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Evidence theory, with its powerful features for uncertainty analysis, provides an alternative to probability theory for representing epistemic uncertainty, which is an uncertainty in a system caused by the impreciseness of data or knowledge that can be conveniently addressed. However, this theory is time-consuming for most applications because of its discrete property. This article describes an adaptive sub-interval perturbation-based computational strategy for representing epistemic uncertainty in structural dynamic analysis with evidence theory. The possibility of adopting evidence theory as a general tool for uncertainty quantification in structural transient response under stochastic excitation is investigated using an algorithm that can alleviate computational difficulties. Simulation results indicate that the effectiveness of the presented strategy can be used to propagate uncertainty representations based on evidence theory in structural dynamics.

The small first passage probability of nonlinear dynamic structures under nonstationary seismic excitation implies a prohibitive computational demand because of the epistemic uncertainties rooted in structure system. In this work, a hybrid Kriging-high dimensional model representation (Kriging-HDMR) methodology for drastically simplifying this task is proposed. The epistemic uncertainties with well-defined bounds but no concrete distribution forms are addressed by interval model. Therefore, the first passage probability of the generic response process that the epistemic uncertainties involved, is represented by the conditional univariate extreme value distribution (EVD) of structural parameters with interval form. Then, a Kriging assisted HDMR together with third moment saddle point approximation (TMSA) is proposed to alleviate the computational burden and provides an accurate depiction of possible model outcome. The differential evolution (DE) interval optimization strategy is performed to accelerate the post process of searching the lower bound (LB) and upper bound (UB) of first passage probability with interval form. Finally, a nine-story shear frame with Bouc–Wen model is presented to demonstrate the accuracy and efficiency of proposed method.