Bi-fidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos expansion

TL;DR

This paper introduces a bi-fidelity method combining dimensionally decomposed generalized polynomial chaos expansion with Fourier-polynomial expansion to efficiently estimate conditional value-at-risk in complex, high-dimensional systems, reducing computational costs.

Contribution

It proposes a novel bi-fidelity approach integrating DD-GPCE and Fourier-polynomial expansion for CVaR estimation in high-dimensional, nonlinear systems, improving accuracy and efficiency over existing methods.

Findings

DD-GPCE provides accurate CVaR estimates with lower computational effort.

The bi-fidelity method effectively combines low- and high-fidelity models for risk assessment.

Numerical examples demonstrate significant efficiency gains in structural and composite material models.

Abstract

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 expansion of the mapping between the stochastic low-fidelity and high-fidelity output data to ensure computational efficiency. The method employs measure-consistent orthonormal polynomials 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.