Drawing of coal washability curves based on machine learning and development of the drawing application

Coal washability curves are crucial for determining beneficiation processes and evaluating separation effectiveness. However, existing drawing methods require manual determination of coordinate axis intersections, depend on empirical formulas, are difficult to automate, and rely heavily on commercial software, which constrains the intelligent development of the coal preparation industry. An automated coal washability curve plotting algorithm based on machine learning is developed to realize intelligent curve generation and reduce dependence on commercial software. The InterFitWashability algorithm is proposed, comprising three core steps: Interpolation-based data augmentation phase — selectively using cubic spline interpolation (for elementary ash and cumulative sink curves) and Akima interpolation (for cumulative float, densimetric, and δ±0.1 content curves with sharp transitions), supplemented by PolynomialFeatures to add higher-order terms, addressing the issue of insufficient float-and-sink experimental data. Extrapolation-based data augmentation phase — extracting mathematical features from upper and lower curve segments separately, applying linear regression models for linear regions and Gaussian process regression models for nonlinear regions to predict and achieve automatic curve extension and determine coordinate axis intersections. Overall fitting phase — training decision tree regression models based on data generated from previous steps to establish a complete unified regression model for final washability curve generation. Three float-and-sink datasets with significantly different coal qualities (easy-to-wash coal, difficult-to-wash coal, and transitional coal samples) were selected to validate algorithm performance. Results show that the InterFitWashability algorithm achieved excellent performance across all three test datasets: mean square error (MSE) rangs from 0.0012 to 0.0364, mean absolute error (MAE) ranges from 0.017 to 0.025, and average curvature below 0.008. Compared to MATLAB-based fitting methods, it outperforms traditional curve fitting and interpolation methods, enabling automated and intelligent washability curve drawing. The algorithm-generated curves exhibit reasonable intersection points with coordinate axes, smooth and natural curve trends without obvious inflection points. For coal samples with different properties, the algorithm demonstrated good adaptability. The InterFitWashability algorithm successfully achieves automated and intelligent drawing of coal washability curves through machine learning methods, outperforming traditional methods in curve trends, fitting errors, and curve smoothness. The algorithm innovatively solves key technical challenges of existing methods: avoiding dependence on empirical formulas by segmentally extracting curve features and extending them separately; improving fitting accuracy of small sample data through data augmentation techniques; eliminating reliance on commercial software through complete development on the open-source Python platform. This algorithm provides new technical support for the intelligent development of the coal preparation industry with broad application prospects.