Feature-Ensemble Model With an Adaptive Self-Ensemble Module for Feed-Grade Monitoring in Froth Flotation

Accurate and stable feed-grade monitoring is essential for flotation and reagent control. Although some monitoring models for feed grade have been developed in recent years, they always use a group of time-series data with a fixed time step as input, and neglect the roles of models at different training steps. Therefore, to enhance the stability and accuracy of the feed-grade monitoring model, we propose a feature-ensemble model with an adaptive self-ensemble module. First, we use multiple groups of input vectors with different time steps as inputs to the monitoring model. Then, we introduce an adaptive self-ensemble module (ASE module) to fully use the models at different training steps with an adaptive adjustment mechanism and a self-ensemble module. After that, we construct a feature-ensemble model (FE model) embedding the ASE module to handle the multiple time series with different time steps. Effectiveness of the proposed monitoring model is validated both on a numerical example and an industrial example in froth flotation. In the numerical example, the root mean squared error (RMSE) of the three FE models with the ASE module decreases by 0.0090 to 0.0159, and the R-squared (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R^{2}$</tex-math></inline-formula>) score increases by 0.0013 to 0.0035, compared with the three single models. In industrial application, the RMSE of the three FE models with the ASE module decreases by 7.20% to 9.70%, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R^{2}$</tex-math></inline-formula> increases by 6.71% to 7.34%, compared with the three single models. This shows our framework can improve the feed-grade monitoring performance.