Experimental Design for Batch-to-Batch Optimization under Model-Plant Mismatch

Abstract

Model errors in model-based optimization procedures can result in suboptimal policies. In that regard, structural mismatch is of particular concern since it results in inaccurate model predictions even when a large amount of data is available for model calibration. The method of simultaneous identification and optimization, proposed in our previous work, addresses the structural model mismatch by adapting the model parameters and matching the predicted to measured gradients thus ensuring progressive convergence to the actual process optimum. In the former implementation of this approach, the gradients have been corrected only at the most recent operating point. To achieve better prediction accuracy of the updated model and to obtain a faster convergence to the optimum, we therefore propose to use cost measurements from previous batch experiments in combination with additional optimally designed new experiments. The advantages of the presented approach versus previous versions of the algorithm are illustrated using two simulated run-to-run optimization case studies.

Efficient cobalt oxalate synthesis process optimization via second‐order modifier adaptation with transfer learning

“…The convergence of a batch-to-batch optimization requires that the model-based estimated gradients of the cost function should match the corresponding plant gradients, so that the cost function can be guaranteed to be consistently improved from one batch to the next. [23] Due to the NCO differences between the model and the actual process, problem (9) needs to be corrected to achieve an equivalent substitution between model-based optimization and actual optimization. According to Papasavvas and François, [26] a similar correction performed at the level of the input-output level named output MA (MAy) was proved to have same theoretical guarantees as MA.…”

“…[ 15 ] Model uncertainty may lead to model–plant mismatch, which is an obstacle to model‐based optimization problems. [ 23 ] According to Hille and Budman, the model uncertainty can be divided into two types [ 23 ] : (1) parametric uncertainty, leading to the inequality between the estimated parameter and the plant caused by noisy or insufficient data; and (2) structural uncertainty due to approximation, simplification, and assumptions of first‐principles models.…”