.2 ANN Predictive Performance To evaluate the ANN model's performance in determining system efficiency across different operating conditions, performance tests were conducted using validation and test data. Figure 3 : ANN empirical (y-axis) and simulated (x-axis) efficiencies. Strict model generalisation with little systematic error is illustrated by data points clustered closely around the 45° reference line in the lower-left panel. Performance metrics are another source confirming accuracy: Mean Absolute Error (MAE): 1.72% Root Mean Square Error (RMSE): 2.31% Coefficient of determination (R²): 0.963 The MAE and RMSE are relatively low, indicating that the model has a slight deviation from simulated efficiencies, and the R² is high, indicating that the ANN accounts for over 96% of the variance in efficiency. In fact, at low or high charging rates, we also observed increased efficiency errors, suggesting that the nonlinearity is significantly worse at these limits. Nonetheless, the impressive predictive performance of the ANN justifies its application as a cheaper surrogate model in optimisation, as it provides a significant reduction in computational cost during the exploration of large parameter spaces. 4.3 Optimisation Outcomes via Genetic Algorithm The Genetic Algorithm (GA) with the ANN surrogate model identified the best charging temperature, charge rate, and coupling material combination. There were more than a thousand potential configurations to monitor. On the other hand, the hybrid approach generated a converged GA after just 100 generations. By consistently including the following high-efficiency configurations: High charging temperatures close to the top of the simulated range (650–700 ◦C), Average charging rates (1.2×) that mediate the timing of heat retention at energy sites. Coupling material of copper because of its high heat conduction rate Although low efficiencies were observed across all stainless steels, aluminium was found to be competitive at intermediate heating rates, indicating that more affordable bulk alternative materials could serve as suitable replacements for more costly high-temperature materials at large scales. The optimisations show that interactions between multiple variables are important. However, efficiency was not solely driven by the charging temperature: the coupling with charge rate and the coupling material had synergistic effects that the GA appropriately accounted for. 4.4 Decision-Tree Performance Classification In addition to the prediction and optimisation parts, a simple decision-tree model to interpret the working conditions was constructed. Table 1 shows the calculated M.I. and PI values for several scenarios. The M.I. values can be negative in low-performance situations. They can take strong positive values in high-performance scenarios, indicating that the system can represent different parameter permutations. The decision tree discovered a few of the important rules, such as: Efficiencies are often higher (> 85%) when operating temperatures are above 600°C and loss rates are below 1.5%. Low-performance cases related to prolonged charging duration and inadequate thermal conduction from the stainless steel coupling. Where P· is at least. At a retention time of 140 hours, the numbers advanced, demonstrating that the sand battery can retain information for days. This is corroborated by the overall composite performance index (OPI), calculated using the Mean Performance Index (MPI) of 84.1%, demonstrating that the sand TES system achieves reliable, repeatable performance across a broad range of operating conditions. By far, this is a more intuitive interpretive framework than the black-box nature of ANNs, offering great interpretative power, a challenge, and a practical tool for the operator. 4.4 Mean Performance Index As per Table 6 the Mean Performance Index (MPI) for the Sand Battery represents the average operational characteristics across multiple performance metrics, including efficiency, retention time, operating temperature, energy loss rate, and cost per MWh.At an average efficiency of 84.1% and a retention time of 114 hours at 590°C, it retains an energy decay rate of 1.54%. The weighted average is 30.6 USD/MWh, which demonstrates a trade-off among energy retention, operational performance, and cost-effectiveness for the thermal-energy-storage system. Table 6 Mean Performance Index (MPI) for sand battery performance. No. Efficiency (%) Retention Time (h) Operating Temp. (°C) Energy Loss Rate (%) Cost / MWh M.I PI 1 85.2 120 600 1.5 30.0 0.165 0.757 2 80.1 110 590 2.0 31.5 0.163 0.756 3 90.3 140 580 1.2 28.5 0.241 0.322 4 70.0 100 570 3.0 33.0 -0.961 -0.854 5 95.0 160 610 1.0 29.0 0.954 0.365 MPI 84.1 114 590 1.54 30.6 5. Discussion This study presents findings that improve our understanding of the operational behaviour and optimisation potential of sand-based thermal energy storage (TES) systems. We show that although sand has desirable thermophysical properties, the heat-transfer limitations of granular media prevent it from serving as an effective thermal energy transport medium, as demonstrated by simulations. Since lower charging rates penetrate the bed more slowly than higher rates, the heating curves also show that some initial heat-penetration advantage is achieved at the higher charging rate. However, that advantage disappears as the bed approaches thermal equilibrium. As shown in previous studies of conduction-dominated thermal regimes, low thermal diffusivity limits the rate at which heat can propagate through granular materials (Chung & Chen, 2022 ), and this behaviour is to be expected. As a result, while fast charging power initially reduces the time spent charging at low SOC levels, it does not improve efficiency in proportion, as more time is spent charging at 75% or 80% SOC. This information implies that sand batteries operate best when heat input is optimized through strictly regulated charging strategies — preferably adaptive ones that modulate the heating process in response to instantaneous temperature gradients to minimize energy losses (Tetteh S et al. 2021 ). This ANN performance once more reinforces the potential of machine-learning techniques for TES modelling. The high predictiveness of R² = 0.963 indicates that the model simultaneously captured the nonlinearity in the input features of charging temperature, charge rate, and coupling material, as well as system efficiency. Thus, the sand bed is a thermodynamically unsteady medium with highly complex relations that are difficult to model analytically. The ANN's high generalisation performance demonstrates its suitability not only for this stand-alone pilot but also for real-time energy management systems that need to make predictions quickly to schedule storage in response to fluctuating renewable-energy inputs. In addition, the lower MAE and RMSE values suggest that the ANN architecture applied in this study achieves a good balance between complexity and predictive accuracy. This contributes to global efforts to deploy AI-controlled devices for energy storage applications (Zhang et al. 2018 ; Mohammad et al. 2018 ). Optimisation framework enhanced with a GA — A genetic algorithm (GA) is a simple and effective way of finding the optimal operating conditions for high performance. The best charging temperatures, charge rates, and material combinations that the GA predicted, given access to the limited library, illustrate the GA's utility for exploring multidimensional, nonlinear search spaces. Specifically, moderate charge rates and high charge temperatures always performed well, suggesting an optimisation between rapid heat loading (high qv & ideal concentration) and long-term heat retention (low s). It is interesting to note that these optimal points align with advice we have gained from experience in high-temperature TES design: aggressive heating often results in higher thermal losses without a parallel increase in the quality of stored energy. Using GA with an ANN to predict efficiencies significantly reduces the computational power required to drive the GA. This makes the interleaving approach feasible for large-scale optimisation problems that would otherwise be computationally infeasible. So, adding the decision-tree model helps improve the interpretability of the system's performance. Although ANNs have the potential for high predictive accuracy, their non-interpretability may restrict the use of operational data and thereby limit their utility by affecting operational decision-making. This constraint is overcome in the proposed decision tree, which produces discriminatory rules for classifying performance grades based on major economic and thermal parameters. By identifying thresholds—for example, the minimum number of days a customer must remain a customer, or the maximum acceptable loss rate from this optimal churn profile—the model produces insights that can be acted on to operate the system. When optimised, the sand TES achieves an impressive Mean Performance Index (MPI) of 84.1%, indicating that sand is very promising for real-world applications with long storage durations. In addition to the performance-based aspects of the hybrid modelling approach, the decision tree's interpretability makes it user-friendly for operators and engineers (Vaid et al., 2011 ). In conclusion, the integrated framework described in this study demonstrates the potential of coupling a physics-based sand TES system model with a data-driven machine learning and global optimisation framework to make significant advances in the analysis and optimisation of these systems. These complementary synergies lead to better predictions, faster optimization, and more effective performance evaluation. The result demonstrates that a low-cost material, such as sand, can serve as an environmentally friendly thermal energy storage medium, providing long-duration storage and facilitating the system-wide integration of renewables. However, the work identifies important avenues for improvement, such as experimental validation, material characterization, and multiscale thermal phenomena. Addressing these issues will make sand batteries more relevant for industrial heat needs, district heating networks, and potentially other similar thermodynamic systems based on hybrid thermal–electrical conversion. Overall, the discussion highlights that Sand TES systems hold significant promise when optimised with AI-driven frameworks for sustainability and long-duration renewable energy storage. Further research in this area can play an important role in transitioning the world to carbon-neutral energy systems. 6. Conclusion A novel ANN–GA decision tree framework was presented in this study for modelling and optimisation of sand-based thermal energy storage systems. The numerical simulation revealed that the thermal behaviour is highly sensitive to charge rate and material selection. Results showed that ANN had superior predictive performance (MAE = 1.72%, RMSE = 2.31%, R² = 0.963). At the same time, GA optimisation identified the optimal operating conditions for high performance. The decision-tree model allowed a transparent mini-category of system performance with an overall MPI of 84.1% The conclusion that AI-augmented optimisation can achieve dramatic improvements in the performance and scalability of sand-based TES systems makes them more viable for widespread integration into large-scale renewable energy storage systems. Declarations Competing interest: The authors declare no competing interests. Funding: No specific funding was allocated for this research paper by any public, commercial, or not-for-profit funding agency. Data Availability No datasets were generated or analysed during the current study. Author Contributions Kriti Vaid led the Conceptualisation, Investigation, Methodology, Validation, Writing review, and editing. Anil Soharu led the Review and editing. Naveen BP led the Conceptualisation, Validation, and Visualisation. Acknowledgements Not applicable References Carmichael RS (2017) Practical handbook of physical properties of rocks and minerals . CRC Press. Vaid, K., Chaurasia, A., Rawat, S., & Dwivedi, U. (2021). Structural and dielectric properties of copper ferrite/LDPE composite. Materials Today: Proceedings , 43: 373–377. Vaid, K., Rathore, D., & Dwivedi, U. (2020) Electromagnetic interference of nickel and copper ferrite LDPE composite. Journal of Composite Materials . Kilic I, Aydin M, Sahin H (2024) Predicting battery capacity with ANN. J Intell Transp Syst Appl , 7(2): 99–112. Prasad JS et al. (2019) Review of thermochemical storage systems. Appl Energy , 254: 113733. Chung KM, Chen R (2022) Black coating of quartz sand towards low-cost solar thermal storage. Solar Energy , 249: 98–106. Poulose T et al. (2022) Power storage using sand. J Energy Storage , 51: 104381. Vaid, K., Chaurasia, A., Rathore, D., & Dwivedi, U. (2020) Dielectric and EMI shielding behaviour of BaTiO₃–CoFe₂O₄/LDPE composite. Polymer Composites . Islam MS, Hannan MA, Shareef H, Mohamed A (2015) Review of energy storage systems in microgrid applications. Int J Renew Energy Res , 5(2): 427–438. Jha ASR, Soroushian P, Aslani F, Lu H (2017) Sand-based energy storage systems. Renew Sustain Energy Rev , 72: 115–129. Khorsand R, Mohammadi-Ivatloo B (2018) ANN and ANFIS for battery SOC estimation: comparative study. Energy , 163: 895–909. Mohammad F et al. (2018) Review of energy storage in microgrids. IEEE Access , 6: 35143–35164. Vaid, K., Dwivedi, U., & Rathore, D. (2020) Dielectric properties of LDPE-based nickel and copper ferrite. J. Phys.: Conf. Series . Kober T et al. (2020) Global energy perspectives. Energy Strategy Rev , 31: 100523. Omar A et al. (2019) Battery management systems in renewable energy. IEEE Access , 7: 160232–160249. Rathika N et al. (2024) Neural network-based EMS for DC microgrid. Electrical Engineering , 106(2): 1–12. Radwan O, Humphrey J (2023) Uses of sand in solar thermal technologies. Sol Energy Mater Sol Cells , 261: 112533. Smith MT et al. (2020) Optimising battery performance with AI. J Energy Storage , 23: 123–135. Vani E et al. (2024) PV–wind–battery microgrid with neural network MPPT. J Electr Syst , 20(5s): 1–10. Tetteh S et al. (2021) Cost-effective electro-thermal energy storage. J Energy Storage , 41: 102829. Zhang J, Liu C, Wang X (2018) ANN optimisation of energy storage systems. IEEE Trans Ind Electron , 65(6): 4697–4705. Mohammad F, Cvetkovic I, Batarseh I, Al-Ohaly A (2018) Review of energy storage system technologies in microgrid applications: issues and challenges. IEEE Access 6:35143–35164. https://doi.org/10.1109/ACCESS.2018.2853721 Vaid, K., Sood, Y. R., & Jarial, R. K. (2011) Identification of harmonic sources in deregulated power sector. (Conference paper). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8298202","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":559073987,"identity":"aa1da5ce-18ce-4a3b-beda-a6d8ced14a47","order_by":0,"name":"Kriti Vaid","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACCQbGBoYEBgYehuMNQK6BBVFaGhvAWs4cAGmRIEYLyBoQuJEA5RMCkrMPtz942GYnw3fz+dUNPwokGPjbuxPwapHmS2xsSGxL5pG8nVN2swfoMIkzZzfg1SLHA/LLGWYeg9s5aTd4gFoMJHKJ0lLPY3DzTNrNP8RokQZrqTjMY3CD/dhtomyR7GFsnJFQcZxH8kwO220ZAwkegn6ROMP+4OMPg2p7vuPHn91888dGjr+9F78WJMBjACaJVQ4C7A9IUT0KRsEoGAUjCAAA0EBICJr7G08AAAAASUVORK5CYII=","orcid":"","institution":"DPG College","correspondingAuthor":true,"prefix":"","firstName":"Kriti","middleName":"","lastName":"Vaid","suffix":""},{"id":559073989,"identity":"52542b19-0701-4554-b16c-9ffae5f28623","order_by":1,"name":"Anil Soharu","email":"","orcid":"","institution":"Amity University","correspondingAuthor":false,"prefix":"","firstName":"Anil","middleName":"","lastName":"Soharu","suffix":""},{"id":559073990,"identity":"8b7a5676-6095-4c3c-a7d5-05c73b3d1a6c","order_by":2,"name":"Naveen 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1","display":"","copyAsset":false,"role":"figure","size":512194,"visible":true,"origin":"","legend":"\u003cp\u003eSand batteries process flow\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8298202/v1/c8dd0034f34ec788da957192.png"},{"id":98429221,"identity":"abd3f2fd-5363-4370-be0f-71d7bdca91e2","added_by":"auto","created_at":"2025-12-17 16:42:58","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":114279,"visible":true,"origin":"","legend":"\u003cp\u003eA simulation graph showing temperature rise over time for different charge rates in the sand battery system.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8298202/v1/7783428aa15fa19d1654fa7f.png"},{"id":98428285,"identity":"597108c1-59fb-41a8-b60f-4fcc1424240e","added_by":"auto","created_at":"2025-12-17 16:41:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":115290,"visible":true,"origin":"","legend":"\u003cp\u003eA scatter plot illustrating predicted versus actual thermal efficiency values, showing high correlation and alignment with the ideal prediction line\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8298202/v1/b76d36e7c7fe110e89369509.png"},{"id":99799182,"identity":"625f40c5-06c5-4bd2-a9ea-7e2dddc21973","added_by":"auto","created_at":"2026-01-08 13:49:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1542959,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8298202/v1/a2b179fb-1f02-4382-b65a-57f3a0adc9be.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimization of Sand Battery Systems for Renewable Energy Storage Using Artificial Neural Networks","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eTransitioning to renewable energy on the timescales required is now one of the signature technological and environmental challenges of the\u0026ensp;21st century. In a bid to reduce high-GHG-emitting fossil fuels, amid rising energy security concerns, and in line with commitments to global climate targets, countries around the world are deploying more solar photovoltaic (PV) and wind energy in power grids. While these renewable energy sources are highly beneficial to the environment and the economy, they have an inherent intermittent nature\u0026ensp;that is highly dependent on weather (Carmichael \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Solar power patterns are affected by changes in cloud cover. However, solar irradiance, and therefore energy production, has a diurnal cycle as well as seasonal variability. At the same time, wind energy is subject to unpredictable atmospheric patterns. The intermittent nature of these sources leads to inevitable supply-demand mismatches that limit the stability and reliability of today's power systems. With the rise in renewable penetration, flexible, scalable long-duration energy storage solutions are urgently needed.