Sensitivity Analysis of Risk Assessment with Data-Driven Dependence Modeling
Résumé
The reliability analysis of complex systems often requires dealing with a computationally expensive simulation code. To estimate the failure probability, a frequently used method aims at propagating the input uncertainties through the black-box model. In this paper, as marginal distributions are assumed provided, the lack of knowledge about the joint distribution of input variables is limited to a copula distribution learnt from an industrial dataset obtained during past experiences. To describe complex and polymorphic patterns of dependence, attention has turned to vine copulas whose main advantage rests on their ability to approximate the whole dependence structure with a simple product of judiciously-selected bivariate copulas. The presented approach couples vine copula fitting to model the joint distribution on input variables and importance sampling to estimate the failure probability. For a given training set, the matrix of Kendall’s rank correlation coefficients, which collects information about dependence intensities, is deeply involved in the inferential procedure leading to the copula vine specification. In this work, a sensitivity analysis is performed to measure the impact of Kendall’s matrix uncertainty due to scarce data on the estimation of the failure probability. As Kendall’s coefficients are dependent random variables, sensitivity analysis is achieved with Borgonovo’s indices, using bootstrap replications of the available data to have a larger amount of estimations. The ranking of sensitivity indices allows identifying the pair of variables on which one has to acquire new samples in order to reduce variability in risk assessment. This methodology is applied on the buckling of a composite plate.
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