An efficient structural uncertainty propagation method based on evidence domain analysis. (1st September 2019) - Cao, Lixiong; Liu, Jie; Wang, Qingyun; Jiang, Chao; Zhang, Lianyi
Highlights: An efficient uncertainty propagation method is proposed based on evidence theory. The inclusion relationship of focal element can be determined in evidence domain. A maximum entropy measurement is proposed by evidence domain analysis. The proposed volume ratio can efficiently calculate the maximum entropy measurement. Abstract: Evidence theory can be used for propagation analysis of structural response with various uncertainties because of its much more flexible and universal framework. However, the discrete characteristic and the ambiguity measure of the propagated result have severely influenced the practicability of evidence theory. Because of the basic probability assignment (BPA), the evidence domain is a countable region composed of all focal elements. Hence, in this study, an efficient uncertainty propagation method is proposed through evidence domain analysis. A multiple linear segment approximation for limit state equation (LSE) rather than structural performance function is firstly constructed, so the support degree of each focal element is directly judged in evidence domain. Then, the belief (Bel) measurement and plausibility (Pl) measurement are calculated by the positional relation of each focal element in the uncertain variable domain without involving response domain. Meanwhile, a volume ratio that can represent the proportion of focal element partly supporting event is calculated by utilizing the approximate LSE. Therefore, a maximum entropy probability measurement between the Bel and Pl can be provided using the volume ratio. One numerical example and two engineering applications are investigated to demonstrate the effectiveness of the proposed method.