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| A structural reliability analysis method based on convex set-probability hybrid model |
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Abstract Because the reliability method under probability theory cannot consider the problem of convex set model under incomplete information, this paper establishes a reliability analysis method under convex set-probability hybrid model based on sample sampling and Laplace progressive integral method. Two different types of convex set models are considered, including ellipsoid model and interval model. Latin hypercube sampling is used to generate sample points in standard space, and then transformed into convex set space by matrix transformation, and the sample points of convex set variables are obtained. These sample points are substituted into the limit state equation, so that the hybrid reliability model is transtormed into the probabilistic reliability model. Laplace progressive integration method is used to solve the failure probability of each limit state equation. The maximum and minimum values of the results are calculated, and the upper and lower bounds of the failure probability are obtained. The coefficient of variation of the failure probability is used to describe the stability of calculation result. The accuracy is verified by three examples, the influence of the number of sample points of convex set variables on the results is discussed and the comparison calculation is carried out by Monte Carlo method under hybrid model. The research shows that the method proposed in this paper has high accuracy and efficiency, it is also applicable to the reliability problems with small failure probability. When the upper and lower bounds of the convex set variables are the same, the results obtained by the interval model and the ellipsoid model are different. In order to stabilize the results, the ellipsoid model requires more convex set sample points than the interval model. If the interval model is used, the number of sample points should be above 3000. If the number of sample points in the convex set is the same, the coefficient of variation of the failure probability calculation result of the ellipsoid model is small, and the stability is higher than interval model. The method proposed in this paper can provide a new idea for the reliability analysis of hybrid model.
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Received: 26 February 2020
Published: 28 October 2020
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2020, Vol. 41 
