Notice of RetractionUncertainty analysis of correlated crack growth parameters using copula functions

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

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When damage tolerance based design and analysis of crack growth process are carried out based on the experimental data, there exist great uncertainties for model parameters, if these parameters were considered to determined value, it will cause a large predicted error. Moreover, if the correlation between these parameters are ignored or not be considered, the scatter of parameters cannot be captured accurately. In order to improve the prediction ability of fatigue life, Copula theory is introduced into fatigue fracture analysis and the measurement of parameter correlation associated with copula functions. Furthermore, the method to choose optimal Copula are introduced, a more appropriate t-Copula-based function is demonstrated to construct the joint probability density function model of log-normal fatigue crack parameters considering the uncertainty of the parameters. As a general approach, the proposed Copula method can not only characterize the correlation between crack growth parameters, but also, in the lack of datasets, model Gaussian-copula to obtain the bivariate joint probability distribution, which expands the application of Copula theory and the parameter uncertainty measures.