Detection and Determination of Damage in RC Frames Using Signal Processing

A Thesis Submitted in Partial Fulfillment of the Requirement for the Degree of Master of Science in Civil Engineering

By:Amir Ezzodin

Supervisors:  Dr. Hosein Naderpour    Prof. Ali Kheyroddin

Advisor:  Prof. Gholamreza Ghodrati Amiri

January 2015


In recent years, the damage detection and structural health monitoring to reduce maintenance costs and improve the safety and reliability of structures is regarded. Structural health monitoring and damage detection is the ability to show the performance of structure and identify and assess any damage in the structure at early stages. Recent developments in the field of sensors and other electronic technologies, makes the non-destructive methods effective, easy and advantageous procedure for damage detection. These methods are usually based on collecting information which is obtained from the structural behavior that identified any change in the structural response as a result of changes in environmental conditions (eg. changes in temperature, displacement, velocity, acceleration, strain, tension, curvature, etc.). Signal based dynamic methods assessed the changes in the characteristics of time-series measured from the structure obtained using signal processing. In other words, the purpose of signal processing is to survey the changes in properties not obtained directly from the time-history and corresponding spectrum. The main objective of this dissertation is evaluation of the methods and the algorithms corresponding to damage detection and structural health monitoring. Then using transformation functions and signal processing method, a model-free output-only procedure is investigated in which with details function of structural responses derived from wavelet decomposition, the structural damage can be evaluated. For this reason, first the RC frame was modeled in OpenSees and a nonlinear time-history finite element analysis was performed and acceleration and displacement time history response was derived. Then applying Wavelet and Fourier transform and the time and location of damage in RC frame could be identified.

Keywords: Damage Detection; RC Frame; Transformation Function; Finite Element Method.



A. Bagheri, G. Ghodrati Amiri and M. Khorasani, "Structural damage identification of plates based on modal data using 2D discrete wavelet transform," Structural Engineering and Mechanics, vol. 40, no. 1, pp. 13-28, 2010.

A. Bagheri, G. Ghodrati Amiri and S. Seyed Razzaghi, "Vibration-based damage identification of plate structures via curvelet transform," Journal of Sound and vibration, vol. 327, no. 3, pp. 593-603, 2009.

A. Dixit and S. Hanagud, "Single beam analysis of damaged beams verified using a strain energy based damage measure," Journal of Solids and Structures, vol. 48, pp. 592-602, 2011.

A. Kheyroddin, H. Naderpour, G. Ghodrati Amiri, S.R. Hoseini Vaez, Influence of carbon fiber reinforced polymers on upgrading shear behavior of RC coupling beams, Iran. J. Sci. Technol. Trans. B Eng. 35 (2011).

A. Kheyroddin, H. Naderpour, Nonlinear finite element analysis of composite RC shear walls, Iran. J. Sci. Technol. Trans. B Eng. 32 (2008).

A. Kheyroddin, H. Naderpour, S.R. Hoseini Vaez, Numerical evaluation of nonlinear response of reinforced concrete shear walls strengthened with CFRP WRAP, in: Proceedings, Annu. Conf. - Can. Soc. Civ. Eng., 2008.

A. Kheyroddin, S.R. Hoseini Vaez, H. Naderpour, Numerical analysis of slab-column connections strengthened with carbon fiber reinforced polymers, J. Appl. Sci. 8 (2008).

A. Kheyroddin, S.R. Hoseini Vaez, H. Naderpour, The effect of applying eccentric load on a finite element model for slab-column connections, in: Proceedings, Annu. Conf. - Can. Soc. Civ. Eng., 2008.

A. Kiremidjian, H. Sohn, M. Dzwonezyk, E.G.Straser, K. Law and T. Meng, "Adaptive Modeling of Enviromental Effects in Modal Paraments for Damage Detection in Civil Structures," DepartmentofCivilandEnvironmental Engineering, Stanford University, Stanford, CA 94305-4020, 1998.

