Artificial Neural Network-based prediction of storage-tank temperatures in hybrid electric water-heating systems with integrated thermal energy storage

Abstract

In this paper, artificial neural network (ANN) models were developed to predict the thermal output temperatures of multifarious electric storage tank water heating (ESTWH) systems integrated with a thermal water storage (TWS) tank and supplemented by waste heat recovery and a solar-assisted heat pump system. The study addresses the substantial energy demand associated with water heating in healthcare facilities by proposing a data-driven predictive framework for a complex hybrid thermal system. Two ANN models were implemented using the Levenberg–Marquardt backpropagation (LMBP) algorithm to model the TWS tank and four ESTWH capacities (100 L–250 L), utilising real sensor measurements combined with simulated operating profiles. Model development was conducted for both single-unit and multi-unit configurations, with ESTWH systems grouped according to storage capacity. Predictive performance was evaluated using the coefficient of determination (R 2 ), root mean square error (RMSE) and mean absolute error (MAE), while model interpretability was enhanced through feature-importance analysis using Garson's algorithm and Olden's connection-weight approach. ANN predictions were systematically compared with dynamic simulation outputs, and residual errors were assessed. A pilot comparative study was further conducted to evaluate the performance of the Levenberg–Marquardt optimiser against Adaptive Gradient Descent and Gradient Descent with Momentum. The developed ANN models achieved excellent predictive performance across all system configurations and seasonal datasets, with R 2 values exceeding 0.99, RMSE below 0.25 °C, and MAE below 0.06 °C. Stable convergence behaviour was observed with no evidence of overfitting. Feature-importance analysis identified ambient temperature, inlet water temperature, and solar-related parameters as the dominant drivers of system behaviour, with seasonal variations influencing relative sensitivities. The strong agreement between ANN predictions and dynamic simulation outputs confirms the robustness and scalability of the modelling framework for integrated dual-source renewable thermal systems. The Levenberg–Marquardt optimiser consistently demonstrated the fastest convergence and lowest prediction error among the evaluated algorithms. This work distinguishes itself from previous studies by applying ANN modelling to a hybrid water heating configuration that simultaneously integrates waste heat recovery, a solar-assisted heat pump, and multiple-sized ESTWH units. This is an integrated architecture not previously investigated using surrogate neural modelling approaches. Furthermore, the study introduces a size-specific performance evaluation (100 L–250 L), revealing the influence of thermal inertia on prediction accuracy, and develops a computationally efficient surrogate model capable of replacing high-fidelity dynamic simulations for real-time temperature forecasting and operational optimisation in complex thermal systems. • TES-integrated ESWHs need accurate tank-temperature prediction for control. • Existing models are slow and ignore seasonal and size-specific behaviors. • LM-trained ANN on normalised summer/winter data; TES + SAHP+WHR; 100–250 L. • Achieves R ≥ 0.95 with low MSE; 250 L model shows the lowest errors. • Enables real-time control, scheduling, and energy-efficiency optimization.