A. Gleiß:

"Identification of Linear Material Flow Systems - A Graph Theoretic Approach";

Betreuer/in(nen), Begutachter/in(nen): M. Deistler; Institut für Ökonometrie, Operations Research und Systemtheorie, 1999.

During the last two decades, Material Flow Analysis (MFA) has become an important instrument in environmental science and pollution research. MFA is a method for capturing, describing and interpreting the metabolism of selected parts of the anthroposphere. Such parts may be regions or production sites in which flows of selected materials, i.e. chemical elements or their compounds, or of goods are measured. The usual procedure in MFA is to represent a system by a block diagram showing the decomposition of the system into subsystems and the flows between the subsystems, additionally containing the flow measurements. >From this flow sheet we directly deduce a system graph, where each vertex represents a subsystem and each (directed) edge a flow. This fact suggests the use of graph theoretic concepts and methods for answering system theoretic questions. In this work it is tried to find an expression and interpretation of, e.g., stability, reachability and identifiability in graph theoretic terms, which, in the consequence, may lead to statements on the material flow level. In other words, we want to decide, whether the underlying material flow system satisfies certain properties, by inspection of the associated system graph. Here we are concerned with identifying the system from the a priori information and the data. The special features of this system identification problem are: The decomposition into subsystems, the law of the conservation of mass within each subsystem and the positivity of the variables involved, i.e. of the flows and of the levels of the stock within the subsystems. In most applications the stock levels, which often are of great practical interest, are not directly observed. However, there are measurements of import, export and internal flows, but in general in all three flow categories there are unobserved flows as well. Typically, there is only one measurement per balancing period (mostly one year) so that in the static case the balance equations, which equate the sum of the inputs of a subsystem to the sum of its outputs according to the law of the conservation of mass, will be used to reduce the degrees of freedom. The problems considered for material flow systems are the reconciliation of the flow measurements, data driven modelling and policy simulation. This thesis presents linear models for the static and the dynamic case. In the static case all three tasks have been investigated to a satisfactory degree. Here, we give procedures for the estimation of measured and unmeasured flows, which are based on a generalised least squares problem, and for the identification of the model parameters as well as a graph theoretic treatment of origins analysis and error propagation. In order to elaborate dynamic material flow models we start from a model class based on a simple stock-building pattern which has a prototype character inasmuch as many results for more sophisticated patterns can be traced back to their analogues for the simple type. In this way we give graph theoretic answers to the questions of stability, reachability, observability and identifiability within the framework of a state space model which is highly structured by the available a priori information

http://publik.tuwien.ac.at/files/pub-tm_379.pdf

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