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An analysis method for structural reliability sensitivity based on the bisection method of sampling

  • 1.

    School of Mechatronic Engineering, Changchun University of Technology, Changchun 130012, China

  • 2.

    School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.09.010
  • Received Date: 27 March 2014
  • Accepted Date: 16 December 2014
  • Rev Recd Date: 16 December 2014
  • Publish Date: 30 September 2015
    Abstract

  • Abstract

    Targeting the problem of limit state equations being often implicit and demanding a great amount of computation, an analysis method was proposed for structural reliability sensitivity based on the bisection method of sampling. Combining with the most probable point method of structure reliability analysis and the bisection method of sampling, the proposed method first linearizes the state equations near the initial point based on Taylor expansion method and determines the optimal step-length based on gradient information; then, it locates the new sampling point by means of bisect sampling step-length of reliability index β; finally, by several iterations, it finds out the most probable point (MPP) that meet the accuracy requirement of the structures and system to calculate reliability and reliability sensitivity of influencing parameters according to the information of the sampled path. Examples of the computation and engineering were given. A comparison with existing methods for solving implicit structure reliability problems indicated that the proposed method possesses the advantages of reliable convergence and less sampling, making it especially suitable for performing reliability analyses of large-scale complicated implicit structures and systems.

    Abstract

    Targeting the problem of limit state equations being often implicit and demanding a great amount of computation, an analysis method was proposed for structural reliability sensitivity based on the bisection method of sampling. Combining with the most probable point method of structure reliability analysis and the bisection method of sampling, the proposed method first linearizes the state equations near the initial point based on Taylor expansion method and determines the optimal step-length based on gradient information; then, it locates the new sampling point by means of bisect sampling step-length of reliability index β; finally, by several iterations, it finds out the most probable point (MPP) that meet the accuracy requirement of the structures and system to calculate reliability and reliability sensitivity of influencing parameters according to the information of the sampled path. Examples of the computation and engineering were given. A comparison with existing methods for solving implicit structure reliability problems indicated that the proposed method possesses the advantages of reliable convergence and less sampling, making it especially suitable for performing reliability analyses of large-scale complicated implicit structures and systems.
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    • References(12)
  • [1]
    Zhang Yimin. Connotation and development of mechanical reliability-based design[J]. Journal of Mechanical Engineering, 2010，46(14)：167-188.
    张义民.机械可靠性设计的内涵与递进[J]. 机械工程学报，2010，46(14)：167-188.
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    Zhao Y G, Ono T. Moment methods for structural reliability [J].Structural Safety, 2001, 23(1): 47-75.
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    Huang B, Du X P. Probabilistic uncertainty analysis by mean-value first order saddle point approximation[J].Reliability Engineering and System Safety, 2008, 93(2):325-336.
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    Du X, Chen W. A most probable point based method for efficient uncertainty analysis[J]. Journal of Design and Manufacturing Automation, 2001, 4(1)：47-66.
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    Zhao Weitao, An Weiguang, Yan Xinchi. Second-order second-moment reliability index[J]. Journal of Harbin Engineering University, 2004,25(2): 240-242.
