Grey-box Identification of Distributed Parameter Systems
Sammanfattning: This thesis considers the problem of making dynamic models for industrial processes by combining physical modelling with experimental data. The focus is on distributed parameter systems, that is, systems for which the model structure involves partial differential equations (PDE). Distributed parameter systems are important in many applications, e.g., in chemical process systems and in intracellular biochemical processes, and involve for instance all forms of transport and transfer phenomena. For such systems, the postulated model structure usually requires a finite dimensional approximation to enable identification and validation using experimental data. The finite dimensional approximation involves translating the PDE model into a set of ordinary differential equations, and is termed model reduction.The objective of the thesis is two-fold. First, general PDE model reduction methods which are efficient in terms of model order for a given level of accuracy are studied. The focus here is on a class of methods called moving mesh methods, in which the discretization mesh is considered a dynamic degree of freedom that can be used for reducing the model reduction error. These methods are potentially highly efficient for model reduction of PDEs, but often suffer from stability and robustness problems. In this thesis it is shown that moving mesh methods can be cast as standard feedback control problems. Existing moving mesh methods are analyzed based on tools and results available from control theory, and plausible explanations to the robustness problems and parametric sensitivity experienced with these methods are provided. Possible remedies to these problems are also proposed. A novel moving finite element method, Orthogonal Collocation on Moving Finite Elements (OCMFE), is proposed based on a simple estimate of the model reduction error combined with a low order linear feedback controller. The method is demonstrated to be robust, and hence puts only small demands on the user.In the second part of the thesis, the integration of PDE model reduction methods with grey-box modelling tools available for finite dimensional models is considered. First, it is shown that the standard approach based on performing model reduction using some ad hoc discretization method and model order, prior to calibrating and validating the reduced model, has a number of potential pitfalls and can easily lead to falsely validated PDE models. To overcome these problems, a systematic approach based on separating model reduction errors from discrepancies between postulated model structures and measurement data is proposed. The proposed approach is successfully demonstrated on a challenging chromatography process, used for separation in biochemical production, for which it is shown that data collected at the boundaries of the process can be used to clearly distinguish between two model structures commonly used for this process.
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