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

2025-09-11

AI Summary

Addressing the challenge of propagating coexisting aleatory and epistemic uncertainties in dynamical systems, this paper proposes a unified uncertainty analysis framework based on an augmented stochastic space. The method decouples the two uncertainty types: aleatory uncertainty is modeled probabilistically, while epistemic uncertainty is represented non-probabilistically via distribution-free probability boxes (p-boxes). Coupled with a decoupled multi-probability density evolution method (M-PDEM), the framework efficiently computes conditional response probability density functions. It seamlessly integrates probabilistic, non-probabilistic, and interval-based modeling paradigms, enhancing both computational efficiency and modeling flexibility. Validated through benchmark nonlinear systems—including a single-degree-of-freedom oscillator, a 10-degree-of-freedom hysteretic structure, and a collision-induced energy-absorbing device—the proposed approach demonstrates superior accuracy and efficiency compared to conventional hybrid uncertainty analysis methods. This work establishes a novel paradigm for robustness assessment of complex engineering dynamical systems under mixed uncertainties.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Propagating hybrid aleatory and epistemic uncertainties in dynamical systems
• Transforming uncertainty inputs into an augmented random space
• Determining conditional probability density functions for complex system responses

Innovation

• Unified framework for hybrid uncertainty propagation
• Decoupled multi-probability density evolution method
• Transforms uncertainties into augmented random space