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

Moritz von Stosch, Rui Oliveira, Joana Peres, Sebastião Feyo de Azevedo

Research output: Contribution to journalArticlepeer-review

136 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)86-101
Number of pages16
JournalComputers and Chemical Engineering
Publication statusPublished - 1 Jan 2014


  • Hybrid grey-box modeling
  • Hybrid modeling
  • Hybrid neural modeling
  • Hybrid semi-parametric modeling
  • Process operation/design
  • Semi-mechanistic modeling


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