Prediction of cleaned coal yield based on different S-shaped curve models in coal cleaning production

Abstract Five S-shaped curve models are proposed to accurately predict the product yield and reduce the waste of precious coal resources during the coal cleaning process. Taking the Hill model (HM) as an example, the derivation process of parameters is described. The model’s accuracy is then verified by calculating the standard deviation, summary statistics, and residual plots for six groups of experimental data. It shows that the optimal prediction models for samples 1 to 6 are HM, the Gompertz model (GM), GM, the Logistic model (LM), the arctangent model (AM), and the normal integral model (NIM), respectively. The mean standard deviations of HM, GM, LM, NIM, and AM are 2.21, 2.23, 2.37, 2.41, and 3.06, respectively, indicating that the prediction accuracy of the five models is also arranged in this order. The prediction results of the optimal model (GM) are then verified by an industrial test in the Liudong Coal Cleaning Plant. The absolute errors of the separation density, cleaned coal yield, and cleaned coal ash are 0.005kg/L, 0.46%, and -0.09%, respectively. The maximum absolute error of the partition coefficients predicted by GM is -2.89%, while the maximum absolute error predicted by NIM alone is 8.19%, which is 5.30% higher than that predicted by GM. Furthermore, the error of the predicted partition coefficients near the separation density is usually greater than that at both ends of the partition curve, which is acceptable and typical. This work demonstrates that the prediction of cleaned coal yield based on different S-shaped curve models in the coal cleaning process is feasible, efficient, economic, and eco-friendly, and it has potential industrial application.