Computational mechanics in terms of mixed aleatory and epistemic uncertain random fields

Computational mechanics in terms of mixed aleatory and epistemic uncertain random fields

Leitung:  Udo Nackenhorst, Amélie Fau
Team:  Mona Madlen Dannert, Rodolfo Fleury
Jahr:  2016
Förderung:  Priority Programme SPP 1886 of German Research Foundation (DFG), State of Lower Saxony
Ist abgeschlossen:  ja

In engineering application, uncertain input variables - such as material or load properties - are often not given by a standard random variable but by random fields. While the first is dependend only on chance and assumed to be constant within the whole domain, the latter is additionally dependend on space. Regarding random field input variables, the local variation can often be determined by experiments (aleatory uncertain data) enabling probabilistic approaches. The spatial correlation, however, is usually hard to determine and therefore imply a lack of knowledge. Such epistemic uncertainties demand for possibilistic approaches.

This project investigates probability box (p-box) approach including probabilistic and possibilistic aspects. This way, both kind of uncertainties can be considered within a random field. The epistemically uncertain correlation length is described by an interval, which is discretised in equidistant steps. For each resulting correlation length, the random field can be decomposed by series expansion, e.g. Karhunen-Loève expansion. For each correlation length step, a stochastic non-linear finite element simulation needs to be perfomed. To increase efficiency, advanced sampling methods, e.g. sparse grid collocation, are investigated as well as model reduction techniques.

The results of such a mixed uncertain analysis are given by p-boxes. Instead of a unique value, an upper and lower bound is enveloping the possible results. With regard to reliability analysis, decision making from such interval valued probabilities needs to be discussed.

This project is part of the priority programme SPP 1886. The funding by the German Research Foundation (DFG) is gratefully acknowledged.