Closed-Loop Dynamic Blending Optimization Based on Variational Bayesian and its Application in Industry

Abstract

There exist uncertainties in raw material components and distribution parameters in blending process. Considering the dynamic uncertainty of distribution parameters and the dynamic change of raw material inventory, a general closed-loop dynamic blending optimization (CDBO) is proposed. The proposed method consists of both data-driven system and model-based system. In the data-driven system, the feedback optimization problem is reconstructed into a linear regression problem, and the variational Bayesian is proposed to obtain the mean and variance of the distribution. Then, according to the incoming raw materials, the mean value of each distribution parameter is adjusted by expert rules. Last, in the model-based system, blending ratio is obtained by chance-constrained programming. To verify the effectiveness of CDBO, a detailed derivation process of variable Bayesian, expert rule and chance-constrained programming are established for zinc smelting process. Numerical studies and an industrial application for zinc smelting process are presented to demonstrate the advantages of the proposed method. Compared with the manual blending, the volatility index of chemical tests data is greatly reduced and the compliance rates of zinc and lead is increased by 6.7% and 3.3%, respectively.