\u003c/p\u003e\u003cp\u003eTraditional electrochemical battery technologies\u0026mdash;primarily lithium-ion, lead\u0026ndash;acid, sodium\u0026ndash;sulfur, and next-generation solid-state batteries\u0026mdash;have been established as sustainable options for short-term grid-scale, electric mobility, and consumer electronics applications. However, its commercial use at a large scale is impeded by problems including degradation during cycling, thermal instability, material scarcity in large quantities\u0026ensp;, and high capital costs. The price fluctuations of lithium and cobalt \u0026mdash; necessary materials for high-performance batteries \u0026mdash; also impose significant environmental and geopolitical constraints due to the concentration of global supply chains. Moreover\u0026ensp;, of course, big batteries also pose recycling problems and long-term environmental risks. The limitations of these storage methods have compelled investigators and policymakers to seek alternative, more environmentally friendly energy storage technologies that use readily available materials, have a low environmental impact, and provide a long service life.\u003c/p\u003e\u003cp\u003eThermal energy storage (TES) offers strong potential as an alternative to electrochemical batteries, with applications in the grid and at an industrial scale. TES technologies, which store\u0026ensp;excess energy as heat and release it when needed, are natural long-duration storage systems. While many TES media have been proposed, such as molten salts, water, concrete, phase-change materials (PCMs), and ceramic composites, sand has recently drawn attention due to its unique combination of wide availability, low cost, thermal stability,\u0026ensp;and safety. Silica Rich Sand is abundant in nature, has no toxicological characteristics, is chemically inert, is thermally stable (\u0026gt;\u0026thinsp;800\u0026deg;C ), and thus is a potential material for high temperature\u0026ensp;sensible heat storage. Compared to molten salts, sand does not exhibit freezing\u0026ndash;melting restrictions or corrosive behaviour, and compared to PCMs, it does not require encapsulation or complex phase management (Vaid et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eJust a few examples of early prototypes and pilot-scale implementations of \"sand batteries\" report storing heat at 600\u0026ndash;700\u0026deg;C for several days. The systems use resistive or inductive heaters to generate thermal energy from excess electricity, which is stored in a silica sand bed within an insulated steel vessel. Another area of promising adaptability is heat extraction via air movement, heat exchangers, or thermal oil loops, allowing the concept to be used for district heating, industrial processes, greenhouse heating, and, perhaps later, even a power-generation cycle coupling. Sand-based batteries provide low-cost conversion capacity, extended operational longevity, and a low environmental footprint, making them a desirable option for seasonal-scale energy storage and grid decarbonisation applications.\u003c/p\u003e\u003cp\u003eNonetheless, important scientific and engineering issues remain to be overcome in the optimisation of sand battery systems. Granular media have low thermal diffusivity, so sand takes a long time to absorb heat, and shallow layers of sand exhibit different temperature distributions. Suppose the system's heating\u0026ensp;is not uniform. In that case, the overall efficiency can be reduced, and thermal losses through the container's boundaries will increase. In addition to grain size distribution, porosity, mineral composition, and water content, grain size also affects the thermal behaviour of sand. Identification of materials and modelling of their coupling (aluminium, copper, steel, etc.) regulates the direct transfer of heat. However, the choice involves trade-offs among thermal conductivity, structural stability, and cost. Finding the best operating conditions, including charging temperature, charge rate, insulation thickness, material, and discharge patterns, requires complex modelling of nonlinear thermal and physical behaviours (Vaid et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo meet these challenges, the health field has new capabilities enabled by artificial intelligence (AI). Machine learning models (MLMs), especially artificial neural networks (ANNs), have shown extraordinary ability to capture complex, nonlinear, and multivariate relationships in many energy systems. ANNs were used for state-of-charge prediction in batteries, renewable generation prediction, optimising microgrid performance, and thermal behaviour analysis in heat storage systems. As they learn from simulation or experimental data and generalise across varied operating conditions, they are best suited for modelling sand TES, where traditional analytical equations cannot accurately capture nonlinear temperature gradients and multi-parameter associations. In addition, using ANNs in conjunction with optimisation algorithms such as Genetic Algorithms (GAs) can considerably improve performance by determining suitable configurations for practical energy storage.\u003c/p\u003e\u003cp\u003eOn the other hand, although there has been significant advancement in the optimisation of energy storage, ANN-based modelling and ANN\u0026ndash;GA hybrid optimisation frameworks have not been applied to sand battery systems in the prevailing body of research. This opens a clear door for the development of sand TES technologies and their potential use.\u003c/p\u003e\u003cp\u003eThe novelty of this study is that it attempts to fill that research gap by developing a coherent modelling methodology based on numerical thermodynamic simulation, ANN prediction, GA optimisation, and decision-tree interpretability. A key objective is to optimize sand battery performance to increase charging efficiency, thermal homogeneity, and functional integrity across a wide range of thermal, material, and geometric parameters. Closing these gaps improves system performance and yields an actionable framework that serves a diverse set of stakeholders involved in renewable energy deployment, such as operators, engineers, and policymakers.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Sand-Based Thermal Energy Storage (TES)\u003c/h2\u003e\u003cp\u003eIn this TES method, called sand-based TES, thermal energy is stored as sensible heat by raising the temperature of a solid medium [8]. Sand is one of those candidates due to its high abundance and stability, as described by Carmichael in 2017. Recent commercial prototypes indicate commercial readiness, with heated sand at 500\u0026ndash;700\u0026deg;C as a potential heat storage system with exceptionally long life (after being heated with excess renewable electricity) (Kilic et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eSand is a promising, non-toxic, low-cost material that could serve as a sustainable substitute, at least for electrochemical storage (especially at grid and industrial scales).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Thermophysical Properties of Sand\u003c/h2\u003e\u003cp\u003eAs per Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Silica sand rich in quartz has an SiO₂ content of 70\u0026ndash;90%, a high melting temperature (\u0026gt;\u0026thinsp;1600\u0026deg;C), low thermal expansion, and\u0026ensp;chemical inertness (Prasad et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This can negatively affect clinker performance or cause gas release at high temperatures (Radwan \u0026amp; Humphrey, 2024).\u003c/p\u003e\u003cp\u003eSize (optimal,\u0026ensp;0.2\u0026ndash;1 mm) achieves good porosity and heat-transfer efficiency. A higher quartz content increases thermal conductivity, thereby facilitating the effective heat transfer (Chung \u0026amp; Chen, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComposition of sand and its behaviours towards sand batteries.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eComponent\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePercentage\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBehaviour towards sand batteries\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQuartz (SiO₂)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e70\u0026ndash;90%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eExcellent thermal stability, high melting point, and chemically inert. Ideal for heat storage.