International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

P. Nandakumar and K. Shankar*

Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India


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ABSTRACT


A new system identification (SI) method based on Transfer Matrix (TM) concept is proposed here to identify structural stiffness. Transfer matrices based on lumped mass and the more accurate consistent mass models are used here, based on displacement measurements in the time domain. The consistent mass based TM is derived from the dynamic stiffness matrix of a beam element. The state vector at a location is the sum of the internal and external contributions of displacements, forces and moments at that point - when multiplied with the (TM), we obtain the adjacent state vectors. The method of identification proposed here involves predicting the displacements at certain locations using the TM, and comparing them with the measured displacements at those locations. The mean square deviations between the measured and predicted responses at all locations are minimized using an optimization algorithm, and the optimization variables are the unknown stiffness parameters in the TM. A non-classical heuristic Particle Swarm Optimization algorithm (PSO) is used, since it is especially suited for global search.  Different strategies for calculating the initial state vector, as well as two identification processes viz., simultaneous and successive methods, are discussed. Numerical simulations are carried out on four examples ranging from a simple spring mass system to a nine member framed structure. The speed and accuracy of identification using this method are good. One main advantage of this method is that it can be applied at any portion of the structure to identify the local parameters in that zone without the need to model the entire global structure.


Keywords: Structural identification; transfer matrix; simultaneous identification; successive ide- ntification; particle swarm optimization.


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REFERENCES


  1. [1] Aditya, G. and Chakraborty, S. 2008. Sensitivity Based Health Monitoring of Structures with Static Response. Scientia Iranica 15, 3: 267-274.

  2. [2] Hjelmstad, K. D. and Shin, S. 1997. Damage Detection and Assessment of Structures from Static response. Journal of Engineering Mechanics, 123, 6: 568-576.

  3. [3] Maia, N. M. M. and Silva, J. M. M. 2001. Modal Analysis Identification Techniques. Philosophical Transactions of the Royal Society, 359: 29-40.

  4. [4] Ma, G. and Eric, M. L. 2005. Structural damage identification using system dynamic properties. Computers and Structures, 83: 2185–2196.

  5. [5] Jinhee, L. Identification of multiple cracks in a beam using vibration amplitudes. Journal of Sound and Vibration, 326: 205-212.

  6. [6] Ghanem, R. and Shinozuka, M. 1995. Structural system identification I: Theory. Journal of Engineering Mechanics, 121, 2: 255-264.

  7. [7] Petsounis, K. A. and Fassois, S. D. 2001. Parameteric Time-Domain Methods for the Identification of Vibrating Structures-A Critical Comparison and Assessment. Mechanical System and Signal Processing, 15, 6: 1031-1060.

  8. [8] Caravani, P., Watson, M. L., and Thomson, W.T. 1977. Recursive Least square Time domain Identification of structural Parameters. Journal of Applied Mechanics, 44, 1: 135-140.

  9. [9] Masaru, H. and Etsuro, S. 1984. Structural Identification by Extended Kalman Filter. Journal of Engineering Mechanics, ASCE110, 12: 1757-1770.

  10. Shinozuka, M., Yun, C. B., and Imai, H.1982. Identification of Linear structural dynamic system. Journal of Engineering Mechanics, ASCE108, 6: 1371-1390.

  11. [11] Lus, H., Betti, R., and Longman, R. W. 1999. Identification of Linear Structural Systems Using Earth quake-induced Vibration Data. Earthquake Engineering and Structural Dynamics, 28: 1449-1467.

  12. [12] Angelis, M. De., Lus, , Betti.R., and Longman, R. W. 2002. Extracting Physical Parameters of Mechanical Models from Identified State-Space Representations. Journal of Applied Mechanics, 69: 617-625.

  13. [13] Kennedy, and Eberhart R. 1995. Particle swarm optimization. Presented in IEEE international conference on neural networks, (IV) Piscataway, NJ: 1942-1948.

