35. Damage detection and identification of parameter matrices using residual force vector
Hee-Chang Eun1, Su-Yong Park2
Kangwon National University, Department of Architectural Engineering, Chuncheon, Korea
E-mail: firstname.lastname@example.org, email@example.com
(Received 20 January 2014; received in revised form 23 January 2014; accepted 26 January 2014)
Abstract. Beginning with incomplete mode shape measurement data, this study presents analytical equations to predict the actual stiffness and mass matrices. The measured modal data, including the measurement, manufacturing and modeling errors, should be updated for subsequent analysis. In this study, the incomplete mode shape data are expanded to a full set of degrees‑of‑freedom (DOFs) based on the generalized inverse method and the concept of residual force vector. The corrected parameter matrices are straightforwardly derived using the estimated mode shape data and the pseudo inverse method. The validity of the proposed method is evaluated based on the number of measured modes in an application, and its limitations are investigated.
Keywords: residual force vector, eigenvalue function, update, constraint, measurement, data expansion.
 Mottershead J. E., Stanway R. Identification of structural vibration parameters by using a frequency domain filter. Journal of Sound and Vibration, Vol. 109, Issue 3, 1986, p. 495‑506.
 Friswell M. I., Penny J. E. T. Updating model parameters from frequency domain data via reduced order models. Mechanical Systems and Signal Processing, Vol. 4, Issue 5, 1990, p. 377‑391.
 Lee U., Shin J. A frequency response function-based structural damage identification method. Computers and Structures, Vol. 80, Issue 2, 2002, p. 117‑132.
 Rahmatalla S., Eun H. C., Lee E. T. Damage detection from the variation of parameter matrices estimated by incomplete FRF data. Smart Structures and Systems, Vol. 9, 2012, p. 55‑70.
 O’Callahan J. A procedure for an improved reduced system (IRS) model. Proceedings of the 7th IMAC, Las Vegas, Nevada, USA, 1989, p. 17‑21.
 Kenneth F. A., Francois H. Dynamic mode shape expansion using mass orthogonality constraints. Proceedings of the 18th IMAC, Texas, USA, 2000, p. 1496‑1502.
 Ewins D. J. Adjustment or updating of models. Sâdhanâ, Vol. 25, 2000, p. 235‑245.
 Avitabile P., O’Callahan J. Dynamic expansion of FRFs for the full FRF matrix. Proceedings of the 19th IMAC, Orlando, Florida, USA, 2001.
 Avitabile P., O’Callahan J. Frequency response function expansion for unmeasured translation and rotation dofs for impedance modeling applications. Mechanical Systems and Signal Processing, Vol. 17, Issue 4, 2003, p. 723‑745.
 Yang Q. W., Liu J. K. Structural damage identification based on residual force vector. Journal of Sound and Vibration, Vol. 305, Issue 1‑2, 2007, p. 298‑307.
 Zhao J., Zhang L. A method for structural damage identification using residual force vector and mode shape expansion. International Conference on Multimedia Technology, Hangzhou, China, 2011, p. 945‑949.
 Yun G. J., Ogorzalek K. A., Dyke S. J., Song W. A parameter subset selection method using residual force vector for detecting multiple damage locations. Structural Control Health Monitoring, Vol. 17, Issue 1, 2010, p. 48‑67.
 Gafka G. K., Zimmerman D. C. Structural damage detection via least squares dynamic residual force minimization with quadratic measurement error inequality constraint. Proceedings of the 14th International Modal Analysis Conference, 1996, p. 1278‑1284.
 Friswell M. I., Mottershead J. E. Finite element model updating in structural dynamics. Solid Mechanics and its Applications, Kluwer Academic Publishers Group, 1995, p. 1‑286.
 Baruch M., Bar-Itzhack I. Y. Optimal weighted orthogonalization of measured modes. AIAA Journal, Vol. 17, Issue 8, 1979, p. 927‑928.
 Baruch M. Optimal correction of mass and stiffness matrices using measured modes. AIAA Journal, Vol. 20, Issue 11, 1982, p. 1623‑1626.
 Berman A. Mass matrix correction using an incomplete set of measured modes. AIAA Journal, Vol. 17, Issue 10, 1979, p. 1147‑1148.
 Berman A., Nagy E. J. Improvement of a large analytical model using test data. AIAA Journal, Vol. 21, Issue 8, 1983, p. 1168‑1173.
 Kabe A. M. Stiffness matrix adjustment using mode data. AIAA Journal, Vol. 23, Issue 9, 1985, p. 1431‑1436.
 Caeser B., Pete J. Direct update of dynamic mathematical models from modal test data. AIAA Journal, Vol. 25, Issue 11, 1987, p. 1494‑1499.
 Zimmerman D. C., Widengren M. Correcting finite element models using a symmetric eigenstructure assignment technique. AIAA Journal, Vol. 28, Issue 9, 1990, p. 1670‑1676.
 Wei F. S. Stiffness matrix correction from incomplete test data. AIAA Journal, Vol. 18, Issue 10, 1980, p. 1274‑1275.
 Wei F. S. Analytical dynamic model improvement using vibration test data. AIAA Journal, Vol. 28, Issue 1, 1990, p. 175‑177.
 Wei F. S. Mass and stiffness interaction effects in analytical model modification. AIAA Journal, Vol. 28, Issue 9, 1990, p. 1686‑1688.
 Lee E. T., Eun H. C. Update of corrected stiffness and mass matrices based on measured dynamic modal data. Applied Mathematical Modelling, Vol. 33, Issue 5, 2009, p. 2274‑2281.
 Lee E. T., Eun H. C. Correction of stiffness and mass matrices utilizing simulated measured modal data. Applied Mathematical Modelling, Vol. 33, Issue 6, 2009, p. 2723‑2729.
 Lee E. T., Rahmatalla S., Eun H. C. Estimation of parameter matrices based on measured data. Applied Mathematical Modelling, Vol. 35, Issue 10, 2011, p. 4816‑4823.
 Eun H. C., Lee E. T., Chung H. S. On the static analysis of constrained structural systems. Canadian Journal of Civil Engineering, Vol. 31, Issue 6, 2004, p. 1119‑1122.
Cite this article
Eun Hee-Chang, Park Su-Yong Damage detection and identification of parameter matrices using residual force vector. Journal of Measurements in Engineering, Vol. 2, Issue 1, 2014, p. 1‑7.
Journal of Measurements in
Engineering. March 2014, Volume 2, Issue 1