Fighting the curse of dimensionality with local model networks

This thesis is settled in the field of data-based modeling (identification) and specifically focuses on the weakening of the effects of the curse of dimensionality with local model networks (LMNs). The methods for fighting the curse of dimensionality originate from the fields of input selection and design of experiments (DoE).
The model type of LMNs allows the distinction in two input spaces - the rule premises input space and the rule consequents input space. The developed input selection techniques exploit this unique property of LMNs and the possibility to assign potential inputs to each input space individually. It is shown that this additional freedom enables input selection methods using LMNs to find a better bias/variance trade-off. Furthermore, one of the two arising input spaces is directly connected to the nonlinear effects of the model, which allows for more detailed interpretations.
The DoE contributions of this thesis concern passive and active learning schemes. Recommendations for passive experimental designs are given based on extensive simulation studies with the help of a function generator. The following three questions are addressed. Should corners (vertices) be measured? Which space-filling experimental design is likely to yield the best model accuracy? What order of experimentation leads to the best model quality in early stages of the measurement process? Eventually, the contribution regarding active learning is an extension of the already existing hierarchical local model tree for design of experiments (Hilomot-DoE), addressing three important issues of modeling simultaneously: (I) optimality, (II) model bias, and (III) model variance.
All developed methods demonstrate their abilities on selected application examples, including the prediction of the fuel consumption of cars, the data-based modeling of the air-mass flow of combustion engines, the metamodeling of fans, and the generation of a dynamic model of a heating, ventilating, and air conditioning system for control design.