A. Ovanesova and L. Suarez, "Applications of wavelet transforms to damage detection in frame structures," Engineering structures, vol. 26, no. 1, pp. 39-49, 2004.

A. Pandey and M. Biswas, "Damage Detection in Structures Using Changes in Flexibility," Journal of Sound and Vibration, vol. 169, no. 1, pp. 3-17, 1994.

A. Pandey, M. Biswas and M. Samman, "Damage Detection from Changes in Curvature Mode Shapes," Journal of Sound and Vibration, vol. 145, pp. 321-332, 1991.

A. Patjawit and W. Kanok-Nukulchai, "Health monitoring of highway bridges based on a global flexibility index," Journal of Engineering Structures, vol. 27, no. 9, p. 1385–1391, 2005.

A. Rahai, Bakhtiari-Nejad and A. Esfandiari, "Damage assessment of structure using incomplete measured mode shapes," Damage assessment of structure using incomplete measured mode shapes, vol. 14, no. 5, pp. 808-829, 2007.

A. Rasouli, G. Ghodrati Amiri, A. Kheyroddin, M. Ghafory-Ashtiany and S. S. Kourehli, "A new method for damage prognosis based on incomplete modal data via an evolutionary algorithm," European Journal of Environmental and Civil Engineering, vol. 18, no. 3, pp. 253-270, 2014.

A. Rytter, "Vibration Based inspection of civil engineering structures," Ph.d. Dissertation, Department of building Technology and structural engineering, Aalborg university, Denmark, 1993.

A. Sharifi and M. Banan, "Energy index method : Technique for identification of structural damage," Journal of Structural Engineering, ASCE, vol. 134, no. 6, pp. 1061-1064, 2008.

B. Weber, P. Paultre and J. Proulx, "Structural damage detection using nonlinear parameter identification with Tikhonov regularization," Structural Control and Health Monitoring, vol. 14, pp. 406-427, 2007.

Bruel and kjaer, Structural Testing- part2 : Modal Analysis and Simulation, Naerum,Denmark, Naerum,Denmark, 1988.

C. Borges, H. Barbosa and A. Lemonge, "A Structural Damage Identification Method Based on Genetic Algorithm and Vibration Data," Int. J. Numer. Meth. Engng, vol. 69, pp. 2663-86, 2007.

C. Burrus, R. Gopinath and H. Guo, Introduction to Wavelets and Wavelet Transforms, Upper Saddle River, New Jersey: Prentice Hall, 1998.

C. Chui, An Introduction to Wavelets, San Diego, CA: Academic Press, 1992.

C. Farrar, S. W. Doebling and D. A. Nix, "Vibration–based structural damage identification," Philosophical Transactions of Royal Society of London Series A:Mathematical , Physical and Engineering Science, vol. 359, no. 1778, pp. 131-149, 2001.

C. Fox, "The Location of Defects in Structures: A Comparison of the Use of Natural Frequency and Mode Shape Data," in The 10th International Model Analysis Conference, 1992.

C. Fox, "The location of defects in structures: A comparison of the use of natural frequency and mode shape data," in The 10 th International Modal Analysis Conference, 522-528, 1992.

C. Hu and M. Afzal, "A Statistical Algorithm for Comparing Mode Shape of Vibration Testing Before and After Damage in Timber," Journal of Wood Science, vol. 52, pp. 429-437, 2006.

C. Li and W. Smith, "A Hybrid Approach for Damage Detection in Flexiblle Structures," in The 35 th AIAA/ASME/ASCE/AHS/ASC Structure,Structional Dynamits and Materials Conference, 1994.

C. Li and W. Smith, "Hybrid approach for damage detection in flexible structures," Journal of Guidance, Control, and Dynamics, vol. 18, no. 3, pp. 419-425, 1995.

