A new method for reliability analysis of structures with mixed random and convex variables

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• A new method for reliability analysis of structures with mixed random and convex variables is proposed. • It is proved that approximation accuracy of projection outlines is crucial for failure probability estimation . • A new projection-outline-based active learning strategy is proposed to sequentially update Kriging model . • A quantification function of metamodel uncertainty is developed for the stopping condition of Kriging model update. • The proposed method is tested by four examples and shows high accuracy and efficiency. This paper proposes a method combining projection-outline-based active learning strategy with Kriging metamodel for reliability analysis of structures with mixed random and convex variables. In this method, it is determined that the approximation accuracy of projection outlines on the limit-state surface is crucial for estimation of failure probability instead of the whole limit-state surface. To efficiently improve the approximation accuracy of projection outlines, a new projection-outline-based active learning strategy is developed to sequentially obtain update points located around the projection outlines. Taking into account the influence of metamodel uncertainty on the estimation of failure probability, a quantification function of metamodel uncertainty is developed and introduced in the stopping condition of Kriging metamodel update. Finally, Monte Carlo simulation is employed to calculate the failure probability based on the refined Kriging metamodel. Four examples including the Burro Creek Bridge and a piezoelectric energy harvester are tested to validate the performance of the proposed method. Results indicate that the proposed method is accurate and efficient for reliability analysis of structures with mixed random and convex variables.