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