  14. [14] Mouser, C. R. and Dunn, S. A., 2005. Comparing Genetic Algorithm and Particle Swarm Optimization for Inverse Problem. ANZIAM Journal, 46: 89-101.

  15. [15] Qie, H., Ling, W., and Bo. L., 2007. Parameter Estimation for Chaotic Systems by Particle Swarm Optimization. Chaos, Solitons and Fractals, 34: 654–661.

  16. [16] Perez, R. E. and Behdinan, K. 2007. Particle Swarm Approach for Structural Design Optimization. Computers and Structures, 85: 1579-1588.

  17. [17] Koh, G., Chen,Y.F. and Liaw, C. Y. 2003. A hybrid Computational Strategy for identification of Structural parameters. Computers and Structures, 81: 107-117.

  18. [18] Begambre, O. and Laier, J.E. 2009. A hybrid Particle Swarm Optimization-Simplex Algorithm (PSOS) for Structural damage Identification. Advances in Engineering Software, 40: 883-891.

  19. [19] Hesheng, T., Songtao., X., and Cunxin, F. 2008. Differential evolution Strategy for Structural System Identification. Computers and Structures, 86: 2004-2012.

  20. [20] Koh, G., Hong, B., and Liaw, C. Y. 2003. Substructural and Progressive structural Identification Methods. Engineering Structures, 25: 1551-1563.

  21. [21] Koh, C. G., Hong, B., and Liaw, C. Y. 2000. Parameter Identification of Large Structural Systems in Time Domain. Journal of Structural Engineering, 126, 8: 957-963.

  22. [22] Sandesh, S. and Shankar, K.2009. Damage Identification of a Thin Plate in the Time Domain with Substructuring-an Application of inverse Problem. International Journal of Applied Science and Engineering, 7: 79-93.

  23. [23] Tee, K. F., Koh, C. G., and Quek, S. T. 2009. Numerical and Experimental Studies of a Substructural Identification Strategy. Structural Health Monitoring, 8, 5: 397-414.

  24. [24] Steidel, R. F. 1978. “An Introduction to Mechanical Vibrations”. Second Ed., John Wiley and Sons, U.S.A.

  25. [25] Meirovitch, L. 2001. “Fundamentals of Vibrations”. First Ed., McGraw-Hill Book Company.

  26. [26] Nandakumar, P. and Shankar, K. 2011. Identification of Structural Parameters Using Transfer Matrix and State Vectors in Time Domain. Presented in the 5th International Conference on Advances in Mechanical Engineering, Surat, India, June 6th to June 8th , 2011.

  27. [27] Khiem, N.T. and Lien, T.V. 2001. A Simplified method for Natural Frequency Analysis of a Multiple cracked Beam. Journal of sound and vibration, 245, 4: 737-751.

  28. [28] Tuma, J. J. and Cheng, F.Y. 1982. “Theory and Problems of Dynamic structural analysis”. McGraw-Hill Book Company.

  29. [29] Walter, W. and Walter, D. P. 2003. “Mechanics of Structures Variational and Computational Methods”. 2nded, CRC Press.

  30. [30] Prashanth, P. and Shankar, K. 2008. A Hybrid Neural Network Strategy for the Identification of Structural Damage using Time Domain Responses. IES Journal Part A: Civil and Structural Engineering, 1, 4: 17-34.

  31. [31] Positioning strain gages to monitor bending, axial, shear and torsional available at: www.omega.com/faq/pressure/pdf/positioning.pdf


ARTICLE INFORMATION


Received: 2011-12-19
Revised: 2012-02-06
Accepted: 2012-02-08
Available Online: 2012-09-01


Cite this article:

Nandakumar, P., Shankar, K. 2012. Estimation of structural parameters using transfer matrices and state vectors. International Journal of Applied Science and Engineering, 10, 181–207. https://doi.org/10.6703/IJASE.2012.10(3).181


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