1,748 research outputs found
Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging
We propose novel methods for Conditional Value-at-Risk (CVaR) estimation for
nonlinear systems under high-dimensional dependent random inputs. We develop a
novel DD-GPCE-Kriging surrogate that merges dimensionally decomposed
generalized polynomial chaos expansion and Kriging to accurately approximate
nonlinear and nonsmooth random outputs. We use DD-GPCE-Kriging (1) for Monte
Carlo simulation (MCS) and (2) within multifidelity importance sampling (MFIS).
The MCS-based method samples from DD-GPCE-Kriging, which is efficient and
accurate for high-dimensional dependent random inputs, yet introduces bias.
Thus, we propose an MFIS-based method where DD-GPCE-Kriging determines the
biasing density, from which we draw a few high-fidelity samples to provide an
unbiased CVaR estimate. To accelerate the biasing density construction, we
compute DD-GPCE-Kriging using a cheap-to-evaluate low-fidelity model. Numerical
results for mathematical functions show that the MFIS-based method is more
accurate than the MCS-based method when the output is nonsmooth. The
scalability of the proposed methods and their applicability to complex
engineering problems are demonstrated on a two-dimensional composite laminate
with 28 (partly dependent) random inputs and a three-dimensional composite
T-joint with 20 (partly dependent) random inputs. In the former, the proposed
MFIS-based method achieves 104x speedup compared to standard MCS using the
high-fidelity model, while accurately estimating CVaR with 1.15% error.Comment: 34 pages, 8 figures, research pape
Bi-fidelity conditional-value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion
Digital twin models allow us to continuously assess the possible risk of
damage and failure of a complex system. Yet high-fidelity digital twin models
can be computationally expensive, making quick-turnaround assessment
challenging. Towards this goal, this article proposes a novel bi-fidelity
method for estimating the conditional value-at-risk (CVaR) for nonlinear
systems subject to dependent and high-dimensional inputs. For models that can
be evaluated fast, a method that integrates the dimensionally decomposed
generalized polynomial chaos expansion (DD-GPCE) approximation with a standard
sampling-based CVaR estimation is proposed. For expensive-to-evaluate models, a
new bi-fidelity method is proposed that couples the DD-GPCE with a
Fourier-polynomial expansions of the mapping between the stochastic
low-fidelity and high-fidelity output data to ensure computational efficiency.
The method employs a measure-consistent orthonormal polynomial in the random
variable of the low-fidelity output to approximate the high-fidelity output.
Numerical results for a structural mechanics truss with 36-dimensional
(dependent random variable) inputs indicate that the DD-GPCE method provides
very accurate CVaR estimates that require much lower computational effort than
standard GPCE approximations. A second example considers the realistic problem
of estimating the risk of damage to a fiber-reinforced composite laminate. The
high-fidelity model is a finite element simulation that is prohibitively
expensive for risk analysis, such as CVaR computation. Here, the novel
bi-fidelity method can accurately estimate CVaR as it includes low-fidelity
models in the estimation procedure and uses only a few high-fidelity model
evaluations to significantly increase accuracy.Comment: Added acknowledgmen
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