ABSTRACT
Hybrid models combine parametric and nonparametric models. The structure of the parametric model is a priori fixed based on fundamental knowledge—mechanistic models. The structure of the nonparametric model is identified from data, or data-driven models. The estimation and prediction performance of the nonparametric models critically depends on the content of information present in the data that were used to identify and discriminate the models. In order to yield data that are rich in information, design of experiment methods are typically employed, as in the case of pure data-driven models. Due to fundamental knowledge (first principles, mechanistic, empirical) that is incorporated into the hybrid model, fewer experiments are typically necessary than for pure data-driven models, and the requirements on the design of experiments are different. In this chapter, basic design of experiment methods will be introduced, and it will be assessed how these methods can be employed to provide information rich data for hybrid model identification and discrimination. It will then be discussed how the design of experiments affects the domain in which the hybrid model produces accurate estimations/predictions, referred to as validity domain. Methods will be presented that allow the characterization of the validity domain, enabling the assessment of whether a new experiment is in the validity domain or outside. Lastly, approaches are discussed that allow a directed extension of the validity domain by using the hybrid model, such as optimal experiment design methods. A simulation case is used to exemplify the approaches.
