A new measurement for structural uncertainty propagation based on pseudo-probability distribution

Uncertainty propagation (UP) offers a powerful tool for describing uncertainties from input parameters to output responses in a system. The existing methods of non-probabilistic UP can only evaluate the upper and lower bounds of structural responses. In this study, a new non-probabilistic UP method is proposed, attempting to provide more detailed quantification of uncertain responses between the lower and upper bounds. A concept of pseudo-probability distribution is proposed under the non-probabilistic UP frame to quantify the possibilities of system responses. The uncertainties of structural parameters are modeled as a multi-dimensional ellipsoid convex set in the proposed UP method. The ellipsoid domain is divided into two parts using the first-order approximation of the system-state function. Then the volume ratio of the divided domain and the whole ellipsoid domain can be used to calculate the pseudo-probability of system responses. The sequential improved Hasofer-Lind-Rackwitz-Fiessler (iHL-RF) algorithm is adopted to effectively obtain the most probable expansive point of system-state function. The proposed UP method can not only provide accurate response bounds, but also objectively quantify the relatively accurate possibilities of each response value. In the numerical examples, the proposed UP method is compared with the Monte Carlo simulation method and traditional non-probabilistic uncertainty propagation method, and the calculated results demonstrate the validity and effectiveness of the proposed UP method.