C. Modena, D. Sonda and D. Zonta, "Damage Localization in Reinforced Concrete Structures by Using . Damping Measurements. In Damage Assessment of Structures," in The International Conference on Damage Assessment of Structures (DAMAS99), Dublin,Ireland, 1999.

C. Papadimitriou, M. Levine-West and M. Milman, "Structural damage detection using modal test data," in Structural Health Monitoring Current Status and Perspectives, Palo Alto, California, Stanford University, 1997, pp. 678-689.

C. Ratcliffe, "Damage detection using a modified laplacian operator on mode shape data," Journal of Sound and Vibration, vol. 204, no. 3, pp. 505-517, 1997.

C. S. Hamey, W. Lestari, P. Qiao and Q. Song, "Experimental Damage Identification of Carbon/Epoxy Composite Beams Using Curvature Mode Shapes," Structural Health Monitoring, vol. 3, no. 4, pp. 333-353, 2004.

C. Tubb and E. Omerdic, "Fault Detection and Handling," Mechatronics Research Centre, University of Wales College, Newport, 2001.

C. Zang and M. Imergun, "Structural Damage Detection Using Artifical Neural Networks and Measured Frf Data Reduced Via Principal Component Projection," Journal of Sound and Vibration, vol. 242, no. 5, pp. 813-827, 2001.

D. Bernal and B. Gunes, "A Flexibility Based Approach for Damage Charactrization:A Benchmark Application," Journal of Engineering Mechanics , ASCE, vol. 130, no. 1, pp. 61-70, 2004.

D. Ewins, Modal Testing: Theory and Practice (Engineering Dynamics), United Kingdom: Research Studies Press Ltd, 1984.

D. Kammer, "Optimal Approximation for Residual Stiffness in Linear System Identification," AIAA Journal, vol. 26, no. 1, pp. 104-112, 1988.

D. Newland, An Introduction to Random Vibration, Spectral & Wavelet Analysis, Mineola, NY: Dover Publication, Inc, 1993.

D. Zimmerman and M. Kaouk, "Eigenstructure Assignment Approach for Stractional Demage Detection," AIAA Journal, vol. 30, no. 7, pp. 1848-1855, 1992.

D. Zimmerman, T. Simmermacbcr and M. Kaouk, "Modal Correlation and System Health Monitoring Using Frequency Domain MeasurementsStructural Health monitoring," Structural Health monitoring, vol. 4, pp. 213-227, 2005.

F. Asma, "Incremental Strategy for Damage Detection in Structures," Journal of MECHANTCA, vol. 73, no. 5, 2008.

F. C. Choi, J. Li, B. Samali and K. Crews, "An experimental study on damage detection of structures using a timber beam," Journal of Mechanical Science and Technology, vol. 21, no. 6, pp. 903-907, 2007.

F. Choi, "Assessment of the Structural Integrity of Timber Bridge Using Dynamic Approach," Faculty of Engineering, University of Thecnology,Sydney, 2007.

F. McKenna, G. L. Fenves, M. H. Scott and B. and Jeremic, "Open System for Earthquake Engineering Simulation – OpenSees," 2000. [Online]. Available:

G. Cardinale and M. Orlando, "Structural evaluation and strengthening of a reinforced concrete bridge," Journal of Bridge Engineering ,ASCE, vol. 9, no. 1, pp. 35-42, 2004.

G. Ghodrati Amiri, A. Bagheri, S. Seyed Razzaghi and A. Asadi, "Structural damage detection in plates using wavelet transform," 2009.

G. Hearn and R. Testa, "Modal Analysis for Damage Detection in Structures," Journal of Structural Engineering, vol. 117, no. 10, pp. 3042-3063, 1991.

G. Yen and K. Lin, "Wavelet packet feature extraction for vibration monitoring," Industrial Electronics, IEEE Transactions on, vol. 47, no. 3, pp. 650-667, 2000.

