Unified Framework for Hybrid Aleatory and Epistemic Uncertainty Propagation via Decoupled Multi-Probability Density Evolution Method

Abstract: This paper presents a unified framework for uncertainty propagation in dynamical systems involving hybrid aleatory and epistemic uncertainties. The framework accommodates precise probabilistic, imprecise probabilistic, and non-probabilistic representations, including the distribution-free probability-box (p-box). A central aspect of the framework involves transforming the original uncertainty inputs into an augmented random space, yielding the primary challenge of determining the conditional probability density function (PDF) of the response quantity of interest given epistemic uncertainty parameters. The recently proposed decoupled multi-probability density evolution method (decoupled M-PDEM) is employed to numerically solve the conditional PDF for complex dynamical systems. Several numerical examples illustrate the applicability, efficiency, and accuracy of the proposed framework. These include a linear single-degree-of-freedom (SDOF) system subject to Gaussian white noise with its natural frequency modeled as a p-box, a 10-DOF hysteretic structure subject to imprecise seismic loads, and a crash box model with mixed random and interval system parameters.