Abstract
In recent years, methods were proposed so as to efficiently perform time-variant reliability analysis. However, importance sampling (IS) for time-variant reliability analysis is barely studied in the literature. In this paper, an IS framework is proposed. A multi-dimensional integral is first derived to define the time-variant cumulative probability of failure, which has the similar expression to the classical definition of time-invariant failure probability. An IS framework is then developed according to the fact that time-invariant random variables are commonly involved in time-variant reliability analysis. The basic idea of the proposed framework is to simultaneously apply time-invariant IS and crude Monte Carlo simulation on time-invariant random variables and stochastic processes, respectively. Thus, the probability of acquiring failure trajectories of time-variant performance function is increased. Two auxiliary probability density functions are proposed to implement the IS framework. However, auxiliary PDFs available for the framework are not limited to the proposed two. Three examples are studied in order to validate the effectiveness of the proposed IS framework.
Highlights
Sustainability 2021, 13, 7776. https://Most mechanical structures and systems are vulnerable against uncertainties, such as loads and material properties
Considering that applying importance sampling (IS) on stochastic processes is difficult, the IS framework proposed in this paper applies time-invariant IS on the time-invariant random variables and samples random trajectories of stochastic processes according to crude Monte Carlo simulation (MCS) in order to generate more failure trajectories of time-variant performance function and enhance the computational efficiency of time-variant reliability analysis
This paper develops a framework of importance sampling for time-variant reliability analysis
Summary
Most mechanical structures and systems are vulnerable against uncertainties, such as loads and material properties. Subset simulations (SS), such as Markov Chain Monte Carlo (MCMC), SS with splitting method [31,32] and SS with splitting and partitioning in time [33], are efficient methods for precisely evaluating time-variant probability of failure They are developed to deal with dynamical systems subject to stochastic excitation, and not applicable to problems involving general stochastic process (e.g., Gaussian processes). Considering that applying IS on stochastic processes is difficult, the IS framework proposed in this paper applies time-invariant IS on the time-invariant random variables and samples random trajectories of stochastic processes according to crude MCS in order to generate more failure trajectories of time-variant performance function and enhance the computational efficiency of time-variant reliability analysis.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