G.G. Amiri, H. Naderpour, S.R.H. Vaez, Numerical evaluation of base-isolated structures with optimized distribution of LRB and FPS isolators, in: 9th US Natl. 10th Can. Conf. Earthq. Eng. 2010, Incl. Pap. from 4th Int. Tsunami Symp., 2010.

H. Abdul Razak and F. Choi, "The effect of corrosion on the natural frequency and modal damping of reinforced concrete beams," Journal of Engineering Structures, vol. 23, no. 9, pp. 1126-1133, 2001.

H. Chen, Y. Yan and J. Jiang, "Vibration-based damage detection in composite wingbox structures by HHT," Mechanical Systems and Signal Processing, vol. 21, no. 1, pp. 307-321, 2007.

H. Esmaeili, A. Kheyroddin, H. Naderpour, Seismic behavior of steel moment resisting frames associated with RC shear walls, Iran. J. Sci. Technol. - Trans. Civ. Eng. 37 (2013).

H. Kim and T. Bartkowicz, "Damage Detection and Health Mealth Monitiring of Large Space Structures," Journal of Sound and Vibration, vol. 27, no. 6, pp. 102-117, 1993.

H. Li, J. Wang and S. Hu, "Using incomplete modal data for damage detection in offshore jacket structures," Ocean Engineering, vol. 35, pp. 1793-1799, 2008.

H. Li, X. Deng and H. Dai, "Structural damage detection using the combination method of EMD and wavelet analysis," Mechanical Systems and Signal Processing, vol. 21, no. 1, pp. 298-306, 2007.

H. Naderpour, A. Kheyroddin, G. Ghodrati Amiri, S.R. Hoseini Vaez, Estimating the behavior of FRP-strengthened RC structural members using artificial neural networks, in: Procedia Eng., 2011.

H. Naderpour, A. Kheyroddin, G.G. Amiri, Prediction of FRP-confined compressive strength of concrete using artificial neural networks, Compos. Struct. 92 (2010).

H. Naderpour, A. Kheyroddin, S.R. Hoseini Vaez, Nonlinear behavior of RC shear walls externally bonded with FRP sheets, in: Proc. 4th Int. Conf. FRP Compos. Civ. Eng. CICE 2008, 2008.

H. Naderpour, G. Ghodrati Amiri, A. Kheyroddin, S.R. Hoseini Vaez, Seismic evaluation of retrofitted RC frames using neuro-fuzzy algorithms, in: Proc. 8th Int. Conf. Struct. Dyn. EURODYN 2011, 2011.

H. Naderpour, R.C. Barros, S.M. Khatami, A new equation of motion to calculate the impact force and the energy dissipation, Civil-Comp Proc. 102 (2013).

H. Naderpour, R.C. Barros, S.M. Khatami, Investigation of buildings collision based on mathematic equation to evaluate the impact force in non-linear viscoelastic Model, Civil-Comp Proc. 106 (2014).

H. Naderpour, R.C. Barros, S.M. Khatami, State-of-the-Art: Building pounding, link elements and the evaluation of impact forces and energy dissipation, Civil-Comp Proc. 102 (2013).

H. Naderpour, S.M. Zahrai, S.M. Kalantary, Nonlinear dynamic response of base-isolated structures with different characteristics of superstructure and isolators, in: Proceedings, Annu. Conf. - Can. Soc. Civ. Eng., 2008.

H. Naderpour, S.R. Hoseini Vaez, G. Ghodrati Amiri, Prevalent pulse influence of near-fault ground motions on base-isolated steel structures, in: Int. Conf. Noise Vib. Eng. 2012, ISMA 2012, Incl. USD 2012 Int. Conf. Uncertain. Struct. Dyn., 2012.

H. Salane and J. Baldwin, "Identification of Modal Properties of Bridge," Journal of Structural Engineering, ASCE, vol. 116, no. 7, pp. 718-723, 1990.

