WIAS Preprint No. 2579, (2019)

Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations


  • Drieschner, Martin
  • Eigel, Martin
    ORCID: 0000-0003-2687-4497
  • Gruhlke, Robert
    ORCID: 0000-0003-3129-9423
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Petryna, Yuri

2010 Mathematics Subject Classification

  • 35R60 47B80 60H35 65C20 65N12 65N22 65N55 65J10


  • Structural failure, experimental and numerical investigations, monomorphic uncertainty modeling, polymorphic uncertainty modeling, artificial neural networks, fuzzy, uncertainty quantification




Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models.

Appeared in

  • Reliab. Eng. Syst. Safety, 203 (2020), pp. 107106/1--107106/12, DOI 10.1016/j.ress.2020.107106 with the new title "Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes".

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