Instantaneous Spectrum Estimation of Earthquake Ground Motions Based on Unscented Kalman Filter Method

LI Ying-min; DONG Yin-feng; LAI Ming

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(11): 1370-1378

LI Ying-min, DONG Yin-feng, LAI Ming. Instantaneous Spectrum Estimation of Earthquake Ground Motions Based on Unscented Kalman Filter Method[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1370-1378.

Citation:

PDF( 573 KB)

Instantaneous Spectrum Estimation of Earthquake Ground Motions Based on Unscented Kalman Filter Method

1.
College of Civil Engineering, Chongqing University, Chongqing 400045, P. R. China;

Received Date: 2006-09-20
Rev Recd Date: 2007-09-04
Publish Date: 2007-11-15

Abstract

Abstract

Representing earthquake ground motion as time varying ARMA model, the instantaneous spectrum can be determined only by the time varying coefficients of the corresponding ARMA model. Then, unscented Kalman filter was introduced to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter method shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former relevant studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.
- unscented Kalman filter,
- earthquake ground motion,
- instantaneous spectrum,
- time varying ARMA model

FullText(HTML)

References(18)

References

[1]	李英民.工程地震动的模型化研究[D].博士学位论文.重庆:重庆建筑大学,1999.
[2]	Conte J P, Pister K S, Mahin S A. Influence of the earthquake ground motion process and structural properties on response characteristics of simple structures[R]. Report No. UCB/EERC-90/09, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1990.
[3]	Cohen L. Time-frequency distributions—a review[J].Proceedings of the IEEE,1989,77(7):941-981. doi: 10.1109/5.30749
[4]	Huang N E, Shen Z, Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proc of the Royal Society of London, Ser A,1998,454(1971): 903-995. doi: 10.1098/rspa.1998.0193
[5]	谢衷洁. 时间序列分析[M].北京: 北京大学出版社, 1990.
[6]	Kalman R E. A new approach to linear filtering and prediction problems[J]. Journal of Basic Engineering, Transactions of the ASME, Ser D,1960,82(1):35-45. doi: 10.1115/1.3662552
[7]	Sorenson H W. Least-square estimation: from Gauss to Kalman[J].IEEE Spectrum,1970,7(7):63-68.
[8]	Ljung L.System Identification—Theory for the User[M].2nd Ed.New Jersey:PTR Prentice Hall, 1999.
[9]	Haykin S.Kalman Filtering and Neural Networks[M].New York: John Wiley and Sons Inc,2001.
[10]	Sanjeev A, Simon M, Neil G,et al.A tutorial on particle filters for on-line no-linear/non-Gaussian Bayesian tracking[J].IEEE Trans on Signal Processing,2002,50(2):174-188. doi: 10.1109/78.978374
[11]	Julier S, Uhlmann J K. A new extension of the Kalman filter to nonlinear system[A].In: Proc of AeroSence:The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls[C].Orlando,Florida:SPIE，1997,182-193.
[12]	Parzen E. Some recent advances in time series modeling[J].IEEE Trans on Automatic Control,1974,19(6):723-730. doi: 10.1109/TAC.1974.1100733
[13]	Jong P, Penzer J. The ARMA model in state space form[J].Journal of Statistics & Probability Letters,2004,70(1):119-125.
[14]	Akaike H. A new look at the statistical model identification[J].IEEE Trans on Automatic Control,1974,19(6):716-723. doi: 10.1109/TAC.1974.1100705
[15]	Broersen P M T. Finite sample criteria for autoregressive order selection[J].IEEE Trans on Signal Processing,2000,48(12):3550-3558. doi: 10.1109/78.887047
[16]	康宜华, 何岭松, 杨叔子. ARMA谱的理论频率分辨力[J]. 华中理工大学学报,1995,23(6):101-104.
[17]	Gustaffasson F, Gunnarsson S, Ljung L. Shaping frequency-dependent time resolution when estimation spectral properties with parametric methods[J].IEEE Trans on Signal Processing,1997,45(4):160-163.
[18]	Dong Y F, Zhen N N, Lai M,et al.Estimation of instantaneous spectrum of earthquake ground motions using neural networks[A].In:Andcrson E DL Ed.Proc the 13th World Conference on Earthquake Engineering[C].Vancouver,Canada:Mira Digital Publishing,2004, PN1446.