Study on missing data imputation and modeling for the leaching process

•Designing simulation experiments to compare performances of GMM-EM and MI.•Presenting optimal data imputation and modeling strategies for each loss state.•Proposing hybrid method GMM-MI that combines the advantages of GMM-EM and MI.

The leaching process is an important component in hydrometallurgy. A predictive model of the leaching rate lays the foundation for soft measurement and process optimization, and data collection is the key in such a modeling effort. However, because of the complexity and harshness of leaching process, data can only be collected sparsely, which results in data deficiency in the modeling process. Therefore, data imputation before modeling seems to be extremely significant. In this paper, expectation maximization imputation based on the Gaussian mixture model (GMM-EM) and multiple imputation (MI) are respectively applied to perform missing data imputation for leaching process under different data loss rates and data loss patterns, and then the imputation performances are evaluated. Simulation experiment results have shown that GMM-EM and MI both have advantages with regard to data imputation. Therefore, MI based on GMM (GMM-MI), which combines the advantages of GMM and MI, is proposed in this paper. The effectiveness of GMM-MI is verified by a series of simulations.