An overview of nonintrusive characterization, propagation, and sensitivity analysis of uncertainties in computational mechanics

In this paper, we offer a short overview of a number of methods that have been reported in the computational-mechanics literature for quantifying uncertainties in engineering applications. Within a probabilistic framework, we describe the characterization of uncertainties using mathematical statistics methods, the propagation of uncertainties through computational models using either Monte Carlo sampling or stochastic expansion methods, and the sensitivity analysis of uncertainties using variance- and differentiation-based methods. We restrict our attention to nonintrusive methods that can be implemented as wrappers around existing computer programs, thus requiring no modification of the source code. We include some recent advances in the propagation and sensitivity analysis of uncertainties that are characterized by arbitrary probability distributions that may exhibit statistical dependence. Finally, we demonstrate the methods integrated in the proposed overview through a nonlinear engineering application relevant to metal forming