Results Analysis in a Constrained Real-Time Optimization (RTO) System

This paper presents a new results analysis strategy for uncertain real-time optimization (RTO) systems. The key contributions of this paper are in I) developing a mathematical formulation describing the confidence region of a partially constrained optimum and 2) applying that formulation in deciding whether the optimizer results should be implemented. The confidence region of the constrained optimum is determined from the confidence region of the unconstrained optimum, when the inequality constraints are not considered. The confidence region of the unconstrained optimum is mapped to the feasible region defined by the inequality constraints to obtain the confidence region of the constrained optimum. This mapping is developed by minimizing the profit loss between the unconstrained and constrained optima. The resulting confidence region of the constrained optimum is used in optimization results analysis; the confidence regions of successive predicted optima are compared to decide if the difference between two optima is statistically significant. The comparison is made by calculating the significance level at which the two confidence regions just overlap. If the value is small, large portions of two 95% confidence regions overlap, and the optimizer result will not be implemented. The new results analysis approach is applied to the Williams-Otto reactor case study with controlled inequality constraints, where it significantly reduced plant variability, while concurrently increasing the operating profit.