An efficient uncertainty propagation analysis method for problems involving non-parameterized probability-boxes

As a kind of imprecise probabilistic model, probability-box (P-box) model can deal with both aleatory and epistemic uncertainties in parameters effectively. The P-box can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box. Currently, the researches involving P-boxes mainly aim at the parameterized P-boxes while the works handling the non-parameterized P-boxes are relatively inadequate. This paper proposes an efficient uncertainty propagation analysis method based on cumulative distribution function discretization (CDFD) for problems with non-parameterized P-boxes, through which the bounds of statistical moments and the cumulative distribution function (CDF) of a response function with non-parameterized P-box variables can be obtained. Firstly, a series of linear programming models are established for acquiring the lower and upper bounds of the first four origin moments of the response function. Secondly, based on the bounds of the origin moments, the CDF bounds for the response function can be obtained using Johnson distributions fitting and an optimization approach based on percentiles. Finally, the accuracy and efficiency of the proposed method are verified by investigating two numerical examples.