The aim of project B03 is the development of a new methodology for the coupling of widely different mathematical models in a network. Moreover, error controllers are developed on the basis of modeled errors and uncertainties using the example of gas networks. These errors and uncertainties in submodels of the complex network are balanced in the overall simulation. Therefore, measures for the errors and uncertainties should be modeled for every submodel and made comparable. This can only succeed on the basis of a detailed model hierarchy, see Figure 1. All the errors and uncertainties in the simulation and optimisation are considered as an error in the finest modeling level using a backward error analysis in the model hierarchy. The estimated error in the finest level forms the mathematical basis for the development of a robust coupling controller. The controller should allow us to control the overall error in such a way that a prescribed simulation or optimisation goal is achieved within a desired tolerance.
Bild 1: Modelhierarchy for gas flow. Source: Domschke, P., Kolb, O. and Lang, J. (2011) 'Adjoint-based control of model and discretisation errors for gas flow in networks', Int. J. Mathematical Modelling and Numerical Optimisation, Vol. 2, No. 2, pp.175-193.
A poster to B03 can be found here.