Topics in Modal Analysis, Volume 10

23 Towards an Automatic Modal Parameter Estimation Framework: Mode Clustering 259 Fig. 23.13 Relation between the expected value of modal contributions and MOC and the Shanon entropy of modal contributions for clusters for data with inconsistency between resonance frequencies -40 -20 0 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 m(MOC) Shanon Entropy(H¥) m(H¥) Acknowledgment The present study is made possible through the financial support of the Swedish Wind Power Technology Center (SWPTC). References 1. Reynders E, Houbrechts J, De Roeck G (2012) Fully automated (operational) modal analysis. Mech Syst Signal Process 29:228–250 2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723 3. Bauer D (2001) Order estimation for subspace methods. Automatica 37(10):1561–1573 4. Verboven P, Parloo E, Guillaume P, Van Overmeire M (2002) Autonomous structural health monitoring – part I: modal parameter estimation and tracking. Mech Syst Signal Process 16(4):637–657 5. Verboven P, Parloo E, Guillaume P, Van Overmeire M (2001) Autonomous modal parameter estimation based on a statistical frequency domain maximum likelihood approach. IMAC XIX, Orlando (FL), USA 6. Goethals I, De Moor B (2002) Model reduction and energy analysis as a tool to detect spurious modes. In: Conference proceedings of the 2002 international conference on noise and vibration engineering, ISMA, Leuven, Belgium, pp 1307–1314 7. Goethals I, Vanluyten B, De Moor B (2004) Reliable spurious mode rejection using self learning algorithms. In: Conference proceedings of the 2004 international conference on noise and vibration engineering, ISMA, Leuven, Belgium, pp 991–1003 8. Vanlanduit S, Verboven P, Guillaume P, Schoukens J (2003) An automatic frequency domain modal parameter estimation algorithm. J Sound Vib 265(3):647–661 9. Chhipwadia KS, Zimmerman DC, James Iii GH (1999) Evolving autonomous modal parameter estimation. In: Conference proceedings of IMAC XXVII, Orlando (FL), USA 10. Lim TW, Cabell RH, Silcox RJ (1996) On-line identification of modal parameters using artificial neural networks. J Vib Acoust Trans ASME 118(4):649–656 11. Magalhães F, Cunha Á, Caetano E (2009) Online automatic identification of the modal parameters of a long span arch bridge. Mech Syst Signal Process 23(2):316–329 12. Carden EP, Brownjohn JMW (2008) Fuzzy clustering of stability diagrams for vibration-based structural health monitoring. Comput-Aided Civ Infrastruct Eng 23(5):360–372 13. Glover K (1984) All optimal Hankel-norm approximations of linear multivariable systems and their L, 1-error bounds . Int J Control 39(6):1115–1193 14. Moore B (1981) Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans Autom Control 26(1):17–32 15. Vakilzadeh MK, Rahrovani S, Abrahamsson T (2013) Modal reduction based on accurate input-output relation preservation. IMAC XXXI, Garden Grove 16. Antoulas AC (2005) Approximation of large-scale dynamical systems. Society for Industrial and Applied Mathematics, Philadelphia 17. Yaghoubi V, Abrahamsson T (2013) The modal observability correlation as a modal correlation metric. In: Conference proceedings of IMAC XXXI, Los Angeles, CA, USA, vol 45, pp 487–494 18. Mckelvey T, Akçay H, Ljung L (1996) Subspace-based multivariable system identification from frequency response data. IEEE Trans Autom Control 41(7):960–979 19. Van Der Auweraer H, Leurs W, Mas P, Hermans L (2000) Modal parameter estimation from inconsistent data sets. IMAC XVIII, San Antonio, Texas, USA 20. Lohr S (2009) Sampling: design and analysis. Cengage Learning 21. Chauhan S, Tcherniak D (2009) Clustering approaches to automatic modal parameter estimation. IMAC XXVII, Orlando 22. Laub AJ (2005) Matrix analysis for scientists and engineers. Siam, Philadelphia 23. Cover TM, Thomas JA (2012) Elements of information theory. John Wiley & Sons, Hoboken

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