TY - JOUR

T1 - Estimation of Response Expectation Bounds under Parametric P-Boxes by Combining Bayesian Global Optimization with Unscented Transform

AU - Ding, Chen

AU - Dang, Chao

AU - Broggi, Matteo

AU - Beer, Michael

N1 - Funding Information: Chen Ding acknowledges the support of the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie project GREYDIENT-Grant Agreement No. 955393. Chao Dang thanks the support from the China Scholarship Council (CSC). Michael Beer appreciates the support of National Natural Science Foundation of China under Grant No. 72271025.

PY - 2024/6

Y1 - 2024/6

N2 - In engineering analysis, propagating parametric probability boxes (p-boxes) remains a challenge because a computationally expensive nested solution scheme is involved. To tackle this challenge, this paper proposes a novel optimization-integration method to propagate parametric probability boxes (p-boxes), mainly focusing on estimating the lower and upper bounds of structural response expectation for linear and moderately nonlinear problems. A model-based optimization scheme, named Bayesian global optimization, is first introduced to explore the space of distribution parameters. Subsequently, an efficient numerical integration method, named unscented transform, is employed to estimate the response expectation with a given set of distribution parameters. Compared with existing optimization-integration methods, the proposed method has three advantages. First, the response expectation bounds are successively estimated, allowing for the reuse of samples generated from the lower-bound estimation in the upper-bound estimation. Second, the approximation error introduced by the numerical integration method is considered. Third, computational efficiency in both the optimization and integration processes is improved. Four applications are investigated to validate the effectiveness of the proposed method, showing its ability to balance computational efficiency and accuracy when evaluating response expectation bounds.

AB - In engineering analysis, propagating parametric probability boxes (p-boxes) remains a challenge because a computationally expensive nested solution scheme is involved. To tackle this challenge, this paper proposes a novel optimization-integration method to propagate parametric probability boxes (p-boxes), mainly focusing on estimating the lower and upper bounds of structural response expectation for linear and moderately nonlinear problems. A model-based optimization scheme, named Bayesian global optimization, is first introduced to explore the space of distribution parameters. Subsequently, an efficient numerical integration method, named unscented transform, is employed to estimate the response expectation with a given set of distribution parameters. Compared with existing optimization-integration methods, the proposed method has three advantages. First, the response expectation bounds are successively estimated, allowing for the reuse of samples generated from the lower-bound estimation in the upper-bound estimation. Second, the approximation error introduced by the numerical integration method is considered. Third, computational efficiency in both the optimization and integration processes is improved. Four applications are investigated to validate the effectiveness of the proposed method, showing its ability to balance computational efficiency and accuracy when evaluating response expectation bounds.

KW - Bayesian global optimization

KW - Gaussian process

KW - Imprecise probability propagation

KW - Parametric probability box (p-box)

KW - Response expectation bounds

KW - Unscented transform

UR - http://www.scopus.com/inward/record.url?scp=85186141404&partnerID=8YFLogxK

U2 - 10.1061/AJRUA6.RUENG-1169

DO - 10.1061/AJRUA6.RUENG-1169

M3 - Article

AN - SCOPUS:85186141404

VL - 10

JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering

SN - 2376-7642

IS - 2

M1 - 04024017

ER -