Accurately Predicting Quartz Sand Thermal Conductivity Using Machine Learning and Grey-Box AI Models

The thermal conductivity of materials is a crucial property with diverse applications, particularly in engineering. Understanding soil thermal conductivity is crucial for designing efficient geothermal systems, predicting soil temperatures, and assessing soil contamination. This paper aimed to predict quartz sand thermal conductivity by using four mathematical models: multiple linear regression (MLR), artificial neural network (ANN), classification and regression random forest (CRRF), and genetic programming (GP). A grey-box AI method, GP, was used for the first time in this topic. Seven inputs affecting thermal conductivity were evaluated in the study, including sand porosity, degree of saturation, coefficient of uniformity, coefficient of curvature, mean particle size, and minimum and maximum void ratios. In predicting thermal conductivity, the MLR model performed poorly, with a coefficient of determination R2 = 0.737 and a mean absolute error MAE = 0.300. Both ANN models using the Levenberg–Marquardt algorithm and the Bayesian Regularization (BR) algorithm outperformed the MLR model with an accuracy of R2 = 0.916 and an error of MAE = 0.151. In addition, the CRRF model had the best accuracy of R2 = 0.993 and MAE = 0.045. In addition, GP showed acceptable performance in predicting sand thermal conductivity. The R2 and MAE values of GP were 0.986 and 0.063, respectively. This paper presents the best GP equation for evaluating other databases. Additionally, the porosity and saturation of the sand were found to have the greatest impact on the model results, while coefficients of curvature and uniformity had the least influence. Overall, the results of this study demonstrate that grey-box artificial intelligence models can be used to accurately predict quartz sand thermal conductivity.