一种自适应PC-Kriging模型的结构可靠性分析方法

doi:10.12068/j.issn.1005-3026.2020.05.010

东北大学学报:自然科学版 ›› 2020, Vol. 41 ›› Issue (5): 667-672.DOI: 10.12068/j.issn.1005-3026.2020.05.010

一种自适应PC-Kriging模型的结构可靠性分析方法

于震梁，孙志礼，张毅博，王健

(东北大学机械工程与自动化学院，辽宁沈阳110819)

收稿日期:2019-09-11 修回日期:2019-09-11 出版日期:2020-05-15 发布日期:2020-05-15
通讯作者: 于震梁
作者简介:于震梁(1982-)，男，辽宁营口人，东北大学博士研究生；孙志礼(1957-)，男，山东巨野人，东北大学教授，博士生导师.
基金资助:
国家自然科学基金资助项目(51775097).

A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model

YU Zhen-liang， SUN Zhi-li， ZHANG Yi-bo， WANG Jian

School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China.

Received:2019-09-11 Revised:2019-09-11 Online:2020-05-15 Published:2020-05-15
Contact: YU Zhen-liang
About author:-
Supported by:
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摘要/Abstract

摘要： 为提高小失效概率及耗时的复杂结构可靠性评估精度和效率，提出了一种基于PC-Kriging(polynomial-chaos-based Kriging)模型与自适应k-means聚类分析相结合的结构可靠性分析方法.PC-Kriging的回归基函数采用稀疏多项式最优截断集合来近似数值模型全局行为，并用Kriging来处理模型输出的局部变化.在基函数的建立上，PC-Kriging采用最小角回归(LAR)计算功能函数可能的多项式基函数集的数量，同时用Akaike信息准则(AIC)来确定最优多项式形式.自适应k-means聚类分析确保每次迭代添加若干个对失效概率贡献较大的样本点.通过两个数值算例分析，结果表明所提出方法在能够保证失效概率估计值的有效性和准确性的同时减小结构功能函数的评估次数.

关键词: PC-Kriging, 可靠性分析, k-means聚类分析, 自适应试验设计, 蒙特卡罗方法

Abstract: To improve the accuracy and efficiency of reliability assessment for complex structures with small failure probability and time-consuming model， a structural reliability analytical method based on PC-Kriging (polynomial-chaos-based Kriging) model and adaptive k-means clustering analysis was proposed. PC-Kriging’s regression basis function approximated the global behavior of the numerical model by using the sparse polynomial optimal truncation set， and Kriging was used to deal with the local variation of the output of the model. PC-Kriging used least angle regression (LAR) to calculate the number of possible polynomial basis function sets of performance function， and adopted Akaike information criterion (AIC) to determine the optimal polynomial form. The adaptive k-means clustering analysis ensured that some of the significant contribution sample points toward the failure probability can be added as the new training samples in each iteration. The results of two numerical examples indicated that the proposed method can not only guarantee the validity and accuracy of the estimation of failure probability but also reduce structural performance function evaluation times.

Key words: PC-Kriging(polynomial-chaos-based Kriging), reliability analysis, k-means clustering analysis, adaptive design of experiment, Monte Carlo method

中图分类号:

TB114.3

于震梁，孙志礼，张毅博，王健. 一种自适应PC-Kriging模型的结构可靠性分析方法[J]. 东北大学学报:自然科学版, 2020, 41(5): 667-672.

YU Zhen-liang， SUN Zhi-li， ZHANG Yi-bo， WANG Jian. A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model[J]. Journal of Northeastern University Natural Science, 2020, 41(5): 667-672.

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一种自适应PC-Kriging模型的结构可靠性分析方法

A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model

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