In the last years, various mathematical theories have been developed to appropriately characterize uncertainties of different natures. The general class of mathematical theories dealing with uncertainty is referred to as the General Information Theory (GIT). Within the field of GIT, the modeling of epistemic uncertainties still remains a challenging task which is addressed in this thesis. In this regard, the novel contribution of this work is concerned with a special interdisciplinary methodology to comprehensive modeling and analysis of mechanical and geotechnical systems with epistemic uncertainties. Uncertainties of epistemic nature are identified and quantified by fuzzy numbers. The propagation of these uncertainties through the considered physical systems is calculated by the uncertainty simulation tool. Finally, the computation of the relative and absolute influence of each uncertain parameter on the resulting uncertainty of the outputs of interest is performed by the uncertainty analysis tool. Both the uncertainty simulation and analysis tool are based on the transformation method. Based on the results of the fuzzy arithmetical simulation and analysis procedure, revealing conclusions for a significantly improved automotive design, for a more credible assessment of the passive safety of a commercial vehicle and for the successful avoidance of landslides, are drawn. A new formulation for the uncertainty analysis tool is proposed in this thesis. The starting point of the new uncertainty analysis is an improved mathematical formulation of the gain factors. Finally, the new uncertainty analysis differs from the traditional one in the central role played by the overall uncertainties of the input parameters, in terms of worst-case intervals and membership functions, with respect to their nominal values. In the effort to reduce the intrinsic subjectivity related to the representation and quantification of uncertainties by fuzzy numbers, some practical guidelines for a rational assessment of fuzzy numbers representing adequately given sources of uncertainty are presented. Particular attention is paid to the assessment of the nominal value, the worst-case interval and the shape of the membership function. Finally, two new measures for fuzzy numbers are developed: the imprecision, in its absolute and relative formulation, and the nonlinearity index. The imprecision of a fuzzy number is defined as a valid metric to measure the relative and absolute amount of uncertainty inherent to a fuzzy number. As shown by different examples, the determination of the imprecision leads to an efficient quantitative measure of the propagation of the uncertainty through the mathematical simulation of a physical system. In addition, the new nonlinearity index is introduced and defined in this thesis as a measure of the nonlinear dependency between the uncertain inputs and the uncertain outputs of interest. The calculation of the nonlinearity index is a practical way to acquire additional information on the mathematical relationship between outputs and inputs which is particularly useful for black-box models where this relationship is not explicitly known.


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    Titel :

    Fuzzy arithmetical modeling and analysis for mechanical and geotechnical systems with epistemic uncertainties


    Beteiligte:
    Turrin, Simone (Autor:in)


    Erscheinungsdatum :

    2011


    Format / Umfang :

    157 Seiten, Bilder, Tabellen, 100 Quellen




    Medientyp :

    Hochschulschrift


    Format :

    Print


    Sprache :

    Englisch




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