Abstract
This chapter is focused on the methods for modal parameter estimation from previously acquired and pretreated time histories of the structural response to ambient vibrations. The fundamental assumptions of OMA methods and the basic concepts of structural dynamics models in time and frequency domain are illustrated, pointing out the common mathematical background behind different and apparently unrelated procedures. Then, criteria for the classification of OMA methods are summarized and fundamental theoretical aspects of well-established and popular OMA techniques are illustrated, providing relevant details for their software implementation. Finally, additional aspects concerning post-processing of modal parameter estimates, validation of layout and modal identification results, and correlation with numerical models are discussed. The ultimate objective of this chapter is to provide the reader all relevant information for implementation and practical application of a number of OMA methods and post-processing tools for validation and correlation. In this sense the implementation details and the basic software provided with the book are intended to fit the needs of both the modal analysts on one hand and undergraduate/graduate students, researchers, and developers on the other. The latter, in fact, are usually interested in writing their own code for further developments or business opportunities, and the accompanying software serves as a reference. On the other hand, modal analysts can find here the tools and the fundamental information to promptly start the modal tests and properly interpret the results. Using the basic software accompanying the book they can take confidence with different OMA procedures and choose their favorite ones. Thus, the chapter can be also intended as a guide supporting the choice among the different commercial software packages available on the market and relying on different OMA methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allemang RJ, Brown DL (1982) A correlation coefficient for modal vector analysis. In: Proc 1st international modal analysis conference, November 8–10, 1982, Orlando, FL
Allemang RJ, Brown DL (1998) A unified matrix polynomial approach to modal identification. J Sound Vib 211(3):301–322
Andersen P (1997) Identification of civil engineering structures using vector ARMA models, Ph.D. thesis. University of Aalborg, Aalborg
Andersen P, Brincker R (1999) Estimation of modal parameters and their uncertainties. In: Proc XVII international modal analysis conference, February 8–11, 1999, Kissimmee, FL
Andersen P, Brincker R, Kirkegaard PH (1996) Theory of covariance equivalent ARMAV models of civil engineering structures. In: Proc XIV international modal analysis conference, February 12–15, 1996, Dearborn, MI
Ans B, Hérault J, Jutten C (1985) Adaptive neural architectures: detection of primitives. In: Proc COGNITIVA’85, June 4–7, 1985, Paris
Aoki M (1987) State space modeling of time series. Springer, Berlin
Asmussen JC, Brincker R, Ibrahim SR (1999) Statistical theory of the vector random decrement technique. J Sound Vib 226(2):329–344
Bartlett MS (1946) The theoretical specification and sampling properties of autocorrelated time-series. J R Stat Soc 8(1):27–41, Supplement
Belouchrani A, Abed-Meraim K, Cardoso JF, Moulines E (1997) A blind source separation technique using second-order statistics. IEEE Trans Signal Process 45:434–444
Bendat JS, Piersol AG (2000) Random data: analysis and measurement procedures, 3rd edn. Wiley, New York, NY
Brincker R, Andersen P (1999) ARMA models in modal space. In: Proc XVII international modal analysis conference, February 8–11, 1999, Kissimmee, FL
Brincker R, Andersen P (1999) Ambient response modal analysis for large structures. In: Proc 6th Int Congr on Sound and Vib, July 5–8, 1999, Copenhagen
Brincker R, Zhang L (2009) Frequency domain decomposition revisited. In: Proc 3rd international operational modal analysis conference, May 4–6, 2009, Portonovo
Brincker R, Krenk S, Kirkegaard PH, Rytter A (1992) Identification of dynamical properties from correlation function estimates. Bygningsstatiske Meddelelser 63(1):1–38
