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Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes
Highlights Kriging based adaptive sampling reliability analyses approaches are considered. Sensitivity to sampling and metamodel uncertainty is formulated and analyzed. New stopping criteria based on total coefficient of variation proposed. Implementation for Monte Carlo and Importance Sampling based approaches provided. Efficiency gains demonstrated on several application problems.
Abstract Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. In this paper, we propose a methodology to quantify the sensitivity of the failure probability estimator to uncertainties generated by the Gaussian process and the sampling strategy. This quantification also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.
Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes
Highlights Kriging based adaptive sampling reliability analyses approaches are considered. Sensitivity to sampling and metamodel uncertainty is formulated and analyzed. New stopping criteria based on total coefficient of variation proposed. Implementation for Monte Carlo and Importance Sampling based approaches provided. Efficiency gains demonstrated on several application problems.
Abstract Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. In this paper, we propose a methodology to quantify the sensitivity of the failure probability estimator to uncertainties generated by the Gaussian process and the sampling strategy. This quantification also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.
Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes
Menz, Morgane (author) / Dubreuil, Sylvain (author) / Morio, Jérôme (author) / Gogu, Christian (author) / Bartoli, Nathalie (author) / Chiron, Marie (author)
Structural Safety ; 93
2021-05-27
Article (Journal)
Electronic Resource
English
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