Dynamic Surrogate Modeling Using Latent Variable Methods and Neural Networks for Market-Driven Operation of an Air Separation Unit

This work presents a dynamic surrogate modeling framework that combines latent variable methods and neural networks for accurate and computationally efficient market-driven dynamic optimization of an air separation plant. The high-dimensional full-order model (FOM) consisting of ≈ 3800 states is projected onto a 10-dimensional latent subspace using principal component analysis (PCA). Following order reduction, a rectified linear unit (ReLU)-activated multilayer perceptron (MLP) neural network is trained to compute step-ahead predictions of the latent states in addition to the squared prediction error (SPE) statistic of the step-ahead prediction. The ReLU network is embedded directly into a discrete time reformulation of the optimization problem using complementarity conditions, and a trust region is enforced during optimization by constraining the SPE along the prediction horizon to be within specified confidence limits. The latent variable-based surrogate model (LV-SM) is validated through multistep-ahead simulation case studies, demonstrating high prediction accuracy for restoration of not only the states directly relevant to optimization but also the entire original state-space. The LV-SM’s performance in dynamic optimization is studied using a market-driven optimization case study, where it achieves a solution nearly identical to the FOM with nearly 3 orders of magnitude reduction in computation time using a two-tiered optimization approach. The results of this work highlight the potential of the LV-SM as a substitute for high-dimensional and complex first-principles-based industrial process models, particularly for use in real-time operations applications.