Optimization of Shell Structures with Fuzzy Probability‐Based Random Fields Using Artificial Neural Networks

The structural design optimization aims for robust structures with minimal use of material resources, leading to slender and thin-walled structures, which entail a higher risk of stability problems. This issue is further influenced by geometrical imperfections, which are subjected 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. Numerical calculations of low probabilities require a very large number of samples, resulting in high computation times. 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 polymorphic uncertainty analysis. ... mehrThe basic 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 of the MCS, compared to the computationally demanding FE model. The main novelty of the presented method is an ANN surrogate model for random field-based FE buckling analysis used to perform optimization tasks considering polymorphic uncertainties.