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFeldspar (KAlSi₃O₈ \u0026ndash; NaAlSi₃O₈ \u0026ndash; CaAl₂Si₂O₈)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5\u0026ndash;15%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDecent thermal properties can undergo phase changes or break down at very high temperatures.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGypsum (CaSO₄\u0026middot;2H₂O)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u0026ndash;5%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDecomposes at relatively low temperatures (~\u0026thinsp;150\u0026ndash;200\u0026deg;C) and releases water vapour, which is unsuitable for stable heat storage.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCarbonates (Calcite - CaCO₃, Dolomite - CaMg(CO₃)₂)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u0026ndash;5%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDecompose at 600\u0026ndash;900\u0026deg;C, releasing CO₂ \u0026mdash; problematic for high-temperature storage.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eClay minerals (Kaolinite, Illite, Montmorillonite)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;5%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePoor thermal conductivity can expand with heat and moisture. Not ideal.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHeavy minerals (Magnetite, Zircon, Ilmenite, etc.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTrace\u0026ndash;1%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSome, such as Magnetite, have strong thermal storage potential. Others vary.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Operational Principles of Sand Batteries\u003c/h2\u003e\u003cp\u003eSand battery technology works on sensible heat storage, where energy is stored as thermal energy in a solid, granular medium, typically silica-rich sand. A sensible heat storage system typically comprises an insulated steel or concrete box filled with sand, electrical heating elements, and an air duct, heat exchanger, or thermal oil circuit to extract the heat. The charging process converts excess electrical energy generated by renewable sources (solar PV or wind) into thermal energy via resistive or inductive heating. This heat is transferred into the sand bed, increasing the temperature from ambient levels to about 600\u0026ndash;800\u0026deg;C due to system design and material limitations.\u003c/p\u003e\u003cp\u003eAs depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, heat transfer in sand occurs principally by conduction and by some convection in the air between the particles. Due to sand's relatively low thermal diffusivity, the heating process leads to nonuniform temperature gradients, with the hottest regions forming around the heating elements. The process of heat diffusion towards the\u0026ensp;periphery of the bed takes time. However, homogenisation can take days (in extreme cases). Characterization of thermal storage capacity by mass\u0026ensp;/ specific heat capacity and in terms of the allowable temperature range of sand. To improve heat storage, quartz-dominant silica sands are often used because they exhibit stable thermophysical properties at elevated temperatures (Poulose T et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn the discharging stage, the thermal energy stored in the storage system is removed and used, for example, for district heating, industrial drying, greenhouse heating, or combined with a thermodynamic cycle for electricity production. The process of heat extraction involves air, water, or thermal oil flowing through tubes or ducts embedded in the sand, extracting heat from the sand, and transporting it to the end application. The success of this part depends on the heat exchanger design, flow rate, and thermal gradient.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eInstead, sand battery systems provide a high-power, low-cost, long-duration storage option. However, performance is highly dependent on the choice of materials, heating strategy, insulation, and geometry, all of which require sophisticated modelling and optimisation tools.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Challenges in Sand TES Systems\u003c/h2\u003e\u003cp\u003eWhile promising, sand-based TES systems still face several technical challenges that limit their efficiency and use at larger scales. Granular sand exhibits low thermal diffusivity, which slows the \u0026ensp;charging process as a large temperature gradient forms across the storage bed. This manner of thermal distribution limits the storage capacity\u0026ensp;allotted. It produces localized heating where there are more heating elements than are being\u0026ensp;utilized. Moreover, long-term storage behaviour, and hence seasonal operation (Vaid et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), is heavily influenced by thermal losses through the walls of the storage container (e.g., insulation imperfections) and by ambient temperature variation. The heat\u0026ndash;transfer behaviour becomes more complicated because sand is a natural material. Its heterogeneity is mainly caused by variations in grain size, mineral composition, and moisture content within a single series. At the same time, thermal decomposition or gas generation at high temperatures further complicates this. Mechanical settling and compaction over several cycles can modify porosity, which, in turn, can affect airflow during heat extraction. Further, the absence of predictive control techniques results in static optimisation of charging and discharging processes, leading to inefficient operation. These challenges highlight an important direction for future system modelling: the need for more sophisticated tools, including machine learning and hybrid numerical\u0026ndash;data-driven frameworks, to represent system behaviour and support optimisation and control accurately.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 AI for Energy Storage Modelling\u003c/h2\u003e\u003cp\u003eArtificial neural networks (ANNs) have been used for forecasting overall lithium-ion battery state-of-charge (Islam et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), thermal system performance (Jha et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and microgrid performance (Khorsand \u0026amp; Mohammadi-Ivatloo, 2018). Their ability to model nonlinear behaviour is a\u0026ensp;good fit for sand TES optimisation.\u003c/p\u003e\u003cp\u003eThe performance of hybrid ANN\u0026ndash;GA systems is generally better in renewable energy applications (Mohammad et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.6 Research Gap\u003c/h2\u003e\u003cp\u003eDespite sand-based thermal energy storage (TES) emerging in recent years as a cost-competitive and sustainable alternative to conventional electrochemical systems, significant knowledge gaps remain. Although studies have examined material characterisation, insulation enhancement through simulations and prototype demonstrations, comprehensive modelling of the nonlinear thermal behaviour of sand beds remains scarce. Currently available analyses are based on simplified conduction models that omit the coupled effects of grain\u0026ensp;structure, thermal gradients, heating rates, and coupling materials. Additionally, few predictive machine-learning models exist that can generalise across varying operational conditions and provide performance evaluation on the go (Vaid et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Although artificial neural networks have been widely used in battery management and thermal system optimisation, their application in sandTES remains under-researched. There have also been no optimisation frameworks that use AI alongside evolutionary algorithms to find optimal charging schedules, operating temperatures, or material configurations (Kober T et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). A third gap is the lack of interpretable decision-support tools (e.g., decision trees) that\u0026ensp;can convert complex system behaviour into meaningful operational actions. Together, these gaps highlight a need for integrated, data-driven solutions that can synergise numerical modelling, AI prediction, and optimisation to improve the design, control, and deployment of sand-based TES at scale.