Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging

Abstract

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.