Thomas Binder, L. Blank, W. Dahmen, Wolfgang Marquardt:
Towards multiscale dynamic data reconciliation
In: R. Berber, C. Kravaris (Eds.): NATO-ASI on , 623-665
Although reconciliation of steady-state process data is routinely applied in industrial practice, the theoretical understanding of the problem and its adequate formulation in a dynamic setting is still not mature. Existing formulation approaches are based on stochastic filters, deterministic observers or mathematical programming techniques. In this contribution, we suggest a general problem formulation of dynamic data reconciliation based on the theory of ill-posed problems and their regularizations. It results in a large-scale dynamic optimization problem which requires efficient numerical solution methods in real-time under strict limitations of computational resources. We explore a novel mathematical framework for the discretization of the dynamic optimization problem and the solution of the discretized nonlinear programming problem based on multiscale approximation. The framework attempts to integrate signal processing and optimization finally leading to a fully adaptive and highly efficient numerical treatment which always provides the best possible estimate which is attainable in the allotted time period.