A Sum-Of-Squares Constrained Regression Approach for Process Modeling

Abstract

Combining empirical relationships with a backbone of first-principle laws allow the modeler to transfer the available process knowledge into a model. In order to get such so-called grey-box models, data reconciliation methods and constrained regression algorithms are key to obtain reliable process models that will be used later for optimization. However, the existent approaches require solving a semi-infinite constrained regression nonlinear problem, which is usually done numerically by an iterative procedure alternating between a relaxed problem and an a posteriori check for constraint violation. This paper proposes an alternative one-stage efficient approach for polynomial regression models based in sum-of-squares (convex) programming. Moreover, it is shown how several desirable features on the regression model can be naturally enforced in this optimization framework. The effectiveness of the proposed approach is illustrated through an academic example provided in the related literature.