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 moments of truncated fat-Tailed distributions. Moreover, the use of tempered alpha-stable distributions is suggested to avoid discontinuous tail cutoffs. Sparse approximation of moment-based arbitrary polynomial chaos is compared to other statistical methods in two industrial aircraft engine simulations: A simulation of transient cycle temperature in a turbine cavity and hot-gas ingestion in the interwheel region. In both cases, sparse approximation of moment based arbitrary polynomial chaos agrees with previous results but obtains them with lower computational effort.

Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations / Ahlfeld, R.; Montomoli, F.; Scalas, E.; Shahpar, S.. - In: JOURNAL OF PROPULSION AND POWER. - ISSN 0748-4658. - 33:4(2017), pp. 881-890. [10.2514/1.b36278]

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

E. Scalas;
2017

Abstract

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 moments of truncated fat-Tailed distributions. Moreover, the use of tempered alpha-stable distributions is suggested to avoid discontinuous tail cutoffs. Sparse approximation of moment-based arbitrary polynomial chaos is compared to other statistical methods in two industrial aircraft engine simulations: A simulation of transient cycle temperature in a turbine cavity and hot-gas ingestion in the interwheel region. In both cases, sparse approximation of moment based arbitrary polynomial chaos agrees with previous results but obtains them with lower computational effort.
2017
Aircraft; Aircraft engines; Engines; Machine design; Polynomial approximation; Product design; Statistics, Alpha-stable distribution; Computational demands; Fat-tailed distributions; Polynomial basis functions; Polynomial chaos expansion; Rare event simulation; Statistical information; Uncertainty quantifications, Probability distributions
01 Pubblicazione su rivista::01a Articolo in rivista
Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations / Ahlfeld, R.; Montomoli, F.; Scalas, E.; Shahpar, S.. - In: JOURNAL OF PROPULSION AND POWER. - ISSN 0748-4658. - 33:4(2017), pp. 881-890. [10.2514/1.b36278]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1668064
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