Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.

[1]  F. Javier Cara,et al.  An approach to operational modal analysis using the expectation maximization algorithm , 2012 .

[2]  Francisco Javier Cara Cañas,et al.  An approach to operational modal analysis using the expectation maximization algorithm , 2012 .

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

[4]  E. Parloo,et al.  AUTONOMOUS STRUCTURAL HEALTH MONITORING—PART I: MODAL PARAMETER ESTIMATION AND TRACKING , 2002 .

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

[6]  H. Akaike.  A new look at the statistical model identification , 1974 .

[7]  H. Van der Auweraer,et al.  Discriminating physical poles from mathematical poles in high order systems: use and automation of the stabilization diagram , 2004, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510).

[8]  Bart Peeters,et al.  System identification and damage detection in civil engineering , 2000 .

[9]  Geert Lombaert,et al.  An augmented Kalman filter for force identification in structural dynamics , 2012 .

[10]  Guido De Roeck,et al.  Finite element model updating and structural damage identification using OMAX data , 2010 .

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

[12]  Hilmi Luş,et al.  Ambient Vibration Analysis with Subspace Methods and Automated Mode Selection: Case Studies , 2008 .

[13]  Michel Verhaegen,et al.  Filtering and System Identification: Frontmatter , 2007 .

[14]  J. Juang.  Applied system identification , 1994 .

[15]  H. Akaike.  Stochastic theory of minimal realization , 1974 .

[16]  James Clary,et al.  Stochastic theory of minimal realization , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[17]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[18]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[19]  V. Verdult,et al.  Filtering and System Identification: A Least Squares Approach , 2007 .

[20]  Guido De Roeck,et al.  Fully automated (operational) modal analysis , 2012 .

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

[22]  Paul Reynolds,et al.  Modal Testing and Finite-Element Model Updating of a Lively Open-Plan Composite Building Floor , 2007 .

[23]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[24]  Edwin Reynders,et al.  System Identification Methods for (Operational) Modal Analysis: Review and Comparison , 2012 .

[25]  Guido De Roeck,et al.  The Local Flexibility method for Vibration-based damage localization and quantification , 2008 .

[26]  M. Scionti,et al.  Stabilisation diagrams: Pole identification using fuzzy clustering techniques , 2005, Adv. Eng. Softw..

[27]  A. Koehler,et al.  A Comparison of the Akaike and Schwarz Criteria for Selecting Model Order , 1988 .

[28]  E. Parloo,et al.  Force identification by means of in-operation modal models , 2002 .