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Methodology","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.1 System Configuration\u003c/h2\u003e\u003cp\u003eThe investigated sand-based thermal energy storage (TES) system consists of a perfectly insulated cylindrical steel vessel filled with quartz sand with a particle size of 100 \u0026micro;m. Silica-rich sand (grain size between 0.4 and 0.6 mm) offers advantageous thermophysical properties, such as a high melting temperature, chemical inertness, and stable thermal conductivity, and was therefore chosen. Resistive heating is used for thermal charging by embedding heating elements within the sand bed and an internal heat exchanger (e.g., metal tubes or channels) for thermal extraction during discharge. To distinguish the variation in heat-transfer performance due to significant differences in thermal conductivity, three possible coupling materials (aluminium, copper, and stainless steel) were studied. Being a supreme conductor, copper is used as a reference. At the same time, aluminium and stainless steel are usable alternative materials for price-sensitive applications (Omar A et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The simulated operational environment resembles that typical of renewable-energy applications, where excess electricity from a photovoltaic or wind system is used to charge the vehicles. This system configuration, hence, takes both practical design considerations and general constraints adopted in large-scale thermal energy storage applications into account.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Thermodynamic Simulation Model\u003c/h2\u003e\u003cp\u003eA transient thermodynamic model was also developed to simulate heat transfer in the sand bed under different charging scenarios. It uses the classical transient heat conduction equation with effective thermal conductivity and adequate volumetric heat capacity to account for the effects of solid grains and interstitial air in granular media. Due to sand's low thermal diffusivity\u0026ensp;, the temporal and spatial evolution of temperature must be well modeled to develop an understanding of charging dynamics. The governing partial differential equation was solved using boundary and initial conditions defined by the location of the heating element, the thickness of the thermal insulation, and the interaction with the ambient. The simulations were performed at charge temperatures from 300 to 700\u0026deg;C and charge rates from 5 to 25\u0026deg;C\u0026middot;min⁻\u0026sup1; as defined in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eKey input parameters for numerical model.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCharging Temperature\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e300\u0026deg;C to 700\u0026deg;C\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCharge/Discharge Rates\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5\u0026deg;C/min to 25\u0026deg;C/min\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCoupling Material Types\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAluminium, copper, stainless steel\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWe define these ranges\u0026ensp;based on likely and extreme operational scenarios for high-temperature TES systems. Furthermore, the respective thermal properties of the coupling materials were assigned to assess their effect on heat propagation. Outputs from the model included temperature evolution maps, radial temperature profiles, steady-state profiles, and thermal efficiency. These outputs\u0026ensp;constituted the initial dataset for downstream machine-learning analysis and optimisation (Radwan O, Humphrey J 2024).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.3 ANN Dataset Preparation\u003c/h2\u003e\u003cp\u003eA 500-scenario dataset exhibiting various charging conditions was generated using Latin Hypercube Sampling (LHS) to ensure adequate, representative training data for the artificial neural network (ANN). In high-dimensional engineering simulations, LHS is preferred\u0026ensp;, as it provides more homogeneous coverage of the parameter space while minimising correlation among sampled variables. There are three input parameters for each simulation scenario (charging temperature, charge rate, and type of coupling material), and four output parameters reflecting the system's efficiency, temperature rise rate, thermal loss indicators, and retention behaviour. Thus, the dataset captures the nonlinear relationships between the input variables and the sand bed's thermal response. The collected data were normalised and subsequently split into three unique subsets: 70% for training and \u0026ensp;15% each for validation and testing. So\u0026ensp;that the rad pattern for the ANN will learn the underlying patterns but keep generalisation for unseen data (Smith MT et al. 2020). Thus, the dataset provides an appropriate basis for an informative ML-driven model that can improve physics-based simulations.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.4 ANN Architecture\u003c/h2\u003e\u003cp\u003eAlso developed was a multilayer feedforward ANN used to map input operational parameters to the system's efficiency empirically. As per Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the selected architecture has an input layer, which corresponds to the three input quantities, namely, charging temperature, charge rate, and coupling material; the first hidden layer, which contains 10 neurons; a second hidden layer with seven neurons; and an output layer, which consists of\u0026ensp;1 neuron, namely, overall system efficiency (Vani E et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The hidden layers used a sigmoid activation function to capture more nonlinear behaviour, and the output layer used a linear activation function.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eArtificial neural network architecture structure.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInput Layer\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3 neurons (charging temperature, charge rate, coupling material)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHidden Layers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2 layers with 10 and 7 neurons, respectively, using the sigmoid activation function\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOutput Layers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1 neuron representing system efficiency\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eBackpropagation with a gradient-descent algorithm was used for training, and learning was assessed using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R\u0026sup2;). The ANN's prediction accuracy was very high; on a test dataset, MAE\u0026thinsp;=\u0026thinsp;1.72%, RMSE\u0026thinsp;=\u0026thinsp;2.31%, and R\u0026sup2; = 0.963, as tabulated in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. These results validate that the ANN generalises well over a wide range of operating conditions and indicate that it can be used as a surrogate model for optimisation and for real-time prediction. The ANN is therefore a computationally efficient substitute for multiple numerical simulations, resulting in reduced computation time whilst maintaining accuracy.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePerformance model values\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMAE\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.72%\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRMSE\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.31%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.963\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Genetic Algorithm Optimisation\u003c/h2\u003e\u003cp\u003eTo determine the optimal operational configurations that maximize efficiency in a sand battery, a Genetic Algorithm (GA) was coupled with the ANN model. Using methods analogous to natural selection, the GA explores the multidimensional parameter space to find high-performing solutions. Each candidate solution in this\u0026ensp;implementation corresponds to a distinct set of charging temperature, charge rate, and coupling material. The ANN output, representing the predicted efficiency, served as the GA fitness function, resulting in a much more efficient optimisation\u0026ensp;process than performing thermodynamic simulations in a loop. Optimisation was performed with a population of 50 candidate solutions, a crossover fraction of 0.8, a mutation rate of 0.01, and up to 100 generations as defined in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. In the GA, candidate solutions were iteratively evolved via crossover and mutation to a best-fitting parameter set. The integrated ANN\u0026ndash;GA hybrid framework combines machine learning and evolutionary optimisation to explore a complex design space efficiently.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eGenetic Algorithm parameters.