Efficient uncertainty computation for modal parameters in stochastic subspace identification

Stochastic Subspace Identification methods have been extensively used for the modal analysis of mechanical, civil or aeronautical structures for the last ten years to estimate modal parameters. Recently an uncertainty computation scheme has been derived allowing the computation of uncertainty bounds for modal parameters. However, this scheme is numerically feasible only for quite low model orders, as the computations involve big matrix products that are memory and computationally taxing. In this paper, a fast computation scheme is presented that reduces the computational burden of the uncertainty computation scheme significantly. The fast computation is illustrated on the modal analysis of two bridges.

[1]  Rik Pintelon,et al.  Uncertainty calculation in (operational) modal analysis , 2007 .

[2]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[3]  Laurent Mevel,et al.  Convergence rates for eigenstructure identification using subspace methods , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[4]  Laurent Mevel,et al.  Confidence Intervals on Modal Parameters in Stochastic Subspace Identification , 2010 .

[5]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[6]  A. Chiuso,et al.  The asymptotic variance of subspace estimates , 2004 .

[7]  Gene H. Golub,et al.  Matrix computations , 1983 .

[8]  Rik Pintelon,et al.  Uncertainty bounds on modal parameters obtained from stochastic subspace identification , 2008 .

[9]  Laurent Mevel,et al.  Nonstationary Consistency of Subspace Methods , 2007, IEEE Transactions on Automatic Control.

[10]  L. Mevel,et al.  Fast multi-order computation of system matrices in subspace-based system identification ☆ , 2012 .

[11]  Laurent Mevel,et al.  Robust Subspace Based Fault Detection , 2011 .

[12]  Laurent Mevel,et al.  Efficient Multi-Order Uncertainty Computation for Stochastic Subspace Identification , 2013 .

[13]  Laurent Mevel,et al.  Modular Subspace-Based System Identification From Multi-Setup Measurements , 2012, IEEE Transactions on Automatic Control.

[14]  G. De Roeck,et al.  DESCRIPTION OF Z24 BENCHMARK , 2003 .

[15]  Guido De Roeck,et al.  REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS , 1999 .

[16]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[17]  Laurent Mevel,et al.  Uncertainty quantification for stochastic subspace identification on multi-setup measurements , 2011, IEEE Conference on Decision and Control and European Control Conference.

[18]  W. Gersch.  On the achievable accuracy of structural system parameter estimates , 1974 .

[19]  Maurice Goursat,et al.  Output-Only Subspace-Based Structural Identification: From Theory to Industrial Testing Practice , 2001 .

[20]  A. Benveniste,et al.  Single sample modal identification of a nonstationary stochastic process , 1985, IEEE Transactions on Automatic Control.