地震动瞬时谱估计的Unscented Kalman滤波方法
|
摘要
用时变ARMA模型描述地震动时程,提出了采用Unscented Kalman滤波技术实现地震动瞬时谱估计的思路.算例分析表明,Unscented Kalman滤波方法较Kalman滤波方法适用范围广,具有较高的时间和频率分辨率,能够更好地跟踪地震动的局部特性,适合处理非线性模型或有突变特性的模型的辨识问题.不同阶数ARMA模型的估计结果还表明,以往被忽略的ARMA模型的理论频率分辨力对地震动瞬时谱估计精度有重要影响,应作为一个参考指标在ARMA模型的判阶中加以考虑.
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.
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.
引文
[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 structuralproperties 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.
[4]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrumfor nonlinear and nonstationary time series analysis[J].Proc of the Royal Society of London,Ser A,1998,454(1971):903-995.
[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 Engi-neering,Transactions of the ASME,Ser D,1960,82(1):35-45.
[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-GaussianBayesian tracking[J].IEEE Trans on Signal Processing,2002,50(2):174-188.
[11]Julier S,Uhlmann J K.A new extension of the Kalman filter to nonlinear system[A].In:Proc ofAeroSence:The11th International Symposium on Aerospace/Defence Sensing,Simulation andControls[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.
[13]Jong P,Penzer J.The ARMA model in state space form[J].Journal of Statistics&Probability Let-ters,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.
[15]Broersen P M T.Finite sample criteria for autoregressive order selection[J].IEEE Trans on SignalProcessing,2000,48(12):3550-3558.
[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 estima-tion 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 mo-tions using neural networks[A].In:Andcrson E DL Ed.Proc the13th World Conference on Earth-quake Engineering[C].Vancouver,Canada:Mira Digital Publishing,2004,PN1446.
[2]Conte J P,Pister K S,Mahin S A.Influence of the earthquake ground motion process and structuralproperties 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.
[4]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrumfor nonlinear and nonstationary time series analysis[J].Proc of the Royal Society of London,Ser A,1998,454(1971):903-995.
[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 Engi-neering,Transactions of the ASME,Ser D,1960,82(1):35-45.
[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-GaussianBayesian tracking[J].IEEE Trans on Signal Processing,2002,50(2):174-188.
[11]Julier S,Uhlmann J K.A new extension of the Kalman filter to nonlinear system[A].In:Proc ofAeroSence:The11th International Symposium on Aerospace/Defence Sensing,Simulation andControls[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.
[13]Jong P,Penzer J.The ARMA model in state space form[J].Journal of Statistics&Probability Let-ters,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.
[15]Broersen P M T.Finite sample criteria for autoregressive order selection[J].IEEE Trans on SignalProcessing,2000,48(12):3550-3558.
[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 estima-tion 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 mo-tions using neural networks[A].In:Andcrson E DL Ed.Proc the13th World Conference on Earth-quake Engineering[C].Vancouver,Canada:Mira Digital Publishing,2004,PN1446.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心