基于区域分解的结构动力学系统首次穿越失效

任丽梅; 徐伟

doi:10.6052/0459-1879-12-355

基于区域分解的结构动力学系统首次穿越失效

任丽梅^1,2, ,,
徐伟¹

1.
西北工业大学理学院, 西安710072
2. 长安大学理学院, 西安710064

基金项目: 国家自然科学基金(10932009,11172233)和长安大学中央高校专项基金(CHD2011JC019)资助项目.

详细信息

通讯作者:
任丽梅,主要研究方向:非线性随机动力学.E-mail:renlm1014@126.com

中图分类号: O324
计量
- 文章访问数: 1514
- HTML全文浏览量: 64
- PDF下载量: 938
出版历程
- 收稿日期: 2012-12-11
- 修回日期: 2013-02-12
- 刊出日期: 2013-05-17

FIRST PASSAGE PROBABILITIES OF STRUCTURAL DYNAMICS SYSTEM BASED ON DOMAIN DECOMPOSITION

Ren Limei^1,2, ,,
Xu Wei¹

1.
College of Science, Northwestern Polytechnical University, Xi'an 710072, China
2. College of Science, Changan University, Xi'an 710064, China

Funds: The project was supported by the National Natural Science Foundation of China (10932009, 11172233) and the Special Fund of Chang'an University (CHD2011JC019).

摘要

摘要: 提出了高斯白噪声激励的线性及非线性结构动力学系统的首次穿越失效概率的估计方法. 对于线性结构动力学系统,失效区域被分解为互斥的基本失效域之和,每个基本失效域可用其设计点完全描述,并以正态分布代替卡方分布估计失效概率中的参数. 对于非线性结构动力学系统,基于Rice穿越理论,将非线性方程转化为与之具有相同平均上穿率的线性化方程,然后利用文中方法对等效线性化方程估计首穿失效概率. 最后给出了线性及非线性结构动力学系统的数值例子,并将所提方法与蒙特卡罗法及重要样本法相比较,模拟结果显示了方法的正确性与有效性.
- 结构可靠性 /
- 首穿失效概率 /
- 区域分解 /
- 等效线性化
Abstract: The first passage problems of linear and nonlinear dynamical systems excited by Gauss white noise are considered. For linear dynamical system, the failure domain can be described as a union of mutually exclusive events, and every event is completely described by a local design point. The paper uses standard Gaussian distribution instead of chi-square distribution to estimate the parameter of first passage probability. For nonlinear dynamical system, the equivalent linear system is carried out based on the out-crossing theory. The linearization principle is that nonlinear and linear systems have the same up-crossing rate for a specified threshold. Finally the paper gives two examples. The results show that the method of the paper suggested is correct and effective by comparing with the Monte Carlo method.
- structural reliability /
- first passage probability /
- domain decomposition /
- equivalent linearization

HTML全文

参考文献(18)

Proppe C, Pradlwarter HJ, Schueller GI. Equivalent linearization and Monte Carlo simulation in stochastic dynamics. Probability Engineering Mechanics, 2003, 18(3): 1-15

Spencer BF, Bergman LA. On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems. Nonlinear Dynam, 1993(4): 357-372

Li W, Xu W. Stochastic optimal control of first passage failure for coupled Duffing-Van der Pol system under Gaussian white noise excitations. Chaos Solitons & Fractal, 2005, 25(5): 1221-1228

Li W, Xu W. First passage problem for strong nonlinear stochastic dynamical system. Chaos Solitons & Fractal, 2006, 28(2): 414-421

徐伟,孙春艳,孙建桥等.胞映射方法的研究和进展.力学进展,2013, 43(1): 91-100 (Xu Wei, Sun Chunyan, Sun Jianqiao, et al. Development and study on cell mapping methods. Advances in Mechanics, 2013, 43(1): 91-100 (in Chinese))

