PDEM-BASED RELIABILITY EVALUATION OF NONLINEAR STOCHASTIC DYNAMICAL SYSTEMS

Abstract eng:
The paper presents a family of original PDEM-based reliability evaluation methods for nonlinear stochastic dynamical systems. In the past years, a family of probability density evolution method (PDEM), which is capable of capturing the instantaneous probability density function of the stochastic response and its evolution, has been developed and applied to stochastic response analysis of linear and nonlinear multi-degree-of-freedom structural systems. Based on this, two methods for dynamic reliability evaluation can be proposed. The first method is to impose an absorbing boundary condition The second method is to capture the extreme value distribution of the related physical quantities. This can be implemented by constructing an appropriate virtual stochastic process and employing the PDEM on the new virtual stochastic dynamical system. It can be proved that the dynamic reliability of the system is equivalent to a one-dimensional integral of the extreme value distribution over the safe domain. Thus, the dynamic reliability can be evaluated through the one-dimensional integral. Further, by introducing the idea of equivalent extreme value event, the system reliability can also be captured. In contrast to the reliability theory based on the excursion process, in the proposed two methods the computation of the expected excursion rate is not needed, let alone the assumptions on the nature of the excursion events. Numerical examples show that the above two methods are both of satisfactory accuracy.

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