The adequate consideration of uncertain parameters in engineering applications is essential for a realistic prediction of state variables, such as displacements or stresses. Uncertainty is omnipresent and polymorphic. The source of the uncertainty and the quality of available information determine whether the uncertainty is aleatoric, epistemic or a combination of both. Aleatoric uncertainty is inherent, unavoidable, and irreducible. Sufficient statistical information is available for the corresponding parameters, enabling them to be modeled and quantified using stochastic variables within the framework of probability theory. Epistemic uncertainty, on the other hand, is avoidable, as it can generally be reduced by better models or additional data. Various uncertainty quantification approaches exist, such as Bayesian inference, random sets, p-boxes, or representations using non-stochastic variables based on possibility theory. Using stochastic variables for aleatory uncertainties and fuzzy variables for epistemic uncertainties lead to fuzzy-stochastic problems. In engineering applications, the underlying computational model is often high-dimensional based on the finite element method. Even if the uncertainty modeling and the solving of the model are successful, the challenge for a practical use lies in the evaluation and interpretation of the results. A pragmatic approach is the combination of statistical quantities on the one hand and defuzzification methods on the other hand. In currently valid security concepts, such as the Eurocode, statistical quantities are standardized with consideration of risk assessment. For fuzzy-valued output variables, there is currently a lack of clear recommendations for engineering applications. At the conference, typical engineering problems will be presented using aleatory and epistemic uncertainties. The focus will be on the decision making and the comparison of different approaches.

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Decision Making Under Aleatory and Epistemic Uncertainties in Engineering Applications

  • Martin Drieschner

摘要

The adequate consideration of uncertain parameters in engineering applications is essential for a realistic prediction of state variables, such as displacements or stresses. Uncertainty is omnipresent and polymorphic. The source of the uncertainty and the quality of available information determine whether the uncertainty is aleatoric, epistemic or a combination of both. Aleatoric uncertainty is inherent, unavoidable, and irreducible. Sufficient statistical information is available for the corresponding parameters, enabling them to be modeled and quantified using stochastic variables within the framework of probability theory. Epistemic uncertainty, on the other hand, is avoidable, as it can generally be reduced by better models or additional data. Various uncertainty quantification approaches exist, such as Bayesian inference, random sets, p-boxes, or representations using non-stochastic variables based on possibility theory. Using stochastic variables for aleatory uncertainties and fuzzy variables for epistemic uncertainties lead to fuzzy-stochastic problems. In engineering applications, the underlying computational model is often high-dimensional based on the finite element method. Even if the uncertainty modeling and the solving of the model are successful, the challenge for a practical use lies in the evaluation and interpretation of the results. A pragmatic approach is the combination of statistical quantities on the one hand and defuzzification methods on the other hand. In currently valid security concepts, such as the Eurocode, statistical quantities are standardized with consideration of risk assessment. For fuzzy-valued output variables, there is currently a lack of clear recommendations for engineering applications. At the conference, typical engineering problems will be presented using aleatory and epistemic uncertainties. The focus will be on the decision making and the comparison of different approaches.