Keywords: polymorphic uncertainty, uncertain time-dependency, timber structure, compressed wood, uncertainty quantification, fuzzy probability-based random process.

Various uncertainties of diverse sources are apparent in structural analysis. Aleatoric uncertainty on the one hand and epistemic uncertainty on the other hand are distinguished. Uncertainty models based on probability theory, such as random variables, random processes and random fields, are capable to formulate uncertain quantities that describe aleatoric uncertainties. Contrarily, uncertainty models based on possibility theory, such as intervals or fuzzy variables, can be used to describe epistemic uncertainties by uncertain quantities. Polymorphic uncertainty models are used in this contribution, to incorporate the aleatoric and epistemic uncertainty characteristics that are present in structural analyses. Therefore, methods to combine fuzzy and stochastic variables are applied to model the uncertain quantities of a structural analysis. This combination results in fuzzy probability-based randomness as polymorphic uncertainty model. Dependencies of uncertain quantities can be distinguished in intradependencies and interdependencies. Intradependencies can be described based on autocorrelation structures, which are the basis for the definition of random processes (time dependency) or random fields (spatial dependency). Time-dependent structural problems are addressed and the influence of the uncertainty of the process on the structural reliability is investigated. Therefore, novel methods are developed to model polymorphic uncertain time intradependency in fuzzy probability-based random processes. Additionally, the extension to join polymorphic uncertain time and space interdependencies is discussed. Methods are developed to model polymorphic uncertainties in cyclic load processes. Hence, fuzzy parametrized autocorrelation structures for cyclic load processes are introduced. A numerical example is computed to show the applicability and advantages of the novel developments. A cyclic load of an oscillating machine affects the subjacent machine foundation, which is built of a compressed wood plate. In this contribution, simulation of compressed wood is performed, based on the finite element method. In order to realistically simulate timber structures consisting of compressed wood components, highly elaborated material models with extensive simulation effort are required. The production process of a compressed wood plate is simulated in a preliminary investigation. The resulting density distribution of the simulated compressed wood component is examined. The data of density distribution is the basis for an uncertainty modelling of the respective spatial intradependency. For the main investigation, the compressed wood component is exposed to a cyclic load function. This basic solution it is used as basis for a polymorphic uncertainty quantification. Resulting from the polymorphic uncertainty quantification, fuzzy-valued reliability measures are evaluated from the stresses and strains of the structure.

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