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePopulation Size\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eCrossover Fraction\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMutation Rate\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMaximum Generations\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e3.6 Decision-Tree Model\u003c/h2\u003e\u003cp\u003eThe ANN and GA offer predictive accuracy and practical optimisation, but at the expense of interpretability. To counter this disadvantage, we created a decision-tree model grounded in operational performance measures, enabling classification of operational scenarios. The tree included variables for charging efficiency, thermal retention time, loss rate, operating temperature, and cost per unit of energy. The internal nodes represent decision rules derived from the dataset, thresholds that split scenarios so that high- and low-performing scenarios can be readily identified. Quantitative evaluation of system performance across a range of operational states is included in the model's Mean Index (M.I.), Performance Index (PI), and aggregated Mean Performance Index (MPI) outputs. Thus, the decision-tree model provides an interpretable diagnostic tool that aids operators in decision-making, helps tune parameters under active conditions, and provides interpretability and guidance for the ANN\u0026ndash;GA framework.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results","content":"\u003cp\u003eThis section presents simulation outcomes, ANN predictive performance, GA optimisation effects, and decision-tree derived performance indices.\u003c/p\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Thermal Charging Behaviour\u003c/h2\u003e\u003cp\u003eThermal charging simulations reveal the short-term behavior of the sand bed at different heat-input rates over a given time period. Temperature profiles within the sand battery for charging rates of 1.0\u0026times;, 1.2\u0026times;, and 1.5\u0026times; are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. At baseline (1.0\u0026times;), the temperature rises slowly over time, consistent with a typical conduction-limited response in a granular material. The bed temperature reaches around 600\u0026deg;C after 10 hours of charging, with various thermal gradients across the core and the external regions.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWhen the charging rate reaches 1.2\u0026times;, the initial temperature increases rapidly, and the sand can reach nearly 620\u0026deg;C in the same time. This behaviour corresponds to higher bed heat flux and a lower delay between the heating element and the adjacent beds. At a rate of 1.5\u0026times;, the maximum, the thermal ramp is the steepest, reaching 648\u0026deg;C after 10 hours. Again, as in the previous conditions, the curve levels off as the system approaches thermal equilibrium.\u003c/p\u003e\u003cp\u003eThat asymptotic behaviour reflects the intrinsic limits of sand's thermal diffusivity: heat transfer slows and slows as the temperature gradient decreases. The ability of higher charge rates to increase energy absorption in the early periods, while producing diminishing returns in the late periods, is consistent with these findings. In actual system operation, this means that efficiency can be improved with an adaptive charging strategy \u0026mdash; for example, if a high flux is used but the thermal gradient is slight, the system may not operate as expected, so the heat input is successively tapered.\u003c/p\u003e\u003cp\u003eSimulations show:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eBaseline (1.0\u0026times;): Temperature rises gradually from 500\u0026deg;C to approximately 600\u0026deg;C after 10 h.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e1.2\u0026times; rate: Faster thermal penetration, reaching\u0026thinsp;~\u0026thinsp;620\u0026deg;C in the same duration.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e1.5\u0026times; rate: Highest thermal intensity, achieving\u0026thinsp;~\u0026thinsp;648\u0026deg;C.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThese curves exhibit an asymptotic tendency toward thermal equilibrium, consistent with conduction-limited thermal transport in granular media (Prasad et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Radwan \u0026amp; Humphrey, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003e4.2 ANN Predictive Performance\u003c/h2\u003e\u003cp\u003eTo evaluate the ANN model's performance in determining system efficiency across different operating conditions, performance tests were conducted using validation and test data. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e: ANN empirical (y-axis) and simulated\u0026ensp;(x-axis) efficiencies. Strict model generalisation with little systematic error is illustrated by data points clustered closely around the 45\u0026deg; reference line in the lower-left panel. Performance metrics\u0026ensp;are another source confirming accuracy:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eMean Absolute Error (MAE): 1.72%\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eRoot Mean Square Error (RMSE): 2.31%\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCoefficient of determination (R\u0026sup2;): 0.963\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe MAE and RMSE are relatively low, indicating that the model has a slight deviation from simulated efficiencies, and the R\u0026sup2; is high, indicating that the ANN accounts for over 96% of the variance in efficiency. In fact, at low or high charging rates, we also observed increased efficiency errors, suggesting that the nonlinearity is significantly worse at these limits. Nonetheless, the impressive predictive performance of the ANN justifies its application as a cheaper surrogate model in optimisation, as it provides a significant reduction in computational cost during the exploration of large parameter spaces.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Optimisation Outcomes via Genetic Algorithm\u003c/h2\u003e\u003cp\u003eThe Genetic Algorithm (GA) with the ANN surrogate model identified the best charging temperature, charge rate, and coupling material combination. There were more than a thousand potential configurations to monitor. On the other hand, the hybrid approach generated a converged GA after just 100 generations.\u003c/p\u003e\u003cp\u003eBy consistently including\u0026ensp;the following high-efficiency configurations:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eHigh\u0026ensp;charging temperatures close to the top of the simulated range (650\u0026ndash;700 ◦C),\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eAverage charging rates (1.2\u0026times;) that mediate the timing of heat retention at energy sites.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCoupling material of copper\u0026ensp;because of its high heat conduction rate\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eAlthough low efficiencies were observed across all stainless steels, aluminium was found to be competitive at intermediate heating rates, indicating that more affordable bulk alternative materials could serve as suitable replacements for more costly high-temperature materials\u0026ensp;at large scales.\u003c/p\u003e\u003cp\u003eThe optimisations show that interactions between multiple variables are important. However, efficiency was not\u0026ensp;solely driven by the charging temperature: the coupling with charge rate and the coupling material had synergistic effects that the GA appropriately accounted for.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Decision-Tree Performance Classification\u003c/h2\u003e\u003cp\u003eIn addition to the prediction and optimisation parts, a simple decision-tree model to interpret the working conditions was constructed. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the calculated M.I. and PI values for several scenarios. The M.I. values can be negative in low-performance situations. They can take strong positive values in high-performance scenarios, indicating that the system can represent different parameter permutations.\u003c/p\u003e\u003cp\u003eThe decision tree discovered a few of the important\u0026ensp;rules, such as:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eEfficiencies are often higher (\u0026gt;\u0026thinsp;85%) when operating temperatures are above 600\u0026deg;C and loss rates are below\u0026ensp;1.5%.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eLow-performance cases related to prolonged charging duration\u0026ensp;and inadequate thermal conduction from the stainless steel coupling.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eWhere P\u0026middot; is at least. At a retention time of 140 hours, the numbers advanced, demonstrating that the sand battery can retain information for days.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis is corroborated by the overall composite performance index (OPI), calculated using the Mean Performance Index (MPI) of 84.1%, demonstrating that the sand TES system achieves reliable, repeatable performance across a broad range of operating conditions. By far, this is a more intuitive interpretive framework than the black-box nature of ANNs, offering great interpretative power, a challenge, and a practical tool for the operator.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e4.4 Mean Performance Index\u003c/h2\u003e\u003cp\u003eAs per Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e the Mean Performance Index (MPI) for the Sand Battery represents the average operational characteristics across multiple performance metrics, including efficiency, retention time, operating temperature, energy loss rate, and cost per MWh.At an average efficiency of 84.1% and a retention time of 114 hours at 590\u0026deg;C, it retains an energy decay rate of 1.54%. The weighted average is 30.6 USD/MWh, which demonstrates a trade-off among energy retention, operational performance, and cost-effectiveness for the thermal-energy-storage system.