Brincker R, Zhang L, Andersen P (2001) Modal identification of output-only systems using frequency domain decomposition. Smart Mat Struct 10:441–445
Cardoso JF, Souloumiac A (1996) Jacobi angles for simultaneous diagonalization. SIAM J Matrix Anal Appl 17:161–164
Cauberghe B (2004) Applied frequency-domain system identification in the field of experimental and operational modal analysis, Ph.D. thesis. Vrije Universiteit Brussels, Brussels
Cauberghe B, Guillaume P, Verboven P, Vanlanduit S, Parloo E (2005) On the influence of the parameter constraint on the stability of the poles and the discrimination capabilities of the stabilisation diagrams. Mech Syst Signal Process 19:989–1014
Chelidze D, Zhou W (2006) Smooth orthogonal decomposition-based vibration mode identification. J Sound Vib 292:461–473
Chopra AK (2000) Dynamics of structures – theory and applications to earthquake engineering, 2nd edn. Prentice Hall, Upper Saddle River, NJ
Cole HA (1968) On-the-line analysis of random vibrations. In: Proc AIAA/ASME 9th structures, structural dynamics and materials Conf, April 1–3, 1968, Palm Springs, CA
Cole HA (1973) On-line failure detection and damping measurement of aerospace structures by random decrement signatures. NASA contractor report CR22-05
Comon P (1994) Independent component analysis, a new concept? Signal Process 36:287–314
De Troyer T, Guillaume P, Steenackers G (2009a) Fast variance calculation of polyreference least-squares frequency-domain estimates. Mech Syst Signal Process 23:1423–1433
De Troyer T, Guillaume P, Pintelon R, Vanlanduit S (2009b) Fast calculation of confidence intervals on parameter estimates of least-squares frequency-domain estimators. Mech Syst Signal Process 23:261–273
Devriendt C, Guillaume P (2007) The use of transmissibility measurements in output-only modal analysis. Mech Syst Signal Process 21(7):2689–2696
Devriendt C, Guillaume P (2008) Identification of modal parameters from transmissibility measurements. J Sound Vib 314:343–356
Devriendt C, De Sitter G, Vanlanduit S, Guillaume P (2009) Operational modal analysis in the presence of harmonic excitations by the use of transmissibility measurements. Mech Syst Signal Process 23:621–635
Devriendt C, Steenackers G, De Sitter G, Guillaume P (2010) From operating deflection shapes towards mode shapes using transmissibility measurements. Mech Syst Signal Process 24:665–677
Even J, Moisan E (2005) Blind source separation using order statistics. Signal Process 85:1744–1758
Ewins DJ (2000) Modal testing: theory, practice and application, 2nd edn. Research Studies Press Ltd., Baldock
Feeny BF, Kappagantu R (1998) On the physical interpretation of proper orthogonal modes in vibrations. J Sound Vib 211:607–616
Felber AJ (1993) Development of a hybrid bridge evaluation system, Ph.D. thesis. University of British Columbia, Vancouver
Franklin GF, Powell JD, Workman ML (2006) Digital control of dynamic systems, 3rd edn. Ellis-Kagle Press, Half Moon Bay, CA
Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht
Gade S, Møller NB, Herlufsen H, Konstantin-Hansen H (2005) Frequency domain techniques for operational modal analysis. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD
Gouttebroze S, Lardies J (2001) On using the wavelet transform in modal analysis. Mech Res Comm 28(5):561–569
Han J-G, Ren W-X, Xu X-X (2005) Wavelet-based modal parameter identification through operational measurements. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Hanson D, Randall RB, Antoni J, Thompson DJ, Waters TP, Ford RAJ (2007) Cyclostationarity and the cepstrum for operational modal analysis of mimo systems – Part I: modal parameter identification. Mech Syst Signal Process 21(6):2441–2458
Herlufsen H, Andersen P, Gade S, Møller N (2005) Identification techniques for operational modal analysis – an overview and practical experiences. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Hermans L, Van Der Auweraer H (1999) Modal testing and analysis of structures under operational conditions: industrial applications. Mech Syst Signal Process 13(2):193–216
Heylen W, Lammens S, Sas P (1998) Modal analysis theory and testing. Katholieke Universiteit Leuven, Leuven
Ho BL, Kalman RE (1966) Effective construction of linear state-variable models from input/output data. Regelungstechnik 14:545–548
