Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review

Traditional structural uncertainty analysis is mainly based on probability models and requires the establishment of accurate parametric probability distribution functions using large numbers of experimental samples. In many actual engineering problems, the probability distributions of some parameter...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2018-06, Vol.57 (6), p.2485-2502
Main Authors: Jiang, C., Zheng, J., Han, X.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Design analysis
Design optimization
Distribution functions
Engineering
Engineering Design
Mathematical models
Parameters
Probability distribution
Probability distribution functions
Reliability analysis
Reliability engineering
Review Paper
Structural reliability
Theoretical and Applied Mechanics
Uncertainty analysis
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Summary:Traditional structural uncertainty analysis is mainly based on probability models and requires the establishment of accurate parametric probability distribution functions using large numbers of experimental samples. In many actual engineering problems, the probability distributions of some parameters can be established due to sufficient samples available, whereas for some parameters, due to the lack or poor quality of samples, only their variation intervals can be obtained, or their probability distribution types can be determined based on the existing data while some of the distribution parameters such as mean and standard deviation can only be given interval estimations. This thus will constitute an important type of probability-interval hybrid uncertain problem, in which the aleatory and epistemic uncertainties both exist. The probability-interval hybrid uncertainty analysis provides an important mean for reliability analysis and design of many complex structures, and has become one of the research focuses in the field of structural uncertainty analysis over the past decades. This paper reviews the four main research directions in this area, i.e., uncertainty modeling, uncertainty propagation analysis, structural reliability analysis, and reliability-based design optimization. It summarizes the main scientific problems, technical difficulties, and current research status of each direction. Based on the review, this paper also provides an outlook for future research in probability-interval hybrid uncertainty analysis.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-017-1864-4