H. Sohn and C. Farrar, "Damage diagnosis using time series analysis of vibration signals," Smart materials and structures, vol. 10, no. 3, p. 446, 2001.

H. Sohn, C. Farrar, F. Hemez, D. Shunk, D. Stinemates and B. Nadler, "A review of structural health monitoring literature: 1996-2001.Report," Los Alamos National Laboratory, New Mexico, 2004.

H. Sohn, J. Czarnecki and C. Farrar, "Structural health monitoring using statistical process control," Journal of Structural Engineering, vol. 126, no. 11, pp. 1356-1363, 2000.

H. Stark, Wavelets and Signal Processing an Application-Based Introduction, Berlin Heidelberg: Springer, 2005.

H. Titi, H. Tabatabai and K. Sobolev, "Feasibility Study for a Freeway Corridor Infrastructure Health Monitoring Instrumentation Testbed," University of Wisconsin-Milwaukee, Milwaukee, 2012.

I. Daubechies, "The Wavelet Transform, Time – Frequency Localization and Signal Analysis," IEEE Transactions on Information Theory, vol. 36, pp. 961-1005, 1990.

J. A. d. Santos, C. M. Soares, C. M. Soares and N. Maia, "Structural damage identification in laminated structures using FRF data," Journal of Composite Structures, vol. 67, no. 2, p. 239–249, 2005.

J. Andersen and M. Fustinoni, Structural Health Monitoring Systems, 2006.

J. B. Mander, M. J. N. Priestley and R. Park, "Theoretical Stress-Strain Model for Confined Concrete," Journal of Structural Engineering, vol. 114, no. 8, pp. 1804-1826, 1988.

J. Caicedo and S. Dyke, "Determination of Member Stiffnesss for Structural Health Monitoring," in The 3rd Word Conference in Structural Control, Italy, 2002.

J. Chance, G. Tomlinson and R. Worden, "A Simplified Approach to the Numerical and Experimental Modeling of the Dynamics Cracked Beam," in The 12 th International Modal Analysis Conference, 1994.

J. Chen and J. Garba, "Analytical Model Improvement Using Modal Test Results," AIAA Journal, vol. 18, no. 6, pp. 684-690, 1980.

J. Ching and J. Beck, "Baysian Analysis of phase II LASC –ASCE Strructural Health Monitoring Experimental Benchmark Data," Journal of Engineering Mechanics, vol. 130, pp. 1233-1244, 2004.

J. Han, W. Ren and Z. Sun, "Wavelet packet based damage identification of beam structure," International Journal of Solids and Structures, vol. 42, no. 26, pp. 6610-6627, 2005.

J. Kim and N. Stubbs, "Improved Damage Identification Method Based Modal Information," Journal of Sound and Vibration, vol. 252, no. 2, p. 223–238, 2002.

J. Ko and Y. Q. Ni, "Technology developments in structural health monitoring of large-scale bridges," Engineering Structures, vol. 27, pp. 1715-1725, 2005.

J. Lee and S. Kim, "Structural damage detection in the frequency domain using neural networks," Journal of Intelligent Material Systems and Structures, vol. 18, no. 8, pp. 785-792, 2007.

J. Mohle and S. Kunnath, "Reinforcing steel material," 2006. [Online]. Available:

J.-T. Kim, Y.-S. Ryu, H.-M. Cho and N. Stubbs, "Damage identification in beam – type structures: frequency-based method vs mode-shape-based method," Engineering structures, vol. 25, no. 1, pp. 57-67, 2003.

K. Nair, A. Kiremidjian and K. Law, "Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure," Journal of sound and vibration, vol. 291, no. 1, pp. 349-368, 2006.

K. Rao, D. Kim and J. Hwang, Fast Fourier Transform: Algorithms and Applications, Berlin Heidelberg: Springer, 2005.

K. Yuen and L. Katafygiotis, "Model updating using noisy response measurements without knowledge of the input spectrum," Earthquake Engineering & Structural Dynamics, vol. 34, no. 2, pp. 167-187, 2005.

