Probabilistic uncertainty based simultaneous process design and control with iterative expected improvement model

•Probabilistic framework for uncertainty representation is proposed.•Iterative learning of surrogate model for optimization.•Expected improvement optimization facilitates the selection of representative data.•Assignment of probability limit for relaxation of output variability constraint.•Applicability demonstrated for single loop and multi-loop control.

The simultaneous design and control aims to achieve economic profits and smooth operation of the process even under uncertainties. However, the over-estimation of the uncertainties leads to conservative design decisions. Because of the disturbance inputs, the cost is not easily evaluated. Unlike the past work of design and control, the proposed probabilistic approach framework directly uses the Gaussian process (GP) model to represent the uncertainty in the input. The GP model that acts as the cost function model is trained by an iterative approach. The variability can be evaluated statistically by the GP model. In addition, the expected improvement optimization is employed to select the representative data, so no redundant data are used in the modeling. The expected improvement searches for the most probable operating condition for improvement based on the predictive distribution from the GP model. The applicability of the proposed method is tested on a mixing tank.