Truncated Karhunen–Loève (KL) representations are used to construct finite dimensional (FD) models for non-Gaussian functions with finite variances. The second moment specification of the random coefficients of these representations are enhanced to full probabilistic characterization by using translation, polynomial chaos, and translated polynomial chaos models, referred to as T, PC, and PCT models. Following theoretical considerations on KL representations and T, PC, and PCT models, three numerical examples are presented to illustrate the implementation and performance of these models. The PCT models inherit the desirable features of both T and PC models. It approximates accurately all quantities of interest considered in these examples.
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Finite dimensional surrogates for extreme events
Numerical solutions of stochastic problems require the representation of random
functions in their definitions by finite dimensional (FD) models, i.e., deterministic functions of time and
finite sets of random variables. It is common to represent the coefficients of these FD surrogates by
polynomial chaos (PC) models. We propose a novel model, referred to as the polynomial chaos
translation (PCT) model, which matches exactly the marginal distributions of the FD coefficients and
approximately their dependence. PC- and PCT- based FD models are constructed for a set of test cases
and a wind pressure time series recorded at the boundary layer wind tunnel facility at the University of
Florida. The PCT-based models capture the joint distributions of the FD coefficients and the extremes of
target times series accurately while PC-based FD models do not have this capability.
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- Award ID(s):
- 2013697
- NSF-PAR ID:
- 10465379
- Date Published:
- Journal Name:
- 14th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP14 Dublin, Ireland, July 9-13, 2023
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Truncated Karhunen–Loève (KL) representations are used to construct finite dimensional (FD) models for non-Gaussian functions with finite variances. The second moment specification of the random coefficients of these representations are enhanced to full probabilistic characterization by using translation, polynomial chaos, and translated polynomial chaos models, referred to as T, PC, and PCT models. Following theoretical considerations on KL representations and T, PC, and PCT models, three numerical examples are presented to illustrate the implementation and performance of these models. The PCT models inherit the desirable features of both T and PC models. It approximates accurately all quantities of interest considered in these examples.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
