A collaborative quasi-Monte Carlo uncertainty propagation analysis method for multiple types of epistemic uncertainty quantified by probability boxes

Various epistemic uncertainties arise in practical engineering problems. In this paper, probability boxes (p-boxes) are used to unify multiple types of epistemic uncertainty, which include intervals, p-boxes and evidence variables. A collaborative interval quasi-Monte Carlo method (CIMCM) is presented to calculate the probability bounds of a model. The interval-based quasi-random sampling technique is applied to sample a range of intervals from unified input p-boxes. An interval that includes all random intervals is constructed. Rosen’s gradient projection method (RGPM) is utilized to solve the extreme output values of the numerical model based on the enveloping interval. A collaborative optimization method is presented to calculate the extreme values of the numerical model, the input variables of which are a range of intervals. The probability bounds of the model are finally computed by a statistical method. The presented method reduces the number of repeated search iterations for a range of optimization problems that include many overlapping domains. Two numerical examples and two engineering cases are investigated to demonstrate the effectiveness of the CIMCM.