A grey-box modeling approach for the reduction of nonlinear systems

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

“…Similarly, after the reduction of a set of equations through e.g. singular perturbation (Chen et al, 2004), residualization (Hahn, Lextrait, & Edgar, 2002) or orthogonal decomposition (Romijn, Ozkan, Weiland, Ludlage, & Marquardt, 2008), it might be desirable to approximate a subset of equations by nonparametric models, whereby a hybrid semi-parametric model is yielded. A solution can be obtained in a computationally efficient way while most of the properties of the original system of equations can be retained.…”

Efficient meta-modelling of complex process simulations with time–space-dependent outputs

“…The rationale is that the process outputs at different time and space locations are strongly correlated, and thus they can be represented by a small number of latent variables that are extracted by principal component analysis (PCA) (Jolliffe, 2002). PCA is a general multivariate statistical projection technique for dimension reduction, and it has wide applications in process data analysis (Venkatasubramanian et al, 2003), model reduction (Gay & Ray, 1995;Hoo & Zhang, 2001;Romijn et al, 2008), among other areas. The central idea of PCA is to project the original ‫ܦ‬ dimensional data, z, onto a space where the variance is maximized: ࢠ = + + .…”

“…The method of "model reduction" is primarily designed to reduce the number of ODEs, which are typically the result of discretizing PDEs, using principal component analysis (PCA) (Gay & Ray, 1995;Hoo & Zhang, 2001) and approximate inertial manifolds (Shvartsman et al, 2000). As indicated by Romijn et al (2008), purely reducing the number of equations does not automatically reduce computation, since the complexity in evaluating the non-linear equations is intact. Following this argument, Romijn et al (2008) combined PCA with a grey-box approach, whereby the non-linear part of the ODEs is approximated by an empirical neural network (NN) model.…”

“…As indicated by Romijn et al (2008), purely reducing the number of equations does not automatically reduce computation, since the complexity in evaluating the non-linear equations is intact. Following this argument, Romijn et al (2008) combined PCA with a grey-box approach, whereby the non-linear part of the ODEs is approximated by an empirical neural network (NN) model. The resulting reduced model runs sufficiently fast for real-time applications, such as model-based predictive and optimizing control.…”

Hybrid modeling of ethylene to ethylene oxide heterogeneous reactor

“…The applications of hybrid model as a proper technique to simulate kinetic models have been reported in many studies, [15,[21][22][23][24][25].…”