Hunt DL (1992) Application of an enhanced coordinate modal assurance criterion (ECOMAC). In: Proc 10th international modal analysis conference, February 3–7, 1992, San Diego, CA
Ibrahim SR (1977) Random decrement technique for modal identification of structures. J Spacecraft Rockets 14(11):696–700
Ibrahim SR, Mikulcik EC (1977) A method for direct identification of vibration parameters from the free response. Shock Vib Bul 47:183–198
Ibrahim SR, Brincker R, Asmussen JC (1996) Modal parameter identification from responses of general unknown random inputs. In: Proc 14th international modal analysis conference, February 12–15, 1996, Dearborn, MI
Jacobsen N-J, Andersen P, Brincker R (2008) Applications of frequency domain curve-fitting in the EFDD technique. In: Proc 26th international modal analysis conference, February 4–7, 2008, Orlando, FL
James GH, Carne TG, Lauffer JP, Nord AR (1992) Modal testing using natural excitation. In: Proc 10th international modal analysis conference, February 3–7, 1992, San Diego, CA
James GH, Carne TG, Lauffer JP (1995) The natural excitation technique (next) for modal parameter extraction from operating structures. J Anal Exp Modal Anal 10(4):260–277
Juang J-N (1994) Applied system identification. PTR Prentice Hall, Englewood Cliffs, NJ
Juang J-N, Pappa RS (1985) An eigensystem realization algorithm for modal parameter identification and model reduction. AIAA J Guid Contr Dynam 8:620–627
Kailath T (1980) Linear systems. Prentice Hall, Englewood Cliffs, NJ
Katayama T (2005) Subspace methods for system identification. Springer, London
Kerschen G, Golinval JC (2002) Physical interpretation of the proper orthogonal modes using the singular value decomposition. J Sound Vib 249:849–865
Kerschen G, Golinval JC, Vakakis AF, Bergman LA (2005) The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview. Nonlin Dynam 41:147–170
Kerschen G, Poncelet F, Golinval JC (2007) Physical interpretation of independent component analysis in structural dynamics. Mech Syst Signal Process 21:1561–1575
Lardies J, Gouttebroze S (2002) Identification of modal parameters using the wavelet transform. Int J Mech Sci 44:2263–2283
Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice Hall, Upper Saddle River, NJ
Magalhaes F, Cunha A (2011) Explaining operational modal analysis with data from an arch bridge. Mech Syst Signal Process 25:1431–1450
Maia NMM, Silva JMM, He J, Lieven NAJ, Lin RM, Skingle GW, To W-M, Urgueira APV (1997) Theoretical and experimental modal analysis. Research Studies Press, Taunton
McNeill SI, Zimmerman DC (2008) A framework for blind modal identification using joint approximate diagonalization. Mech Syst Signal Process 22:1526–1548
Mohanty P (2005) Operational modal analysis in the presence of harmonic excitations, Ph.D. thesis. Technische Universiteit Delft, Delft
Mottershead JE, Link M, Friswell MI (2011) The sensitivity method in finite element model updating: a tutorial. Mech Syst Signal Process 25(7):2275–2296
Olsen P, Brincker R (2013) Using random response input in Ibrahim Time Domain. In: Proc XXXI International Modal Analysis Conference, February 11–14, 2013, Garden Grove, CA
Pandit SM (1991) Modal and spectrum analysis: data dependent systems in state space. Wiley, New York, NY
Pandit SM, Wu SM (1983) Time series and system analysis with applications. Wiley, New York, NY
Pappa RS, Elliott KB, Schenk A (1992) A consistent mode indicator for the eigensystem realization algorithm. NASA Report TM-107607
Peeters B (2000) System identification and damage detection in civil engineering, Ph.D. thesis. Katholieke Universiteit Leuven, Leuven
Peeters B, De Roeck G (1999) Reference-based stochastic subspace identification for output-only modal analysis. Mech Syst Signal Process 13(6):855–878
Peeters B, Van der Auweraer H (2005) PolyMAX: a revolution in operational modal analysis. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Pintelon R, Guillaume P, Rolain Y, Schoukens J, Van Hamme H (1994) Parametric identification of transfer functions in the frequency domain – a survey. IEEE Trans Automat Contr 39(11):2245–2260
Pintelon R, Guillaume P, Schoukens J (2007) Uncertainty calculation in (operational) modal analysis. Mech Syst Signal Process 21:2359–2373
