Differentiating effects of input aleatory and epistemic uncertainties on system output: A separating sensitivity analysis approach

Sensitivity analysis (SA), aiming at identifying and prioritizing the most influential inputs to output, has been extensively investigated in simulation-based system design under uncertainty. Existing SA methods mainly focus on the influence of either aleatory uncertainty or epistemic uncertainty of inputs on the overall uncertainty of output. In many engineering scenarios, inputs, however, encompass both aleatory and epistemic uncertainties (also called hybrid uncertainties) and are, oftentimes, represented by probability boxes (p-boxes). In this paper, hybrid uncertainties of inputs are modeled by parametric p-boxes. A separating sensitivity analysis (SSA) approach is, then, proposed to differentiate the effects of the aleatory and epistemic uncertainties of inputs on the aleatory and epistemic uncertainties of output, respectively. SSA is carried out by three steps: (1) A double loop procedure is implemented to facilitate the uncertainty propagation when the inputs are parametric p-box variables, (2) the maximum variance metric is put forth to quantify the output aleatory uncertainty, while the area metric is used to measure the output epistemic uncertainty, and (3) SSA is executed based on the uncertainty measures by degenerating a parametric p-box variable to a random quantity or an interval value. Moreover, high order SSA is developed to measure the joint effects of inputs on the output. A numerical example, along with two engineering cases of a cantilever beam and a NACA0012 airfoil, is exemplified to demonstrate the feasibility of the proposed method.