[1]杜秀丽,姚 奕.基于跳-扩散过程的振动系统的模态识别方法(英文)[J].南京师大学报(自然科学版),2014,37(04):1.
　Du Xiuli,Yao Yi.Modal Identification Method of the Vibratory SystemBased on the Jump-Diffusion Process[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(04):1.
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基于跳-扩散过程的振动系统的模态识别方法(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第37卷
期数:
2014年04期
页码:
1
栏目:
数学
出版日期:
2014-12-31

文章信息/Info

Title:
Modal Identification Method of the Vibratory SystemBased on the Jump-Diffusion Process
作者:
杜秀丽; 姚 奕
南京师范大学数学科学学院,江苏 南京 210023
Author(s):
Du Xiuli; Yao Yi
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
关键词:
模态识别; 跳-扩散过程; CAR模型; 多幂变差; 极大似然估计
Keywords:
modal identification; jump-diffusion process; CAR model; multi-power variation; maximum likelihood estimator
分类号:
O324,O211.63
文献标志码:
A
摘要:
本文提出了Lévy激励下LTI系统的一种时域模态识别方法.系统响应可看做是一个跳-扩散过程.基于二次变差和多幂次变差的性质,跳-扩散过程被分解成扩散过程和纯跳激励的过程,二者都具有和原系统相同的未知参数.最后通过扩散过程的极大似然估计方法来估计Lévy激励下LTI系统的参数.数值结果表明该方法估计精度高.
Abstract:
In this paper,we put forward a new time-domain modal identification method of LTI system driven by a special Lévy process.The system response can be seen as a jump-diffusion process.Based on the properties of the quadratic variation and multi-power variation,the jump-diffusion process is decomposed into the diffusion process and the pure jump-driven process,both processes have the same unknown parameters as those included in the LTI system.The parameters of the LTI system are identified by the exact maximum likelihood estimation method of the diffusion process.The numerical results demonstrate that the method has high precision.

参考文献/References:

[1] Brockwell P,Davis R A,Yu Y,et al.Continuous-time Gaussian Autoregression[J].Statistica Sinica,2007,17(1):63-80.
[2]Du X L,Wang F Q.Modal identification based on Gaussian continuous time autoregressive moving average model[J].Journal of Sound and Vibration,2010,329(20):4 294-4 312.
[3]Barndorff-Nielsen O E,Shephard N.Power and bipower variation with stochastic volatility and jumps[J].Journal of Financial Econometrics,2004,2(1):1-37.
[4]Woerner H C J.Estimation of integrated volatility in stochastic volatility models[J].Applied Stochastic Models in Business and Industry,2005,21(1):27-44.
[5]Todorov V.Estimation of continuous-time stochastic volatility models with jumps using high-frequency dada[J].Journal of Econometrics,2009,148(2):131-148.
[6]Lee S,Hannig J.Detecting jumps from Lévy jump diffusion processes[J].Journal of Financial Economics,2010,96(2):271-290.
[7]Fan J Q,Yao Q W.Nonlinear Time Series:Nonparametric and Parametric Methods[M].New York:Springer-Verlag,2005.

备注/Memo

备注/Memo:
Received data:2014-08-16.
Foundation item:Supported by NSFC(11201235),Program of Natural Science Research of Jiangsu Higher Education Institution of China(12KJB110010),Philosophy and Social Science Fund of Jiangsu Higher Education Institution of China(2013SJD790031),China Postdoctoral Science Foundation(2013M541697),Postdoctoral Foundation of Jiangsu Province(1302044C).
Corresponding author:Yao Yi,Ph.D,associate professor,majored in time series.E-mail:05302@njnu.edu.cn
更新日期/Last Update: 2014-12-31