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System reliability analysis by multi-cut targeted random sampling

The reliability of a constructed and/or manufactured system is defined as the probability that the structure does not violate a limit state during a desired duration of time. While the current state-of-art focuses mostly on methods to determine component level reliability, few methods exist that are robust enough to handle problems concerning system level reliability. With advancements in non-linear structural mechanics, high computing power, and due to their simplicity, Monte Carlo simulations (MCS) are often the only means to determine the reliability, and thus have dominated the field of reliability for decades. Several modifications of the MCS have emerged that have proven to be useful. Subset simulations, line sampling, importance sampling, and their variants, are perhaps the most celebrated methods among the existing methods.
The study reported in the paper belongs to the class of simulation-based methods that utilize stratified sampling concepts to obtain an estimator for reliability with reduced variance. The proposed method is an extension of the Targeted Random Sampling approach developed earlier by the authors to problems of higher dimensions (component and system level reliability). An initial stratification based on Markov Chain Monte Carlo (MCMC) simulation is propositioned after which the method progresses by adding samples to the existing strata sequentially. A striking feature of the method is that the stratification is performed in the probability space, and the probability of failure is reported as the total probability content of the unsafe region. The method is shown to convergence faster when compared with the method earlier developed by the authors and with reduced variance when compared to other widely used methods for problems with moderate-to-high dimension (<50). Extension of the method to dynamic reliability is discussed.

Author(s):

Sundar VS    
Post doctoral researcher, Johns Hopkins University
United States

Michael Shields    
Assistant Professor, Johns Hopkins University
United States