Hybrid semi-parametric modeling in process systems engineering: Past, present and future

Hybrid semi-parametric models consist of model structures that combine parametric and nonparametric submodels based on different knowledge sources. The development of a hybrid semi-parametric model can offer several advantages over traditional mechanistic or data-driven modeling, as reviewed in this paper. These advantages, such as broader knowledge base, transparency of the modeling approach and cost-effective model development, have been widely recognized, not only in academia but also in the industry.In this paper, the most common hybrid semi-parametric modeling and parameter identification techniques are revisited. Applications in the areas of (bio)chemical engineering for process monitoring, control, optimization, scale-up and model-reduction are reviewed. It is outlined that the application of hybrid semi-parametric techniques does not automatically lead into better results but that rational knowledge integration has potential to significantly improve model-based process operation and design.