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Modal identification of system driven by Lévy random excitation based on continuous time AR model. (English) Zbl 1253.93132

Summary: Based on the continuous time AR model, this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated Lévy random excitation. The structural dynamic equation is first transformed into the observation equation and the state equation (namely, stochastic differential equation). Based on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Then by virtue of the Girsanov theorem, we present the exact maximum likelihood estimators of parameters. Finally, the modal parameters are identified by eigenanalysis. Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.

MSC:

93E12 Identification in stochastic control theory
60G51 Processes with independent increments; Lévy processes
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[1] Arunasis C, Biswajit B, Mira M. Identification of modal parameters of a mdof system by modified L-P wavelet packets. J Sound Vib, 2006, 295(3–5): 827–837 · doi:10.1016/j.jsv.2006.01.037
[2] Yang J N, Lei Y, Pan S W, et al. System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: Normal modes. Earthq Eng Struct Dynam, 2003, 32(9): 1443–1467 · doi:10.1002/eqe.287
[3] Chen J Y, Wang J Y, Lin G. A structural parameter identification method without input information. Eng Mech, 2006, 23(1): 6–10
[4] Poulimenos A G, Fassois S D. Parametric time-domain methods for non-stationary random vibration modeling and analysis: A critical survey and comparison. Mech Syst Signal Pr, 2006, 20(4): 763–816 · doi:10.1016/j.ymssp.2005.10.003
[5] Howard F, Torsten S, Magnus M, et al. Estimation of continuous-time AR process parameters from discrete-time data. IEEE T Signal Pr, 1999, 47(5): 1232–1244 · Zbl 0967.62064 · doi:10.1109/78.757211
[6] Eric K L, Torsten S. Identification of continuous-time AR processes from unevenly sampled data. Automatica, 2002, 38(4): 709–718 · Zbl 1004.93013 · doi:10.1016/S0005-1098(01)00244-8
[7] Brockwell P J. Lévy-driven CARMA processes. Ann Inst Statist Math, 2001, 52(1): 1–18
[8] Tina M, Robert S. Multivariate CARMA processes. Stoch Proc Appl, 2007, 117(1): 96–120 · Zbl 1115.62087 · doi:10.1016/j.spa.2006.05.014
[9] Brockwell P, Davis R A, Yu Y. Continuous-time aaussian autoregression. Stat Sinica, 2007, 17(1): 63–80 · Zbl 1145.62070
[10] David A. Lévy Process and Stochastic Calculus. Cambridge: Cambridge University Press, 2004
[11] Jean J, Albert N. Limit Theorems for Stochastic Processes. Berlin: Springer-Verlag, 1980 · Zbl 0635.60021
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