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

TL;DR

This paper introduces a novel surrogate modeling approach combining polynomial chaos and Kriging for efficient CVaR estimation in high-dimensional dependent systems, improving accuracy and computational speed.

Contribution

The paper develops a new DD-GPCE-Kriging surrogate and integrates it into multifidelity importance sampling for unbiased CVaR estimation in complex high-dimensional problems.

Findings

MFIS-based method outperforms MCS in nonsmooth output scenarios.

Achieves 104x speedup over standard MCS with high accuracy.

Successfully applied to complex engineering problems with many dependent inputs.

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.