Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data
ISSN: 0264-4401
Article publication date: 22 March 2022
Issue publication date: 7 June 2022
Abstract
Purpose
For fast calculation of complex structure in engineering, correlations among input variables are often ignored in uncertainty propagation, even though the effect of ignoring these correlations on the output uncertainty is unclear. This paper aims to quantify the inputs uncertainty and estimate the correlations among them acorrding to the collected observed data instead of questionable assumptions. Moreover, the small size of the experimental data should also be considered, as it is such a common engineering problem.
Design/methodology/approach
In this paper, a novel method of combining p-box with copula function for both uncertainty quantification and correlation estimation is explored. Copula function is utilized to estimate correlations among uncertain inputs based upon the observed data. The p-box method is employed to quantify the input uncertainty as well as the epistemic uncertainty associated with the limited amount of the observed data. Nested Monte Carlo sampling technique is adopted herein to ensure that the propagation is always feasible. In addition, a Kriging model is built up to reduce the computational cost of uncertainty propagation.
Findings
To illustrate the application of this method, an engineering example of structural reliability assessment is performed. The results indicate that it may significantly affect output uncertainty whether to quantify the correlation among input variables. Furthermore, an additional advantage for risk management is obtained in this approach due to the separation of aleatory and epistemic uncertainties.
Originality/value
The proposed method takes advantage of p-box and copula function to deal with the correlations and limited amount of the observed data, which are two important issues of uncertainty quantification in engineering. Thus, it is practical and has the ability to predict accurate response uncertainty or system state.
Keywords
Acknowledgements
The authors gratefully appreciate the financial support for this work provided by the National Natural Science Foundation of China (No. 12072146 and 11872059), National Safety Academic Foundation of China (No. U1730129) and Innovation and Development Foundation of CAEP (No.CX2019014).
Conflicts of interest: On behalf of all authors, the corresponding author states that there is no conflict of interest.
Citation
Shen, Z., Zang, C., Chen, X., Hu, S. and Liu, X.-e. (2022), "Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data", Engineering Computations, Vol. 39 No. 6, pp. 2144-2161. https://doi.org/10.1108/EC-04-2021-0205
Publisher
:Emerald Publishing Limited
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