基于降维可视化与Kriging的齿轮振动可靠性分析

杨丽; 佟操

doi:10.13224/j.cnki.jasp.2016.04.028

基于降维可视化与Kriging的齿轮振动可靠性分析

doi: 10.13224/j.cnki.jasp.2016.04.028

杨丽¹,
佟操²

1. 沈阳理工大学装备工程学院, 沈阳 110159;
2. 中国科学院沈阳自动化研究所, 沈阳 110016

基金项目:

沈阳理工大学重点实验室开放基金(4771004kfs26)

国家自然科学基金(51205052)

辽宁省教育厅科学研究项目(L2015469)

详细信息

作者简介:
杨丽(1980-),女,河北石家庄人,副教授,博士,主要从事机械可靠性、传动机构动力学分析等研究.

中图分类号: V215.7;TB114.3
计量
- 文章访问数: 1001
- HTML浏览量: 116
- PDF量: 441
- 被引次数: 0
出版历程
- 收稿日期: 2015-09-09
- 刊出日期: 2016-04-28

Reliability analysis of gear vibration based on dimensionalityreduction visualization and Kriging

YANG Li¹,
TONG Cao²

1. School of Equipment Engineering, Shenyang Ligong University, Shenyang 110159, China;
2. Shengyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

摘要

摘要: 针对齿轮振动可靠性分析时计算量大、计算精度低等问题,提出一种基于降维可视化技术和Kriging模型的可靠性分析方法.通过Monte Carlo法生成抽样点,采用降维可视化技术将多维空间降至二维极特征空间,通过Kriging模型预测失效域与安全域的分界线,在预测分界线时,借助Kriging非线性预测和误差分析的特性,通过一种主动学习选点的方式建立Kriging预测模型,来提高样本点的利用率.通过齿轮振动可靠性的算例表明:相比于传统的降维可视化技术,调用极限状态函数由975次减少为149次,计算时间由12400s减小为1810s,可靠度与100000次Monte Carlo模拟计算结果基本吻合一致,验证了该算法的正确性和有效性.
- 可靠性分析 /
- 降维可视化 /
- Kriging模型 /
- 齿轮 /
- 非线性振动
Abstract: To solve the problems of large computation and low precision during gear vibration reliability analysis, a reliability analysis method based on dimensionality reduction visualization and Kriging was proposed. Sample points were generated by Monte Carlo method. These points were transformed into two-dimensional pole feature space, and then Kriging model was used to predict the dividing line of safe and failure regions. When predicting the dividing line, an active learning approach of selecting points was introduced to establish Kriging model so that the utilization rate of sample points was improved dramatically, thanks to the properties of nonlinear prediction and error estimation of Kriging. Through gear vibration reliability analysis, and by comparing with traditional dimensionality reduction visualization technique, it is shown that the number of calls to the performance function changes from 975 numbers to 149 numbers, and calculation time changes from 12400s to 1810s. What's more, the result of this method is consistent with that of 100000 Monte Carlo simulation, so the efficiency and correctness is validated.
- reliability analysis /
- dimensionality reduction visualization /
- Kriging model /
- gear /
- nonlinear vibration

HTML

参考文献(20)

[1]	李润方,王建军.齿轮系统动力学[M].北京:科学出版社,1997.
[2]	吴勇军,王建军.一种考虑齿轮副连续啮合过程的接触有限元动力学分析方法[J].航空动力学报,2013,28(5):1192-1200. WU Yongjun,WANG Jianjun.A contact finite element method for dynamic analysis of continuous engaged gear pairs[J].Journal of Aerospace Power,2013,28(5):1192-1200.(in Chinese)
[3]	邵忍平,徐志锋,曹精明.裂纹故障齿轮结构声振特性与模拟研究[J].航空动力学报,2010,25(6):1327-1334. SHAO Renping,XU Zhifeng,CAO Jingming.Acoustic vibration characteristic of crack gear structure and simulation[J].Journal of Aerospace Power,2010,25(6):1327-1334.(in Chinese)
[4]	Harr M E.Reliability based design in civil engineering[M].New York:McGraw-Hill,1987.
[5]	张明.结构可靠度分析:方法与程序[M].北京:科学出版社,2009.
[6]	Au S K,Beck J L.A new adaptive importance sampling scheme for reliability calculations[J].Structural Safety,1999,21(2):135-158.
[7]	Au S K,Beck J L.Important sampling in high dimensions[J].Structural Safety,2003,25(2):139-163.
[8]	McKay M D,Beckman R J,Conover W J.Comparison the three methods for selecting values of input variable in the analysis of output from a computer code[J].Technometrics,1979,21(2):239-245.
[9]	Hurtado J E.Dimensionality reduction and visualization of structural reliability problems using polar features[J].Probabilistic Engineering Mechanics,2012,29(7):16-31.
[10]	Gupta S,Manohar C S.Reliability analysis of randomly vibrating structures with parameter uncertainties[J].Journal of Sound and Vibration,2006,297(3/4/5):1000-1024.
[11]	Papoulis A.Probability,random variables and stochastic processes[M].New York:McGraw-Hill,1991.
[12]	Jones D R,Schonlau M,Welch W J.Efficient global optimization of expensive black-box functions[J].Journal of Global Optimization,1998,13(4):455-492.
[13]	Ranjan P,Bingham D,Michailidis G.Sequential experiment design for contour estimation from complex computer codes[J].Technometrics,2008,50(4):527-541.
[14]	Bichon B J,Eldred M S,Swiler L P,e al.Efficient global reliability analysis for nonlinear implicit performance functions[J].AIAA Journal,2008,46(10):2459-2468.
[15]	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.
[16]	佟操,孙志礼,杨丽,等.一种基于Kriging和Monte Carlo的主动学习可靠度算法[J].航空学报,2015,36(9):2942-2951. TONG Cao,SUN Zhili,YANG Li,et al.A active learning reliability method based on Kriging and Monte Carlo[J].Acta Aeronautica et Astronautica Sinica,2015,36(9):2942-2951.(in Chinese)
[17]	TONG Cao,SUN Zhili,ZHAO Qianli,et al.A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling[J].Journal of Mechanical Science and Technology,2015,29(8):3183-3193.
[18]	刘纪涛,刘飞,张为华.Kriging模型在固体火箭发动机装药可靠性分析中的应用[J].航空动力学报,2010,25(1):193-197. LIU Jitao,LIU Fei,ZHANG Weihua.Application of Kriging model to reliability analysis of solid rocket motor grain[J].Journal of Aerospace Power,2010,25(1):193-197.(in Chinese)
[19]	Sacks J,Welch W J,Mitchell T J,et al.Design and analysis of computer experiments[J].Statistical Science,1989,4(4):409-423.
[20]	孙志礼,陈良玉.实用机械可靠性设计理论与方法[M].北京:科学出版社,2003.