Olaf Kahrs, Wolfgang Marquardt:
The validity domain of hybrid models and its application in process optimization
Chemical Engineering and Processing, 2007, 46(11), 1054-1066
Hybrid modeling is an attractive approach for processes, whose underlying physical phenomena, such as chemical reactions or heat and mass transfer, are not fully understood. A hybrid model consist of rigorous model parts that represent available process knowledge, and empirical model parts to describe the unknown phenomena. One of the key advantages of hybrid models over empirical models is that a hybrid model may be able to extrapolate, that is the prediction may be valid beyond the identification data domain, which is valuable in many applications such as process optimization and control. However, the validity domain of the hybrid model is not universal and has to be checked during model application. This paper, therefore, presents two validity criteria for generally structured algebraic hybrid models: the convex hull criterion checks whether each empirical model part only interpolates the data encountered during model identification; the confidence interval criterion calculates confidence intervals for the hybrid model prediction. These criteria are used to ensure the validity of the hybrid model during steady-state optimization of an ethylene glycol production process.
Hybrid modeling; Validity domain; Extrapolation; Process optimization; Data driven modeling; Rigorous models