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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.
Jian Wang; Xiang Gao; Zhili Sun. An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes. Sustainability 2021, 13, 7776 .
AMA StyleJian Wang, Xiang Gao, Zhili Sun. An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes. Sustainability. 2021; 13 (14):7776.
Chicago/Turabian StyleJian Wang; Xiang Gao; Zhili Sun. 2021. "An Importance Sampling Framework for Time-Variant Reliability Analysis Involving Stochastic Processes." Sustainability 13, no. 14: 7776.
Crude Monte Carlo simulation (MCS) is the most robust and easily implemented method for performing time-variant reliability analysis (TRA). However, it is inefficient, especially for high reliability problems. This paper aims to present a random simulation method called the multilevel Monte Carlo (MLMC) method for TRA to enhance the computational efficiency of crude MCS while maintaining its accuracy and robustness. The proposed method first discretizes the time interval of interest using a geometric sequence of different timesteps. The cumulative probability of failure associated with the finest level can then be estimated by computing corrections using all levels. To assess the cumulative probability of failure in a way that minimizes the overall computational complexity, the number of random samples at each level is optimized. Moreover, the correction associated with each level is independently computed using crude MCS. Thereby, the proposed method can achieve the accuracy associated with the finest level at a much lower computational cost than that of crude MCS, and retains the robustness of crude MCS with respect to nonlinearity and dimensions. The effectiveness of the proposed method is validated by numerical examples.
Jian Wang; Xiang Gao; Zhili Sun. A Multilevel Simulation Method for Time-Variant Reliability Analysis. Sustainability 2021, 13, 3646 .
AMA StyleJian Wang, Xiang Gao, Zhili Sun. A Multilevel Simulation Method for Time-Variant Reliability Analysis. Sustainability. 2021; 13 (7):3646.
Chicago/Turabian StyleJian Wang; Xiang Gao; Zhili Sun. 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis." Sustainability 13, no. 7: 3646.