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Description
The structural design optimization aims for a robust structure with minimal use of material resources, leading to slender and thin-walled structures, which entails a higher risk of stability problems. This issue is further influenced by geometrical imperfections, which are subject to uncertainties. In a common stochastic approach, imperfections can be simulated as random fields with the Karhunen-Loeve-Expansion (KLE) and applied to a finite element (FE) model as geometric deviations. Thus, the probability of a loss of stability can be determined via Monte Carlo Simulation (MCS). To quantify additional epistemic uncertainties within random field simulations, the concept of polymorphic uncertainty modeling is used. In that case, optimization-based interval or fuzzy analyses are required to compute, e.g., imprecise failure probabilities.
In the context of a reliability analysis in civil engineering, the probability of failure has to be lower than a given threshold value, depending on the structure’s consequence class. Numerical calculations of such low probabilities, require a very large number of samples, resulting in high computation times. Accounting for polymorphic uncertainty within optimization tasks for shell structures significantly further increases the computational effort, as it requires a triple-loop of optimization, fuzzy/interval analysis, and stochastic analysis.
A challenge in surrogate modeling with random fields is the high number of input variables. In order to reduce the computation time, a surrogate model based on Artificial Neural Networks (ANNs) is developed to replace the FE buckling analysis for the stochastic analysis. The idea is to use the random numbers of the KLE series as inputs for the ANN. In the training process, the training samples are computed by a geometrical nonlinear FE model. After successful training, the surrogate model is able to predict the buckling load with negligible computation time, compared to the MCS using the computationally demanding FE model. The novelty of the presented method is the ANN surrogate model for the buckling analysis to perform optimization tasks considering polymorphic uncertainties. As advantage, the computation time can be further reduced by truncating the KLE series according to a quality index. The required number of terms in the KLE series determines the number of input neurons and therefore, the computational effort of the ANN training. Numerical examples demonstrate that the presented ANN approach can be used reliably in structural optimization problems with polymorphic uncertain parameters.