徐伟,李伟,靳艳飞等.耦合Duffing-van der Pol系统的首次穿越问题.力学学报,2005, 37(5): 620-625 (Xu Wei,Li Wei,Jin Yanfei, et al. First-passage problem for coupled Duffing-van der Pol systems.Chinese Jounal of Theoretical and Applied Mechanics,2005, 37(5): 620-625 (in Chinese))

任丽梅,徐伟,肖玉柱等.基于重要样本法的结构动力学系统的首次穿越.力学学报,2012, 44(3): 648-652 (Ren Limei,Xu Wei,Xiao Yuzhu, et al. First excursion probabilities of dynamical systems by importance sampling. Chinese Jounal of Theoretical and Applied Mechanics, 2012, 44(3): 648-652 (in Chinese))

Au SK, Beck JL. First excursion probability for linear systems by very efficient importance sampling. Probability Engineering Mechanics, 2001, 16(3): 193-207

Juu O, Hiroaki T. Importance sampling for stochastic systems under stationary noise having a specified power spectrum. Probability Engineering Mechanics, 2009, 24(4): 537-544

Pradlwarter HJ, Schueller GI. Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation. Probability Engineering Mechanics, 1999, 14(3): 213-227

Olsen AI, Naess A. An importance sampling procedure for estimating failure probabilities of Non-linear dynamic systems subjected to random noise. J Non-linear Mechanics, 2007(42): 848-863

Katafygiotis LS, Cheung SH. Domain decomposr-tion method for calculating the failure probability of linear dynamic systems subjected to Gaussian stochastic loads. Journal of Engineering Mechanics, 2006(20): 475-486

Yuen KV, Katafygiotis LS. An efficient simulation method reliability analysis of linear dynamical systems using simple additive rules of probability. Probability Engineering Mechanics, 2005, 20(2): 109-114

Zuev KM, Katafygiotis LS. The Horseracing Simulation algorithm for evaluation of small failure probabilities. Probability Engineering Mechanics, 2011, 26(2): 157-164

Der Kiureghian A.The geometry of random vibrations and solutions by FORM and SORM. Probability Engineering Mechanics, 2000,15(2): 81-90

Valdebenito MA, Pradlwarter HJ, Schueller GI. The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities. Structural Safety, 2010(32): 101-111

Oksendal B. Stochastic Differential Equations: An Introduction with Application. 5th edn. Berlin: Springer, 1998

Soong TT, Grigoriu M. Random Vibration of Mechancial and Structural Systems. Englewood Cliffs, NJ: Prentice-Hall, 1997

施引文献(11)

期刊类型引用(7)

1.	刘敏，卢飞扬，占金青，吴剑，朱本亮. 考虑最小尺寸约束的内嵌可移动压电驱动柔顺机构拓扑优化设计. 中国机械工程. 2025(02): 255-264 . 百度学术
2.	江旭东，马佳琪，熊志，滕晓艳，王亚萍. 基于多分辨率-多边形单元建模策略的多材料结构动刚度拓扑优化方法. 工程力学. 2024(02): 222-235 . 百度学术
3.	周焕林，郭鑫，王选，方立雪，龙凯. 考虑几何非线性的多相多孔结构拓扑优化设计. 吉林大学学报(工学版). 2024(10): 2754-2763 . 百度学术
4.	孙岩，邓学霖，何良莉，姚海艳. 界面离散网格点数据重规整化方法. 计算机辅助设计与图形学学报. 2022(05): 804-810 . 百度学术
5.	马晶，赵明宣，王浩淼，刘湃，亢战. 考虑界面力学性能的组件及结构的协同优化. 力学学报. 2021(06): 1758-1768 . 本站查看
6.	李宏宇，孙鹏文，张兰挺，牛磊，龙凯. 基于ICM的风力机叶片多相材料拓扑优化设计. 太阳能学报. 2021(12): 261-266 . 百度学术
7.	程长征，卞光耀，王选，龙凯，李景传，吴乔国. 连续纤维增强复合材料结构基频最大化设计. 力学学报. 2020(05): 1422-1430 . 本站查看