基于广义子集模拟和自适应Kriging模型的非线性随机动力系统的时变可靠性分析

摘要
图/表
参考文献(17)
相关文章 (4)

全文: PDF (1435 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要针对非线性随机动力系统在非平稳高斯随机过程激励下的时变可靠性问题，提出一种广义子集模拟（GSS）和主动学习Kriging模型结合Monte Carlo的自适应更新（AK-MCS）高效计算方法（GSS-AK-MCS）。基于全概率定理，将非线性随机动力系统的时变可靠性转化为一个双层嵌套问题：内层通过GSS算法解决非平稳随机激励下累积失效概率的计算；外层自适应地构建系统随机参数与累积失效概率之间的Kriging代理模型，基于代理模型实现随机系统的可靠性分析。以两个非线性结构系统的时变可靠性分析为例，验证所提出方法的可行性。数值算例结果表明：GSS-AK-MCS方法不受非平稳随机激励的频谱特征的影响，与传统的MCS和Kriging模型方法比较，显著提高了非线性随机动力系统的时变可靠性计算效率。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	唐和生1
	2
	郭雪媛1
	薛松涛1

关键词 ：非线性随机动力系统, 非平稳随机激励, 时变可靠性, 广义子集模拟, AK-MCS法

Abstract：A GSS-AK-MCS method, which combines the generalized subset simulation algorithm (GSS) with the adaptive Kriging model(AK-MCS), is proposed for the time-variant reliability analysis of nonlinear stochastic dynamic systems excited by non-stationary Gaussian stochastic processes. Based on the total probability theorem, the time-variant reliability problem is transformed into a two-layer nested time-invariant problem. In the inner layer, the cumulative probability of failure under non-stationary random excitation is calculated by the GSS algorithm. In the outer layer, a Kriging model is constructed for the nonlinear relationship between random parameters and cumulative probability of failure. The feasibility of the proposed method is verified by two numerical case studies. The numerical results indicate that the GSS-AK-MCS method is not affected by the spectral characteristics of non-stationary random excitation and shows good accuracy. The proposed method improves the computational efficiency of time-variant reliability analysis significantly.

Key words： nonlinear stochastic dynamic systems non-stationary random excitation time-variant reliability generalized subset simulation algorithm AK-MCS method

收稿日期: 2020-04-22 出版日期: 2021-11-15

引用本文:

唐和生1,2，郭雪媛1，薛松涛1. 基于广义子集模拟和自适应Kriging模型的非线性随机动力系统的时变可靠性分析[J]. 振动与冲击, 2021, 40(21): 47-54.
TANG Hesheng1,2, GUO Xueyuan1, XUE Songtao1. Time-varying reliability analysis of nonlinear stochastic dynamic systems based on generalized subset simulation and adaptive Kriging model. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(21): 47-54.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I21/47

[1] Rice S O. Mathematical analysis of random noise[J]. Bell System Technical Journal, 1944, 23(3):282-332.
[2] Andrieu-Renaud C, Sudret B, Lemaire M. The PHI2 method: a way to compute time-variant reliability[J]. Reliability Engineering & System Safety, 2004, 84(1):75-86.
[3] Hu Z, Du X. Time-dependent reliability analysis with joint upcrossing rates[J]. Structural & Multidisciplinary Optimization, 2013, 48(5):893-907.
[4] 张德权，韩旭，姜潮，等. 时变可靠性的区间PHI2分析方法[J]. 中国科学（物理学力学天文学），2015，45(5):36-48.
ZHANG De-quan, HAN Xu, JIANG Chao, et al. The interval PHI2 analysis method for time-dependent reliability[J]. Scientia Sinica Pysica,Mechanica & Astronomica, 2015，45(5):36-48.
[5] 乔红威，吕震宙. 非平稳随机激励下随机结构的动力可靠性分析[J]. 固体力学学报，2008，(01):36-40.
QIAO Hong-wei, LU Zhen-zhou. Dynamic reliability analysis of stochastic structures under non-stationary random excitation[J]. Acta Mechanica Solida Sinica, 2008, (01):36-40.
[6] 刘彦辉，刘小换，谭平，等. 层间组合隔震结构随机动力可靠度分析[J]. 振动工程学报，2019,32(02):138-144.
LIU Yan-hui, LIU Xiao-huan, TAN Ping, et al. Dynamic reliability for inter-story hybrid isolation structure[J]. Journal of vibration engineering, 2019, 32(02):138-144.
[7] 刘强，王妙芳. 基于首次超越破坏时间概率的结构动力可靠性分析[J]. 应用力学学报，2019,36(02):480-484.
LIU Qiang, WANG Miao-fang. The reliability analysis of structures based on failure probability of first-passage time[J]. Chinese Journal of Applied Mechanics, 2019, 36(02):480-484.
[8] Wang Zequn, Wang Pingfeng. A nested extreme response surface approach for time-dependent reliability-based design optimization[J]. Journal of Mechanical Design, 2012,134(12):121007.
[9] Wang Z, Chen W. Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation[J]. Structural Safety, 2017, 64:76-86.
[10] 阚琳洁，张建国，邱继伟. 柔性机构时变可靠性分析的时变随机响应面法[J]. 振动与冲击，2019, 38(02):258-263.
KAN Lin-jie, ZHANG Jian-guo, QIU Ji-wei. Time-varying stochastic response surface method for the time-varying reliability analysis of flexible mechanisms [J]. Journal of vibration and shock, 2019, 38(02):258-263.
[11] 陈建兵，李杰. 结构随机地震反应与可靠度的概率密度演化分析研究进展[J]. 工程力学，2014, 31(04):1-10.
CHEN Jian-bing, LI Jie. Probability density evolution method for stochastic seismic response and reliability of structures[J]. Engineering Mechanics, 2014, 31(04):1-10.
[12] 顾镇媛，王曙光，杜东升，等. 基于概率密度演化法的隔震结构随机地震响应与可靠度分析[J]. 振动与冲击，2018, 37(15):97-103.
GU Zhen-yuan, WANG Shu-guang, DU Dong-sheng, et al. Random seismic responses and reliability of isolated structures based on probability density evolution method[J]. Journal of vibration and shock, 2018, 37(15):97-103.
[13] 任丽梅. 基于失效域重构和重要抽样法的结构动力学系统首穿失效概率[J]. 应用数学和力学，2019,40(4):463-472.
REN Li-mei. The First Passage Failure Probabilities of Dynamical Systems Based on the Failure Domain Reconstruction and Important Sampling Method[J]. Applied Mathematics and Mechanics, 2019, 40(4):463-472.
[14] Wang Z, Mourelatos Z P, Li J et al. Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals[J]. Journal of Mechanical Design, 2014, 136(6):61008.
[15] Hu Z, Du X. A sampling approach to extreme value distribution for time-dependent reliability analysis[J]. Journal of Mechanical Design, 2013, 135(7):071003.
[16] Li H S, Ma Y Z, Cao Z. A generalized Subset Simulation approach for estimating small failure probabilities of multiple stochastic responses[J]. Computers & Structures, 2015, 153:239-251.
[17] Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation[J]. Structural Safety, 2011, 33(2):145-154.