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMean Performance Index (MPI) for sand battery performance.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEfficiency (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRetention Time (h)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOperating Temp. (\u0026deg;C)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eEnergy Loss Rate (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCost / MWh\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eM.I\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003ePI\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e85.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e30.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.165\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.757\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e80.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e110\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e590\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e31.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.163\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.756\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e90.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e140\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e580\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e28.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.241\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.322\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e70.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e570\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e3.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e33.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-0.961\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e-0.854\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" 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colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003e84.1\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e114\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e590\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e1.54\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e30.6\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eThis study presents findings that improve our understanding of the operational behaviour and optimisation potential of sand-based thermal energy storage (TES) systems. We show that although sand has desirable thermophysical properties, the heat-transfer limitations of granular media prevent it from serving as an effective thermal energy transport medium, as demonstrated by simulations. Since lower charging rates penetrate\u0026ensp;the bed more slowly than higher rates, the heating curves also show that some initial heat-penetration advantage is achieved at the higher charging rate. However, that advantage disappears as the bed approaches thermal equilibrium. As shown in previous studies of conduction-dominated thermal regimes, low thermal diffusivity limits the rate at which heat can propagate through granular materials (Chung \u0026amp; Chen, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and\u0026ensp;this behaviour is to be expected. As a result, while fast charging power initially reduces the time spent charging at low SOC levels, it does not improve efficiency in proportion, as more time is spent charging at 75% or 80% SOC. This information implies that sand batteries operate best when heat input is optimized through strictly regulated charging strategies \u0026mdash; preferably adaptive ones that modulate the heating process in response to instantaneous temperature gradients to minimize energy losses (Tetteh S et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThis ANN performance once more reinforces the potential of machine-learning techniques for TES modelling. The high predictiveness of R\u0026sup2; = 0.963 indicates that the model simultaneously captured the nonlinearity in the input features of charging temperature, charge rate, and coupling material, as well as system efficiency. Thus, the sand bed is a thermodynamically unsteady medium with highly complex relations that are difficult to model analytically. The ANN's high generalisation performance demonstrates its suitability not only for this stand-alone pilot but also for real-time energy management systems that need to make predictions quickly to schedule storage in response to fluctuating renewable-energy inputs. In addition, the lower MAE and RMSE values suggest that the ANN architecture applied in this study achieves a good balance between complexity and predictive accuracy. This contributes to global efforts to deploy AI-controlled devices for\u0026ensp;energy storage applications (Zhang et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Mohammad et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eOptimisation framework enhanced with a\u0026ensp;GA \u0026mdash; A genetic algorithm (GA) is a simple and effective way of finding the optimal operating conditions for high performance. The best charging temperatures, charge rates, and material combinations that the GA predicted, given access to the limited library, illustrate the GA's utility for exploring multidimensional, nonlinear search spaces. Specifically, moderate charge rates and high charge temperatures always performed well, suggesting an optimisation between rapid heat loading (high qv \u0026amp; ideal concentration) and long-term heat retention (low s). It is interesting to note that these optimal points align with advice we have gained from experience in high-temperature TES design: aggressive heating often results in higher thermal losses without a parallel increase in the quality of stored energy. Using GA with an ANN to predict efficiencies significantly reduces the computational power required to drive the GA. This makes the interleaving approach feasible for large-scale optimisation problems that would otherwise be computationally infeasible.\u003c/p\u003e\u003cp\u003eSo, adding the decision-tree model \u0026ensp;helps improve the interpretability of the system's performance. Although ANNs have the potential for high predictive accuracy, their non-interpretability may restrict the use of operational data and thereby limit their utility by affecting operational decision-making. This constraint is overcome in the proposed decision tree, which produces discriminatory rules for classifying performance grades based on major economic and thermal parameters. By identifying thresholds\u0026mdash;for example, the minimum number of days a customer must remain a customer, or the maximum acceptable loss rate from this optimal churn profile\u0026mdash;the model produces insights that can be acted on to operate the system.\u003c/p\u003e\u003cp\u003eWhen optimised, the sand TES achieves an impressive Mean Performance Index (MPI) of 84.1%, indicating that sand is very promising for real-world applications with long storage durations. In addition to the performance-based aspects of the hybrid modelling approach, the decision tree's interpretability makes it user-friendly for operators and engineers (Vaid et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn conclusion, the integrated framework described\u0026ensp;in this study demonstrates the potential of coupling a physics-based sand TES system model with a data-driven machine learning and global optimisation framework to make significant advances in the analysis and optimisation of these systems. These complementary synergies lead to better predictions, faster optimization, and more effective performance evaluation. The result demonstrates that a low-cost material, such as sand, can serve as an environmentally friendly thermal energy storage medium, providing long-duration storage and facilitating the system-wide integration of renewables. However, the work identifies important avenues for improvement, such as experimental validation, material characterization, and multiscale thermal phenomena. Addressing these issues will make sand batteries more relevant for industrial heat needs, district heating networks, and potentially other similar thermodynamic systems based on hybrid thermal\u0026ndash;electrical conversion. Overall, the discussion highlights that Sand TES systems hold significant promise when optimised with AI-driven frameworks for sustainability and long-duration renewable energy storage. Further research in\u0026ensp;this area can play an important role in transitioning the world to carbon-neutral energy systems.