Objective PDF-Shaping Based Stochastic Optimization With Probabilistic Constraints and Its Application

The optimal operation of complicated industrial processes is mainly reflected in the optimization of objective functions, such as product quality and energy consumption. The conventional use of the mean-value of objective function is difficult to describe all the information of the optimized objective when the system is subjected to random uncertainties. In this article, the probability density function (PDF) of the objective function to be optimized is introduced to describe and evaluate the impact of the randomness and uncertainty to the optimization of objective function. A stochastic optimization method based on the objective PDF-shaping with probabilistic constraints is then proposed. For this purpose, firstly the kernel density estimation method is used to estimate the PDF of the objective function. Then, the idea of stochastic distribution control is applied to the objective function PDF-shaping with the probabilistic constraints-based stochastic optimization for industrial processes. The output PDF control and minimum entropy with mean constraint-based optimization methods are proposed. Finally, the optimal decision variables are obtained by optimizing the reconstructed objective function. Both numerical simulation and industrial experiment on a blast furnace ironmaking process have demonstrated the effectiveness and superiority of the proposed method.