Optimized ANN-based mathematical model and software application for predicting raw mix lime saturation factor for high-quality cement production

The rapid increase in population drives a growing demand for expanded infrastructure. Cement quality, crucial for infrastructure performance, is largely influenced by a well-controlled raw mix lime saturation factor (LSF). Accurate LSF estimation relies on integrating precise mathematical formulas into elemental composition analyzers. However, the formulas traditionally utilized in the cement industry, often fall short of capturing underlying complexities of the process. Thus, there is need for more robust mathematical formula to accurately estimate LSF. This study develops LSF predictive models by employing artificial neural networks (ANN) optimized with particle swarm optimization (PSO), Levenberg–Marquardt (LM), and genetic algorithms (GA), using two thousand four hundred and sixty data points obtained via cross belt-analyzer. Dependable variables selected were lime, silica, alumina, and iron oxide. To enhance the practicality and ease of use, the models (LM-ANN, PSO-ANN, and GA-ANN) were converted into mathematical equations and further integrated into software application, in form of simple calculator. The models were validated using 5-fold cross-validation with random sampling, demonstrating consistent, generalization capability, and reliable performance across key metrics including coefficient of determination (R²), root mean squared error (RMSE), and mean absolute error (MAE). The models' performance was benchmarked against the established model proposed by Bogue (1966). The LM-ANN model outperformed both Bogue’s and the other evaluated models, achieving superior results across key metrics: R² = 0.9885, RMSE = 1.7828, relative squared error (RSE) = 9.99×10⁻⁷. While all three models are suitable for practical deployment, the LM-ANN model is strongly recommended for industrial applications. The mathematical model can be integrated into elemental composition analyzers to enhance real-time process optimization and improve cement production efficiency. Meanwhile, the software application will serve as a smart tool for rapid LSF estimation and consistent monitoring of analyzer reliability in cement production.