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eA novel ANN\u0026ndash;GA decision tree framework was presented in this study for modelling\u0026ensp;and optimisation of sand-based thermal energy storage systems. The numerical simulation revealed that the thermal behaviour is highly sensitive to charge rate and material selection.\u003c/p\u003e\u003cp\u003eResults showed that ANN had superior predictive performance (MAE\u0026thinsp;=\u0026thinsp;1.72%, RMSE\u0026thinsp;=\u0026thinsp;2.31%, R\u0026sup2; = 0.963). At the same time, GA optimisation identified the optimal operating conditions for high performance. The decision-tree model allowed a transparent mini-category of system performance with an overall MPI\u0026ensp;of 84.1%\u003c/p\u003e\u003cp\u003eThe conclusion that AI-augmented optimisation can achieve dramatic improvements in the performance and scalability of sand-based TES systems makes them more viable for widespread integration into large-scale renewable energy storage systems.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompeting interest:\u003c/strong\u003e The authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e No specific funding was allocated for this research paper by any public, commercial, or not-for-profit funding agency.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e No datasets were generated or analysed during the current study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e Kriti Vaid led the Conceptualisation, Investigation, Methodology, Validation, Writing review, and editing. Anil Soharu led the Review and editing. Naveen BP led the Conceptualisation, Validation, and Visualisation.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e Not applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eCarmichael RS (2017) \u003cem\u003ePractical handbook of physical properties of rocks and minerals\u003c/em\u003e. CRC Press.\u003c/li\u003e\n \u003cli\u003eVaid, K., Chaurasia, A., Rawat, S., \u0026amp; Dwivedi, U. (2021). Structural and dielectric properties of copper ferrite/LDPE composite.\u0026nbsp;\u003cem\u003eMaterials Today: Proceedings\u003c/em\u003e, 43: 373\u0026ndash;377.\u003c/li\u003e\n \u003cli\u003eVaid, K., Rathore, D., \u0026amp; Dwivedi, U. (2020) Electromagnetic interference of nickel and copper ferrite LDPE composite.\u0026nbsp;\u003cem\u003eJournal of Composite Materials\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eKilic I, Aydin M, Sahin H (2024) Predicting battery capacity with ANN. \u003cem\u003eJ Intell Transp Syst Appl\u003c/em\u003e, 7(2): 99\u0026ndash;112.\u003c/li\u003e\n \u003cli\u003ePrasad JS et al. (2019) Review of thermochemical storage systems. \u003cem\u003eAppl Energy\u003c/em\u003e, 254: 113733.\u003c/li\u003e\n \u003cli\u003eChung KM, Chen R (2022) Black coating of quartz sand towards low-cost solar thermal storage. \u003cem\u003eSolar Energy\u003c/em\u003e, 249: 98\u0026ndash;106.\u003c/li\u003e\n \u003cli\u003ePoulose T et al. (2022) Power storage using sand. \u003cem\u003eJ Energy Storage\u003c/em\u003e, 51: 104381.\u003c/li\u003e\n \u003cli\u003eVaid, K., Chaurasia, A., Rathore, D., \u0026amp; Dwivedi, U. (2020) Dielectric and EMI shielding behaviour of BaTiO₃\u0026ndash;CoFe₂O₄/LDPE composite.\u0026nbsp;\u003cem\u003ePolymer Composites\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eIslam MS, Hannan MA, Shareef H, Mohamed A (2015) Review of energy storage systems in microgrid applications. \u003cem\u003eInt J Renew Energy Res\u003c/em\u003e, 5(2): 427\u0026ndash;438.\u003c/li\u003e\n \u003cli\u003eJha ASR, Soroushian P, Aslani F, Lu H (2017) Sand-based energy storage systems. \u003cem\u003eRenew Sustain Energy Rev\u003c/em\u003e, 72: 115\u0026ndash;129.\u003c/li\u003e\n \u003cli\u003eKhorsand R, Mohammadi-Ivatloo B (2018) ANN and ANFIS for battery SOC estimation: comparative study.\u0026nbsp;\u003cem\u003eEnergy\u003c/em\u003e, 163: 895\u0026ndash;909.\u003cbr\u003eMohammad F et al. (2018) Review of energy storage in microgrids. \u003cem\u003eIEEE Access\u003c/em\u003e, 6: 35143\u0026ndash;35164.\u003c/li\u003e\n \u003cli\u003eVaid, K., Dwivedi, U., \u0026amp; Rathore, D. (2020) Dielectric properties of LDPE-based nickel and copper ferrite.\u0026nbsp;\u003cem\u003eJ. Phys.: Conf. Series\u003c/em\u003e.\u003c/li\u003e\n \u003cli\u003eKober T et al. (2020) Global energy perspectives. \u003cem\u003eEnergy Strategy Rev\u003c/em\u003e, 31: 100523.\u003c/li\u003e\n \u003cli\u003eOmar A et al. (2019) Battery management systems in renewable energy. \u003cem\u003eIEEE Access\u003c/em\u003e, 7: 160232\u0026ndash;160249.\u003c/li\u003e\n \u003cli\u003eRathika N et al. (2024) Neural network-based EMS for DC microgrid. \u003cem\u003eElectrical Engineering\u003c/em\u003e, 106(2): 1\u0026ndash;12.\u003c/li\u003e\n \u003cli\u003eRadwan O, Humphrey J (2023) Uses of sand in solar thermal technologies. \u003cem\u003eSol Energy Mater Sol Cells\u003c/em\u003e, 261: 112533.\u003c/li\u003e\n \u003cli\u003eSmith MT et al. (2020) Optimising battery performance with AI. \u003cem\u003eJ Energy Storage\u003c/em\u003e, 23: 123\u0026ndash;135.\u003c/li\u003e\n \u003cli\u003eVani E et al. (2024) PV\u0026ndash;wind\u0026ndash;battery microgrid with neural network MPPT. \u003cem\u003eJ Electr Syst\u003c/em\u003e, 20(5s): 1\u0026ndash;10.\u003c/li\u003e\n \u003cli\u003eTetteh S et al. (2021) Cost-effective electro-thermal energy storage. \u003cem\u003eJ Energy Storage\u003c/em\u003e, 41: 102829.\u003c/li\u003e\n \u003cli\u003eZhang J, Liu C, Wang X (2018) ANN optimisation of energy storage systems. \u003cem\u003eIEEE Trans Ind Electron\u003c/em\u003e, 65(6): 4697\u0026ndash;4705.\u003c/li\u003e\n \u003cli\u003eMohammad F, Cvetkovic I, Batarseh I, Al-Ohaly A (2018) Review of energy storage system technologies in microgrid applications: issues and challenges.\u0026nbsp;\u003cem\u003eIEEE Access\u003c/em\u003e 6:35143\u0026ndash;35164. https://doi.org/10.1109/ACCESS.2018.2853721\u003c/li\u003e\n \u003cli\u003eVaid, K., Sood, Y. R., \u0026amp; Jarial, R. K. (2011) Identification of harmonic sources in deregulated power sector. (Conference paper).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Sand battery, Thermal energy storage, Artificial Neural Networks, Renewable energy optimisation, Genetic Algorithm, Heat transfer modelling","lastPublishedDoi":"10.21203/rs.3.rs-8298202/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8298202/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAs renewable energy\u0026ensp;systems become increasingly intertwined globally, the need for low-cost, large-scale, and environmentally benign long-duration energy storage technologies has intensified. Silica-rich materials found in deserts have led to the implication that sand-based thermal energy storage (TES) systems should be developed in advance. Due to unavoidable heat-transfer limitations, nonuniform thermal distribution, and scepticism about the intelligent optimisation framework, system performance still operates within its limits.\u003c/p\u003e\u003cp\u003eIn this paper, we present a framework for optimizing sand battery systems using Artificial Neural Networks to improve operational efficiency. We developed a numerical thermodynamic model that simulates temperature dynamics within a silica sand bed as a function of key input parameters\u0026ensp;, including charging temperature (300\u0026ndash;700\u0026deg;C), charge/discharge rate (5\u0026ndash;25\u0026deg;C\u0026middot;min⁻\u0026sup1;), and coupling material type. A multilayer ANN trained on a dataset of 500 simulated scenarios generated using Latin Hypercube Sampling. As a result, the ANN demonstrated high predictive ability (MAE\u0026thinsp;=\u0026thinsp;1.72%; RMSE\u0026ensp;= 2.31%; R\u0026sup2; = 0.963). Afterward, a Genetic Algorithm (GA) was used to find operating conditions with the highest efficiency.\u003c/p\u003e\u003cp\u003eWe then derive a decision-tree model that classifies storage performance based on efficiency, retention time, energy loss rate, and cost. The Mean Performance Index (MPI) achieved was 84.1%, suggesting a high degree of overall fitness of sand-based TES for long-term storage.\u003c/p\u003e\u003cp\u003eThe combined ANN\u0026ndash;GA\u0026ndash;Decision-tree framework is a promising tool for improving the performance of sand batteries, paving the way for computerized, intelligent optimization and supporting economies of scale for low-cost renewable energy storage technology.\u003c/p\u003e","manuscriptTitle":"Optimization of Sand Battery Systems for Renewable Energy Storage Using Artificial Neural Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-12 11:48:19","doi":"10.21203/rs.3.rs-8298202/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"97d71805-0726-497a-b632-4e44df6fdb07","owner":[],"postedDate":"December 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-08T01:39:09+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-12 11:48:19","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8298202","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8298202","identity":"rs-8298202","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}