TY - JOUR

T1 - An efficient meta-model-based method for uncertainty propagation problems involving non-parameterized probability-boxes

AU - Zhang, Kun

AU - Chen, Ning

AU - Liu, Jian

AU - Yin, Shaohui

AU - Beer, Michael

N1 - Funding Information: The paper is supported by the National Natural Science Foundation of China (Grant No. 52275247 and 51905162 ), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004 ), the Natural Science Foundation of Hunan Province (Grant No. 2022JJ30132 ) and the Hunan Provincial Science and Technology Department (Grant No. 2020GK2013 , 2021JC0005 ). The author would also like to thank reviewers for their valuable suggestions.

PY - 2023/10

Y1 - 2023/10

N2 - To capture inevitable aleatory and epistemic uncertainties in engineering problems, the probability box (P-box) model is usually an effective quantification tool. The non-parameterized P-box is more general and more flexible than parameterized P-box. While the efficiency of uncertainty propagation methods for non-parameterized P-box is crucial and demands urgently to improve. This paper proposes an efficient meta-model-based method for uncertainty propagation problems involving non-parameterized probability-boxes. In which, the typical Kriging meta-model is first utilized to build the mapping relationship between the non-parameterized P-box variables with the system response. Then, the constructed Kriging model is applied for interval analysis, and the cumulative distribution function of the response function can be obtained using interval Monte Carlo. During building the meta-model, an active learning strategy is proposed and applied to reduce the amount of training data needed from the perspective of exploration and exploitation. Since the prediction variance of Kriging model is not used, the proposed active learning method is not limited to Kriging model and can be applied in any existing meta-models. The numerical examples demonstrate that the proposed method has high accuracy and efficiency in handling nonlinearity, high-dimensional and complex engineering problems.

AB - To capture inevitable aleatory and epistemic uncertainties in engineering problems, the probability box (P-box) model is usually an effective quantification tool. The non-parameterized P-box is more general and more flexible than parameterized P-box. While the efficiency of uncertainty propagation methods for non-parameterized P-box is crucial and demands urgently to improve. This paper proposes an efficient meta-model-based method for uncertainty propagation problems involving non-parameterized probability-boxes. In which, the typical Kriging meta-model is first utilized to build the mapping relationship between the non-parameterized P-box variables with the system response. Then, the constructed Kriging model is applied for interval analysis, and the cumulative distribution function of the response function can be obtained using interval Monte Carlo. During building the meta-model, an active learning strategy is proposed and applied to reduce the amount of training data needed from the perspective of exploration and exploitation. Since the prediction variance of Kriging model is not used, the proposed active learning method is not limited to Kriging model and can be applied in any existing meta-models. The numerical examples demonstrate that the proposed method has high accuracy and efficiency in handling nonlinearity, high-dimensional and complex engineering problems.

KW - Active learning

KW - Interval Monte Carlo

KW - Kriging model

KW - Non-parameterized P-box

KW - Uncertainty propagation analysis

UR - http://www.scopus.com/inward/record.url?scp=85164214922&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2023.109477

DO - 10.1016/j.ress.2023.109477

M3 - Article

AN - SCOPUS:85164214922

VL - 238

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

M1 - 109477

ER -