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基于Bregman距离函数的可靠性分析

杜秀云 薛齐文 刘旭东

杜秀云, 薛齐文, 刘旭东. 基于Bregman距离函数的可靠性分析[J]. 应用数学和力学, 2016, 37(6): 609-616. doi: 10.3879/j.issn.1000-0887.2016.06.006
引用本文: 杜秀云, 薛齐文, 刘旭东. 基于Bregman距离函数的可靠性分析[J]. 应用数学和力学, 2016, 37(6): 609-616. doi: 10.3879/j.issn.1000-0887.2016.06.006
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

基于Bregman距离函数的可靠性分析

doi: 10.3879/j.issn.1000-0887.2016.06.006
基金项目: 国家自然科学基金(10802015);辽宁省自然科学基金联合基金(2015020119)
详细信息
    作者简介:

    杜秀云(1976—), 女, 讲师, 博士(E-mail: duxiuyun@sohu.com);薛齐文(1976—), 男, 教授, 博士(通讯作者. E-mail: xueqiwen@djtu.edu.cn).

  • 中图分类号: TG156

Reliability Analysis Based on Bregman Distances

Funds: The National Natural Science Foundation of China(10802015)
  • 摘要: 针对概率结构可靠性问题,引入Bregman距离函数,建立了基于同伦算法(HM)的可靠性分析模型.利用极限状态方程,将可靠性指标求解转化为一个非线性约束优化问题.结合同伦思想的基本理论和Bregman距离函数,构造同伦方程组,采用路径跟踪算法对该方程组进行求解.通过相应的数值算例探讨了不同函数形式以及不同程度非线性问题的可靠性计算,并与其他方法计算结果进行了对比,分析结果表明该模型能够有效求解概率结构可靠性问题.
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出版历程
  • 收稿日期:  2015-11-27
  • 修回日期:  2015-12-23
  • 刊出日期:  2016-06-15

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