东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2017, Vol. 38 ›› Issue (7): 1002-1006.DOI: 10.12068/j.issn.1005-3026.2017.07.019

• 机械工程 • 上一篇    下一篇

一种基于Kriging模型的机械结构可靠性分析方法

刘阔1， 李晓雷2， 王健3   

  1. (1. 大连理工大学 机械工程学院， 辽宁 大连116024; 2. 哈尔滨工业大学 机电工程学院， 黑龙江 哈尔滨150001; 3. 东北大学 机械工程与自动化学院， 辽宁 沈阳110819)
  • 收稿日期:2016-01-20 修回日期:2016-01-20 出版日期:2017-07-15 发布日期:2017-07-07
  • 通讯作者: 刘阔
  • 作者简介:刘阔(1983-)，男，河北石家庄人，大连理工大学副教授.
  • 基金资助:
    中央高校基本科研业务费专项资金资助项目(DUT16RC(3)122).

An Analysis Method of Mechanical Structural Reliability Based on the Kriging Model

LIU Kuo1， LI Xiao-lei2， WANG Jian3   

  1. 1. School of Mechanical Engineering， Dalian University of Technology， Dalian 116024， China; 2. School of Mechatronics Engineering， Harbin Institute of Technology， Harbin 150001， China; 3. School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China.
  • Received:2016-01-20 Revised:2016-01-20 Online:2017-07-15 Published:2017-07-07
  • Contact: LIU Kuo
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摘要： 通过分析现有机械结构可靠性抽样方法存在的不足以及影响失效概率估计精度的主要因素，提出了一种基于Kriging模型及自适应抽样方法的机械结构可靠性分析方法.该抽样方法将随机抽样与聚类算法相结合，能够在概率上保证新增样本点落在对失效概率贡献较大的区域，避免对非重要区域的不必要抽样.以大数定律及中心极限定理为基础，推导了所提出的Kriging模型的收敛条件.通过两个算例说明所提出方法的迭代收敛过程、准确性及稳定性，结果表明，该方法能够在较少调用结构功能函数情况下得到失效概率较准确的估计值.

关键词: Kriging模型, 机械结构可靠性, 失效概率, 自适应抽样方法, 蒙特卡罗方法

Abstract: Based on an analysis of the drawbacks of the existing mechanical structure reliability sampling methods and the main factors influencing the estimation accuracy of failure probability， an analysis method of mechanical structural reliability based on the Kriging model and adaptive sampling strategy is proposed. The proposed sampling strategy combines random sampling and clustering algorithm， and ensures in probability that the new sample points locate themselves in the area that makes significant contribution to failure probability and avoids unnecessary sampling in the unimportant areas. The condition of convergence for the proposed Kriging model is deduced mainly based on the law of large numbers and central limit theorem. Two examples are adopted to illustrate the convergence process， accuracy and stability of the proposed method. The results show that the proposed method can estimate failure probability with high accuracy in the condition that the number of calls to structural performance function is small.

Key words: Kriging model, mechanical structural reliability, failure probability, adaptive sampling strategy, Monte Carlo method

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