A new uncertainty propagation method for problems with parameterized probability-boxes

This paper proposes a new uncertainty propagation method for problems with parameterized probability-boxes (p-boxes), which could efficiently compute the probability bounds of system response function. In practical engineering, these probability bounds are often very important for reliability analysis or risk assessment of a structure or system. First, based on the univariate dimension reduction method (UDRM), an optimized UDRM (OUDRM) is presented to calculate the bounds on statistical moments of response function. Then, utilizing the bounds on moments, a family of Johnson distributions fitting to the distribution function of response can be acquired using the moment matching method. Finally, by using an optimization approach based on percentiles, the probability bounds of the response function can be successfully obtained. Four numerical examples are investigated to demonstrate the effectiveness of the proposed method.