Stochastic Linear Dynamic Models for Material Flow Analysis

In the course of this project, static and dynamic stochastic models for the analysis of material flows were examined. Conditions for stability, reachability and identifyability have been investigated, using also graph theoretic approaches. Since even simple material flow models can show a highly complex structure, the software tool MAcFlow was developed for the graphic entering, for the estimation of model parameters and for the subsequent system analysis and simulation of static models. The considered model classes are especially suitable where measurements of material flows exist only for one or for a few time instances, if considerable inaccuracies are present or if the relevant material flows cannot be observed directly. The advantage of the methods is that redundant information on the system structure is used for the reduction of uncertainties with respect to the size of the material flows. This can be the basis of risk minimisation. DYNAMIC MATERIAL FLOW MODELS The dynamics of material flow systems is caused by stock accumulation. An interesting case is where stock accumulation and depletion obey certain patterns, since then one can try to identify the model parameters underlying the chosen stock type. In collaboration with partners from the previous EU-project MacTEmPo, three stock types (exact residence time, residence time in accordance with a discretised, truncated normal distribution and stock depletion proportional to the stock level (geometric pattern)) were defined. These patterns have been examined on stability, reachability and identifyability. EXTENSIONS OF THE STATIC CASE The static case was further extended, motivated by different applications. Especially the recognition and treatment of inconsistencies of the a priori information and the extension to Multi-Level-Models were investigated. Methodological extensions as well as the distinction between technological subsystems and distributor subsystems, that enable a restricted modelling of non-linear system behaviour, were developed and implemented into the available software tool MAcFlow.