Surrogate Modeling Approach for Nonlinear Blending Processes

Abstract

Surrogate models have been increasingly used for predicting the behavior of functions or systems as an alternative to complex or unknown formulations. In this work, we address the use of surrogates for the blending operations of continuous processes, in which nonlinear equations are successfully approximated by simpler linear or bilinear formulas. The surrogate model building framework consists of four main steps. First, training and testing data sets are constructed by using the Latin Hypercube Sampling (LHS) technique in addition to nonlinear blending equations derived from material balances. Second, a data improvement procedure based on data normalization is performed to mitigate numerical issues and biased surrogates. Third, a mixed-integer quadratic programming (MIQP) formulation based on the least-squares regression builds optimizable surrogate functions for the variables of interest from the blending operations. Fourth, a performance check evaluates the accuracy and robustness of the surrogate model. Several features concerning surrogate model building strategies are investigated in this work, including data set size, surrogate size, complexity, and functional form, statistical analyses on the reliability of the predictions, and performance of the surrogates when embedded in optimization environments. The method is tested over a blending operations problem and the results indicate that the surrogates are properly built, have high accuracy, and successfully replace the original blending formulation within optimization environments. This methodology can be further employed for larger and more complex systems, especially when multiple blending operations are performed throughout the plant.