Poncelet F, Golinval JC, Kerschen G, Verhelst D (2007) Output-only modal analysis using blind source separation techniques. Mech Syst Signal Process 21:2335–2358
Rainieri C, Fabbrocino G, Cosenza E (2010) Some remarks on experimental estimation of damping for seismic design of civil constructions. Shock Vib 17:383–395
Reynders E (2009) System identification and modal analysis in structural mechanics, Ph.D. thesis. Katholieke Universiteit Leuven, Leuven
Reynders E, Houbrechts J, De Roeck G (2012) Fully automated (operational) modal analysis. Mech Syst Signal Process 29:228–250
Reynders E, Pintelon R, De Roeck G (2008) Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mech Syst Signal Process 22:948–969
Richardson M, Schwarz B (2003) Modal parameter estimation from operating data. Sound Vib 302:1–8
Rodrigues J, Brincker R, Andersen P (2004) Improvement of frequency domain output-only modal identification from the application of the random decrement technique. In: Proc XXII international modal analysis conference, January 26–29, 2004, Dearborn, MI
Ruzzene M, Fasana A, Garibaldi L, Piombo B (1997) Natural frequencies and dampings identification using wavelet transform: application to real data. Mech Syst Signal Process 11(2):207–218
Schoukens J, Pintelon R (1991) Identification of linear systems: a practical guide to accurate modeling. Pergamon Press, London
Shih CY, Tsuei YG, Allemang RJ, Brown DL (1988) Complex mode indication function and its applications to spatial domain parameter estimation. Mech Syst Signal Process 2(4):367–377
Srikantha Phani A, Woodhouse J (2007) Viscous damping identification in linear vibration. J Sound Vib 303:475–500
Tamura Y, Suganuma S-Y (1996) Evaluation of amplitude-dependent damping and natural frequency of buildings during strong winds. J Wind Eng Ind Aerodyn 59:115–130
Tong L, Liu RW, Soon VC, Huang YF (1991) Indeterminacy and identifiability of blind identification. IEEE Trans Circ Syst 38:499–509
Van Overschee P, De Moor B (1993) Subspace algorithm for the stochastic identification problem. Automatica 29(3):649–660
Van Overschee P, De Moor B (1996) Subspace identification for linear systems: theory - implementation – applications. Kluwer Academic Publishers, Dordrecht
Vandiver JK, Dunwoody AB, Campbell RB, Cook MF (1982) A mathematical basis for the random decrement vibration signature analysis technique. J Mech Des 104(2):307–313
Verboven P (2002) Frequency-domain system identification for modal analysis, Ph.D. thesis. Vrije Universiteit Brussels, Brussels
Verboven P, Guillaume P, Cauberghe B, Vanlanduit S, Parloo E (2005) A comparison of frequency-domain transfer function model estimator formulations for structural dynamics modeling. J Sound Vib 279(3–5):775–798
Vold H, Kundrat J, Rocklin T, Russell R (1982) A multi-input modal estimation algorithm for mini-computers. SAE Trans 91(1):815–821
Waters TP (1995). Finite element model updating using measured frequency response functions, Ph.D. thesis. University of Bristol, Bristol
Yi J-H, Yun C-B (2004) Comparative study on modal identification methods using output-only information. Struct Eng Mech 17(3–4):445–466
Zhang L, Wang T, Tamura Y (2005) A frequency-spatial domain decomposition (FSDD) technique for operational modal analysis. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Zhang L, Brincker R, Andersen P (2005) An overview of operational modal analysis: major development and issues. In: Proc 1st international operational modal analysis conference, April 26–27, 2005, Copenhagen
Zhou W, Chelidze D (2007) Blind source separation based vibration mode identification. Mech Syst Signal Process 21:3072–3087
Author information
Authors and Affiliations
4.1 Electronic Supplementary Material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rainieri, C., Fabbrocino, G. (2014). Output-only Modal Identification. In: Operational Modal Analysis of Civil Engineering Structures. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0767-0_4
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0767-0_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0766-3
Online ISBN: 978-1-4939-0767-0
eBook Packages: EngineeringEngineering (R0)