Symbolic regression based hybrid semiparametric modelling of processes: An example case of a bending process

Hybrid semiparametric models integrate physics-based ( "white-box ", parametric) and data-driven ( "black-box ", non-parametric) submodels. Black-box models are often implemented using artificial neural networks (ANNs). In this work, we investigate the fitness of symbolic regression (SR) for black-box modelling. The main advantage of this approach is that a trained hybrid model can be expressed in closed form as an algebraic equation. We examine and test the idea on a simple example, namely the v-shape bending of a metal sheet, where an analytical solution for the stamping force is readily available. We explore unconstrained and hybrid symbolic regression modelling to show that hybrid SR models, where the regression tree is partly fixed according to a-priori knowledge, perform much better than purely data-driven SR models based on unconstrained regression trees. Furthermore, the generation of algebraic equations by this method is much more repeatable, which makes the approach applicable to process knowledge discovery.