Quantum mechanics

Algorithm

Gaussian

Engineering

Autocorrelation

Uncertainty quantification

Statistics

Covariance matrix

Applied mathematics

Probabilistic logic

Computer science

Mathematical optimization

Probabilistic design

Engineering design process

Covariance

Mechanical engineering

Physics

Mathematics

Fuzzy logic

Kriging

Artificial intelligence

Structural engineering

Structural Safety

Geometric imperfections are part of the disagreement between theoretically and experimentally determined buckling loads of cylindrical shells. Due to the random nature of the initial deviations, a probabilistic approach is used to predict the buckling loads, where spatial varying imperfections are modeled as Gaussian random fields. The shape of the fields depends, among others, on the autocorrelation structure, which depends on the manufacturing process. Underlying uncertainties like a small sample size or imprecise measurements make it practically impossible to define a crisp correlation function. In addition, rather subjective assumptions with regard to the numerical and probabilistic model have to be considered. Thus, in this paper the classical probabilistic approach is extended to a fuzzy stochastic approach aiming at a more realistic description of the imprecise correlation structure. Consequently, by using both aleatory and epistemic uncertainties it is possible to make more reliable statements to the buckling loads. The first task is to find suitable functions to fit the evaluated correlation structure from measurements. Therefore, the imperfection data bank from Delft University (Arbocz and Abramovich, 1979) is used where different shell types are investigated. Subsequently, the crisp functions are extended to fuzzy functions using the fitting parameters for a fuzzy bunch parameter description. More exactly, a polymorphic uncertainty model from Graf et al. (2015) is used to take into account natural variability and incompleteness. The fuzzy analysis is very time consuming. Hence, the EOLE method Li and Kiureghian (1993) is used for an efficient spectral decomposition of the covariance matrix. A HDMR-metamodel allows a fast α-level optimization for the fuzzy analysis. Finally, mean and quantile values of the stability loads are presented as fuzzy variables with the aim to consider aleatory and epistemic uncertainties in the design process.

Polymorphic uncertainty modeling for the simulation of geometric imperfections in probabilistic design of cylindrical shells