    赵维涛, 安伟光, 严心池. 二阶二次矩可靠性指标[J].哈尔滨工程大学学报,2004,25(2): 240-242.
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    Richard J F, Zhang W. Efficient high-dimensional importance sampling [J]. Journal of Econometrics, 2007, 141(2):1 385-1 411.
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    Au S K, Beck J L. A new adaptive importance sampling scheme for reliability calculations [J].Structural Safety, 1999, 21(2):135-158.
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    Song Shufang, Lu Zhenzhou, Zheng Chunqing. Directional simulation for sensitivity analysis of structural reliability[J]. Chinese Journal of Solid Mechanics, 2008, 29(3)：264-271.
    宋述芳,吕震宙,郑春青.结构可靠性灵敏度分析的方向(重要)抽样法[J]. 固体力学学报，2008，29(3)：264-271.
    [9]
    Zhang Feng, Lyu Zhenzhou, Cui Lijie. [J]. Improved reliability sensitivity estimation and its variance analysis by a novel β hyper-plane based importance sampling method[J]. Chinese Journal of Engineering Mathematics, 2011, 28(2)：176-186.
    张峰,吕震宙,崔利杰.基于β面截断重要抽样法可靠性灵敏度估计及其方差分析[J].工程数学学报，2011，28(2)：176-186.
    [10]
    Yang Jie, Zhao Deyou. Rotation gradient algorithm for calculating structural reliability index[J]. Journal of Dalian University of Technology, 2011，51(2)：221-225.
    杨杰，赵德有.结构可靠性指标计算的旋转梯度算法[J].大连理工大学学报，2011，51(2)：221-225.
    [11]
    令锋，傅守忠，陈树敏，等. 数值计算方法[M]，北京：国防工业出版社，2012：66-78.
    [12]
    Wang Lianming, Song Baoyu, Zhou Yan, et al. Modeling and simulation of automobile ride[J]. Journal of Harbin Institute of Technology, 1998，30(5)：80-84.
    王连明，宋宝玉，周岩，等.汽车平顺性建模及其仿真研究[J].哈尔滨工业大学学报，1998，30(5)：80-84.
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    [1]
    Zhang Yimin. Connotation and development of mechanical reliability-based design[J]. Journal of Mechanical Engineering, 2010，46(14)：167-188.
    张义民.机械可靠性设计的内涵与递进[J]. 机械工程学报，2010，46(14)：167-188.
    [2]
    Zhao Y G, Ono T. Moment methods for structural reliability [J].Structural Safety, 2001, 23(1): 47-75.
    [3]
    Huang B, Du X P. Probabilistic uncertainty analysis by mean-value first order saddle point approximation[J].Reliability Engineering and System Safety, 2008, 93(2):325-336.
    [4]
    Du X, Chen W. A most probable point based method for efficient uncertainty analysis[J]. Journal of Design and Manufacturing Automation, 2001, 4(1)：47-66.
    [5]
    Zhao Weitao, An Weiguang, Yan Xinchi. Second-order second-moment reliability index[J]. Journal of Harbin Engineering University, 2004,25(2): 240-242.
    赵维涛, 安伟光, 严心池. 二阶二次矩可靠性指标[J].哈尔滨工程大学学报,2004,25(2): 240-242.
    [6]
    Richard J F, Zhang W. Efficient high-dimensional importance sampling [J]. Journal of Econometrics, 2007, 141(2):1 385-1 411.
    [7]
    Au S K, Beck J L. A new adaptive importance sampling scheme for reliability calculations [J].Structural Safety, 1999, 21(2):135-158.
    [8]
    Song Shufang, Lu Zhenzhou, Zheng Chunqing. Directional simulation for sensitivity analysis of structural reliability[J]. Chinese Journal of Solid Mechanics, 2008, 29(3)：264-271.
    宋述芳,吕震宙,郑春青.结构可靠性灵敏度分析的方向(重要)抽样法[J]. 固体力学学报，2008，29(3)：264-271.
    [9]
    Zhang Feng, Lyu Zhenzhou, Cui Lijie. [J]. Improved reliability sensitivity estimation and its variance analysis by a novel β hyper-plane based importance sampling method[J]. Chinese Journal of Engineering Mathematics, 2011, 28(2)：176-186.
    张峰,吕震宙,崔利杰.基于β面截断重要抽样法可靠性灵敏度估计及其方差分析[J].工程数学学报，2011，28(2)：176-186.
    [10]
    Yang Jie, Zhao Deyou. Rotation gradient algorithm for calculating structural reliability index[J]. Journal of Dalian University of Technology, 2011，51(2)：221-225.
    杨杰，赵德有.结构可靠性指标计算的旋转梯度算法[J].大连理工大学学报，2011，51(2)：221-225.
    [11]
    令锋，傅守忠，陈树敏，等. 数值计算方法[M]，北京：国防工业出版社，2012：66-78.
    [12]
    Wang Lianming, Song Baoyu, Zhou Yan, et al. Modeling and simulation of automobile ride[J]. Journal of Harbin Institute of Technology, 1998，30(5)：80-84.
    王连明，宋宝玉，周岩，等.汽车平顺性建模及其仿真研究[J].哈尔滨工业大学学报，1998，30(5)：80-84.
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