Variance-based sensitivity analysis of dynamic systems with both input and model uncertainty

Abstract

This paper develops a methodology to compute variance-based sensitivity indices for dynamic systems with time series inputs and outputs, while accounting for both aleatory and epistemic uncertainty sources, and both random process and random variable inputs. We present semi-analytical methods for computing sensitivity indices for linear systems with Gaussian random process inputs, and for the general case of nonlinear systems with non-Gaussian random process inputs. The novel elements in this approach are the treatment of model form error, quantifying the cumulative effects of uncertainty sources over time, and evaluating sensitivity indices for multi-physics models. Bayesian state and parameter estimation methods are incorporated to quantify the model uncertainty arising from unknown model parameters and model form errors, and sensitivity indices are computed before and after model updating. The proposed methods are illustrated for (a) a linear Timoshenko beam erroneously modeled as an Euler-Bernoulli beam, and (b) hypersonic flow behavior of a flexible panel represented by a coupled multi-physics nonlinear model.