Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach

Abstract

Engineering analyses of structures may be confronted with many sources of uncertainty, which may be of different types, such as parametric uncertainties versus modeling errors, and which may pertain to different structural components when complex structures are analyzed. Soize, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, Int. J. Numer. Meth. Eng., 81:939–970, 2010 has recently introduced a generalized probabilistic modeling approach, which can individually represent parametric uncertainties and modeling errors and which can individually represent sources of uncertainty pertaining to different structural components of complex structures. In this paper, we propose to augment this generalized probabilistic modeling approach with a stochastic sensitivity analysis in order to quantify and gain insight into separate impacts of distinct sources of uncertainty on quantities of interest. We demonstrate the proposed methodology by applying it to two computational-mechanics models involving uncertainty.