TY - JOUR

T1 - Hybrid uncertainty propagation based on multi-fidelity surrogate model

AU - Liu, Jinxing

AU - Shi, Yan

AU - Ding, Chen

AU - Beer, Michael

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (Grant 52205252 ), the National Natural Science Foundation of Sichuan Province (Grant 2023NSFSC0876 ), the Alexander von Humboldt Foundation of Germany, and the China Scholarship Council (CSC).

PY - 2024/3/1

Y1 - 2024/3/1

N2 - There always exist multiple uncertainties including random uncertainty, interval uncertainty, and fuzzy uncertainty in engineering structures. In the presence of hybrid uncertainties, the hybrid uncertainty propagation analysis can be a challenging problem, which suffers from the computational burden of double-loop procedure when numerical simulation techniques are employed. In this work, a novel method for efficient hybrid uncertainty propagation analysis with the three types of uncertainties is proposed. Generally, multi-fidelity surrogate models, such as Co-Kriging, can greatly improve the computational efficiency by leveraging information from a low-fidelity model to build a high-fidelity approximate model. However, the traditional multi-fidelity surrogate model methods always calculate the hybrid uncertainty propagation result by combining with several numerical simulation techniques. This process can introduce post-processing errors unless unlimited number of samples are used, which is impossible in engineering application. In order to address this issue, the analytical solutions of the output mean and output variance are derived based on the Co-Kriging, and the resulting mean and variance are both random variables. Moreover, a new adaptive framework is established to strengthen the estimation accuracy of the hybrid uncertainty propagation result, by combining the augmented expected improvement function and the derived mean random variable. Several applications are introduced to demonstrate the effectiveness of the proposed method for solving hybrid uncertainty propagation problems.

AB - There always exist multiple uncertainties including random uncertainty, interval uncertainty, and fuzzy uncertainty in engineering structures. In the presence of hybrid uncertainties, the hybrid uncertainty propagation analysis can be a challenging problem, which suffers from the computational burden of double-loop procedure when numerical simulation techniques are employed. In this work, a novel method for efficient hybrid uncertainty propagation analysis with the three types of uncertainties is proposed. Generally, multi-fidelity surrogate models, such as Co-Kriging, can greatly improve the computational efficiency by leveraging information from a low-fidelity model to build a high-fidelity approximate model. However, the traditional multi-fidelity surrogate model methods always calculate the hybrid uncertainty propagation result by combining with several numerical simulation techniques. This process can introduce post-processing errors unless unlimited number of samples are used, which is impossible in engineering application. In order to address this issue, the analytical solutions of the output mean and output variance are derived based on the Co-Kriging, and the resulting mean and variance are both random variables. Moreover, a new adaptive framework is established to strengthen the estimation accuracy of the hybrid uncertainty propagation result, by combining the augmented expected improvement function and the derived mean random variable. Several applications are introduced to demonstrate the effectiveness of the proposed method for solving hybrid uncertainty propagation problems.

KW - Adaptive framework

KW - Analytical solution

KW - Hybrid uncertainties

KW - Multi-fidelity surrogate model

KW - Uncertainty propagation

UR - http://www.scopus.com/inward/record.url?scp=85181584674&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2023.107267

DO - 10.1016/j.compstruc.2023.107267

M3 - Article

AN - SCOPUS:85181584674

VL - 293

JO - Computers and Structures

JF - Computers and Structures

SN - 0045-7949

M1 - 107267

ER -