This article presents a case study on predicting the particle size of copper ore grinding with stochastic configuration networks (SCNs). A set of temporal data was collected from the copper ore grinding process for building the predictive model. The well-known least absolute shrinkage and selection operator (LASSO) is employed for temporal feature selection. Then, an SCN model is constructed to estimate the residual between the output of the LASSO model and the product particle size. The weights of the linear model and the output weights of the SCN model are optimized simultaneously using the elastic-net regularization method to improve the prediction performance. An analysis on the selected input variables is given, which is helpful to better understanding the output results. Comparative experiments are carried out to demonstrate the effectiveness and merits of the proposed modeling techniques in terms of the model's accuracy, reliability, and interpretability.

Several difficult-to-measure production qualities or environment pollution indices of industrial process must be measured using offline laboratory instruments. Soft measurement method is often used to perform online prediction of such parameters. Only small-sample modeling data with high-dimensional input features can be obtained due to the limitations and complex characteristics of the measurement device and process, respectively. Therefore, a new multisource latent feature selective ensemble (SEN) modeling approach is proposed in this study. First, input features are divided into different subgroups according to the characteristics of the modeling data. Second, the extracted multisource latent features evolve from the multi-layered selection algorithms, which are specified by feature reduction ratio, feature contribution ratio and mutual information value orderly for each subgroup. Finally, in order to construct candidate sub-models, an adaptive hyper-parameter selection algorithm based on the multi-step grid search is employed in terms of the reduced features. Sequentially, the optimized ensemble submodels with their weighting strategies are adaptively determined to build the final SEN model. The proposed method is verified by using benchmark nearinfrared data, high dimensional mechanical frequency spectrum data and industrial dioxin emission concentration data.

Accurate prediction and reliable optimization of metallurgical processes are essential for improving the efficiency and stability of copper smelting under complex operating conditions. This work develops an uncertainty–aware hybrid learning framework to predict copper smelting indicators from feed composition and support multi–objective feed–composition optimization. The framework integrates a Transformer–based multi–task uncertainty model (TMUM) with target–specific histogram–based gradient boosting regressors (HGBR), where bias correction, variance calibration, and uncertainty propagation are introduced to obtain reliable, fused predictions. The calibrated surrogate model is further coupled with a reference–vector–guided evolutionary algorithm (RVEA) to optimize multiple process objectives while considering prediction uncertainty. The proposed TMUM–HGBR model achieves coefficients of determination of 0.8317, 0.8824, and 0.8373 for three key indicators, with 95% prediction interval coverage probabilities of 93.6%, 92.7%, and 94.1% on the independent test set. Random 5–fold cross–validation confirmed the stability of the model, and a prospective evaluation on newly collected production data, with the prediction state updated from available laboratory results, showed that the model tracked all three indicators. The optimization results reveal a trade–off between copper enrichment and impurity reduction, with predicted slag basicity remaining close to its historical reference. The framework provides data–driven decision support for feed–composition adjustment within the studied production conditions.