Smart optimization with PPCR modeling in the presence of missing data, time delay and model-plant mismatch

Abstract

In this paper, a data-driven smart optimization algorithm is presented to identify the optimal operating point of the process and the path from the current operating condition to the optimal operating condition. To model the plant dynamics, a locally weighted semi-supervised probabilistic principal component regression (PPCR) model that is robust to missing data and can handle the time-invariant delay is developed in this paper. Being a locally weighted linear model, a nonlinearity index is utilized to control the accuracy of approximation of the local model. In addition, an updating strategy on the delay range is proposed to reduce the computational effort of real-time modeling. To account for the model–plant mismatch, a penalty term in the form of a robust Gaussian process regression is incorporated into the optimization problem. Finally, to ensure that the algorithm reaches different regions of search space and avoid convergence to local optimum, an exploration step with the aid of acquisition functions is utilized. The performance of the developed approach is illustrated through an experimental case study on a hybrid tank system, and the practical applicability of the algorithm is demonstrated through an industrial example.