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Abstract In traditional reliability theory based on surrogate model, sampling methods are often used to obtain failure probability, the correlation of random variables and the influence of the uncertainty of the surrogate model are often not considered. This paper proposes a reliability analysis method combining (Back propagation) BP neural network and Laplace progressive integration method, which is called BP-Lap method. Latin hypercube sampling method and a learning function are adopted to generate sample points. Based on function approximation theory, the limit state function and its first and second partial derivatives are all approximated by the BP network. The trained BP network is used to solve the failure probability by the Laplace progressive integration method, and ten-fold cross-validation method is used get the failure probability interval. Four numerical examples are used to verify the effectiveness of the BP-Lap method under correlated and uncorrelated random variables respectively. The research shows that BP-Lap method can measure the influence of the uncertainty of the surrogate model on the failure probability, and obtain the the upper and lower bounds of failure probability. BP-Lap method is suitable for both explicit and implicit limit state functions, and has higher accuracy for reliability problems with correlated random variables.
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Received: 21 September 2020
Published: 27 August 2021
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2021, Vol. 42 
