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Rare event simulation is vital for industrial design because some events, so-called black swans, can have fatal consequences despite their low probability of occurrence. Finding low-probability events far off the mean design is a challenging task for realistic engineering models because they are characterized by high computational demands, many input variables, and often insufficient statistical information to build parametric probability distributions. Therefore, an adaptive and arbitrary polynomial chaos method, called sparse approximation of moment-based arbitrary polynomial chaos, is suggested in this work. Sparse approximation of moment-based arbitrary polynomial chaos creates custom polynomial basis functions and grids based on statistical moments to avoid incorrect statistical assumptions. The contribution of this work is that it is derived how rare event simulation can conveniently be integrated into adaptive sparse grid methods by calculating polynomial chaos expansions based on the statistical m...

Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations