DU Xiu-yun, XUE Qi-wen, LIU Xu-dong. Reliability Analysis Based on Bregman Distances[J]. Applied Mathematics and Mechanics, 2016, 37(6): 609-616. doi: 10.3879/j.issn.1000-0887.2016.06.006
Citation: DU Xiu-yun, XUE Qi-wen, LIU Xu-dong. Reliability Analysis Based on Bregman Distances[J]. Applied Mathematics and Mechanics, 2016, 37(6): 609-616. doi: 10.3879/j.issn.1000-0887.2016.06.006

Reliability Analysis Based on Bregman Distances

doi: 10.3879/j.issn.1000-0887.2016.06.006
Funds:  The National Natural Science Foundation of China(10802015)
  • Received Date: 2015-11-27
  • Rev Recd Date: 2015-12-23
  • Publish Date: 2016-06-15
  • A reliability analysis model based on the homotopy algorithm was established to address probabilistic reliability problems of uncertain structures through introduction of Bregman distances. By means of the limit state equations, solution of the reliability index was transformed to a nonlinear constrained optimization problem. According to the homotopy theory and the Bregman distances, the system of homotopy equations was constructed and solved with the path-tracking algorithm. The reliability calculations for different types of functions and different degrees of nonlinear problems were discussed via numerical examples, and the results were compared with those out of previous methods. The results show that the proposed analysis model solves the probabilistic reliability problems of uncertain structures with high efficiency and good accuracy.
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