Fast uncertainty computation for multi-order subspace-based method with QR decompositions
Email tác giả liên hệ:
binhlx@hcmute.edu.vnTừ khóa:
Stochastic Subspace Identification, Multi-order, QR Decomposition, Uncertainty Computation, Operational Modal AnalysisTóm tắt
In Operational Modal Analysis, the Stochastic Subspace Identification (SSI) does not yield the exact system matrices, hence there is uncertainty in the estimates of modal parameters (natural frequencies, damping ratios, mode shapes). From that, it is necessary to evaluate the uncertainty of modal parameters. Recently, a new algorithm (multi-order subspace-based method) for determining modal parameters obtained from SSI has been proposed using QR decomposition (QRD). This new multi-order SSI method will partition the up-shifting observability matrix into smaller matrices, then the new state transition matrix is identified by using these smaller matrices. The article will propose a new algorithm for computing the uncertainty on modal parameters obtained from this multi-order SSI (MOSSI) based on QR decomposition (QRD). The new uncertainty algorithm only computes uncertainty bounds at the highest model order and gives bounds at lower orders by mean of selection matrices.
Tải xuống: 0
Tài liệu tham khảo
D. Bauer and M. Jansson, Analysis of the asymtotic properties of the moesp type of subspace algorithms, Automatica. 36, pp. 497-509, 2000.
D. Bauer, M. Deistler, and W. Scherre, Consistency and asymtotic normality of some subspace algorithms without observed inputs, Automatica. 35, pp. 1243-1254, 2002.
W. E. Larimore, System identification, reduced order filters and modelling via canonical variate analysis, In the American Control Conference, pp. 445–451, 1983.
P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems: Theory, Implementation, Applications, Kluwer, 1996.
M. Deistler, K. Peternell, and W. Scherrer, Consistency and realtive efficiency of subspace methods, Automatica. 31, pp. 1865-1875,1995.
A. Chiuso and G. Picci, Asymptotic variance of subspace methods by data orthogonalization and model decoupling: A comparative analysis, Automatica. 40, pp. 1705-1717, 2004.
P. Van Overschee and B. De Moor, N4sid: Subspace algorithms for the identification of combined deterministic-stochastic systems, Automatica. 30, no. 1, pp. 75-93, 1994.
M. Verhaegen, Identification of the deterministic part of mimo state space models given in innovation forms from input-output data, Automatica. 30, pp. 61-74, 1994.
M. Viberg, Subspace-based methods for the identification of linear time-invariant systems, Automatica. 31, no. 12, pp. 1835-1851, 1995.
T. McKelvey, H. Akçay, and L. Ljung, Subspace-based multivariable system identification from frequency response data, IEEE Transactions on Automatic Control. 41, no. 7, pp. 960-979, 1996.
M. Dohler and L. Mevel, Fast multi-order stochastic subspace identification, In Proceedings of the 18th IFAC World Congress, pp. 6523 – 6528, Milan, Italy, 2011.
B. Peeters and G. De Roeck, Reference-based stochastic subspace identification for output-only modal analysis, Mechanical Systems and Signal Processing. 13, pp. 855–878, 1999.
E. Reynders, R. Pintelon and G. De Roeck, Uncertainty bounds on modal parameters obtained from stochastic subspace identification, Mechanical Systems and Signal Processing. 22, no. 4, pp. 948–969, 2008.
X.-B. Lam and L. Mevel, Uncertainty quantification for eigensystem-realization-algorithm, a class of subspace system identification, In Proceedings of the 18th IFAC World Congress, pp. 6529 – 6534, Milan, Italy, 2011.
R. Pintelon, P. Guillaume and J. Schoukens, Uncertainty calculation in (operational) modal analysis, Mechanical Systems and Signal Processing. 21, pp. 2359–2373, 2007.
X. Chang and C. Paige, Componentwise perturbation analyses for the QR factorization, Numerische Mathematik. 88, no. 2, pp. 319–345, 2001.
A. Benveniste and L. Mevel, Non-stationary consistency of subspace methods, IEEE Transactions on Automatic Control. AC-52, no. 6, pp. 974–984, 2007.
M. Dohler, X.-B. Lam and L. Mevel, Confidence intervals on modal parameters in stochastic subspace identification, In Proceedings of the 34th IABSE Symposium, 7 pages, Venice, Italy, 2010.
X. W. Chang, C. C. Paige and G. W. Stewart, Perturbation analyses for the QR factorization, SIAM Journal of Matrix Analysis and Applications. 18, pp. 775–791, 1997.
G. Golub and C. Van Loan, Matrix computations, Johns Hopkins: University Press, 3rd edition, 1996.
D. M. Siringoringo, T. Nagayama, Y. Fujino, D. Su and C. Tandian, Observed dynamic characteristics of an overpass bridge during a fullscale destructive testing, In The Fifth International Conference on Bridge Maintenance, Safety, Management and Life-Cycle Optimization, pp. 330, 2010.
W. Gersch, On the achievable accuracy of structural system parameter estimates, Journal of Sound and Vibration. 34, no. 1, pp. 63–79, 1974.
Tải xuống
Đã Xuất bản
Cách trích dẫn
Giấy phép
Tác phẩm này được cấp phép theo Giấy phép quốc tế Creative Commons Attribution-NonCommercial 4.0 .
Bản quyền thuộc về JTE.