L. Bisby and M. Briglio, "An Introduction to Structural Health Monitoring," A Canadian Network of Centres of Excellence, 2004.

L. Chiang, E. Russell and R. Braatz, Fault Detection and Diagnosis in Industrial Systems, London: Springer Verlag, 2001.

L. Yam, YanY and J. Jiang, "Vibration-based damage detection for composite structures using wavelet transform and neural network identification," Composite Structures, vol. 60, no. 4, pp. 403-412, 2003.

M. Ahmadi, H. Naderpour, A. Kheyroddin, Utilization of artificial neural networks to prediction of the capacity of CCFT short columns subject to short term axial load, Arch. Civ. Mech. Eng. 14 (2014).

M. Chandrashekhar and R. Ganguli, "Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic," Journal of Sound and Vibration, vol. 326, no. 3-5, p. 939–957, 2009.

M. Choi and I. Kwon, "Damage detection system of a real steel truss bridge by neural networks," Smart Structures and Materials 2000: Smart Systems for Bridges, Structures, and Highways, 2000.

M. Dilena and A. Morassi, "Structural Health Monitoring of Rods Based on Natural Frequency and Antiresonant Frequency Measurements," Structural Health Monitoring, vol. 8, no. 2, pp. 149-173, 2009.

M. Friswell and J. Mottersheed, "Model Updating in Structural Daynamic : A Survey," Journal of Sound and Vibration, vol. 167, pp. 347-375, 1993.

M. I. Friswell, J. E. T. Penny and D. Wilson, "Using Vibration Data and Statistical Measure to locate Damage in structures," Modal Analysis : The International Journal of Analytical and Experimental Modal Analysis, vol. 9, no. 4, pp. 239-254, 1994.

M. J. Schoettler, J. I. Restrepo, G. Guerrini, D. E. Duck and F. Carrea, "A Full-Scale, Single-Column Bridge Bent Tested by Shake-Table Excitation," Center for Civil Engineering Earthquake Research, Reno, NV, 2012.

M. Kaouk and D. Zimmerman, "Reducing the Required Number of Modes for Structural Damage Assessment," in The 36 th AIAA/ASME/ASCE/AHS/ASC Structure,Structural Dynamics ,and Materials Conference, 1995.

M. Kaouk and D. Zimmerman, "Structural Damage Detection Using Measured Modal Data and No Original Analytical Model," in The 12 th International Modal Analytis Conference, 1994.

M. Limongeli, "Frequency response function interpolation for damage detection under changing environment," Journal of Mechanical System and Signal Processing, vol. 24, pp. 2898-2913, 2010.

M. Limongelli, "The interpolation damage detection method for frames under seismic excitation," Journal of Sound and Vibration, vol. 330, no. 22, p. 5474–5489, 2011.

M. M. Ge and E. Lui, "Structural Damage Identification Using System Dynamics Properties," Computer and Structures, vol. 83, pp. 2185-2196, 2005.

M. M. Ge, E. Lui and A. Khanse, "Non-Proportional Damage Identification in Steel Frames," Engineering Structures, vol. 32, pp. 523-533, 2010.

M. Misiti, Y. Misiti, G. Oppenheim and J. Poggi, Wavelet Toolbox for Use with MATLAB, Hill Drive Natick, MA: The Math Works, Inc, 2002.

M. Richardson and D. Formenti, "Parameter estimation from frequency response measurement using rational fraction polynomials," in The 1st International Modal Analysis Conference, Orlando, Florida, 1982.

M. Rucka and K. Wilde, "Application of continuous wavelet transform in vibration based damage detection method for beams and plates," Journal of sound and vibration, vol. 297, no. 3, pp. 536-550, 2006.

M.A. Shayanfar, H. Naderpour, Investigation of effective parameters on structural reliability of reinforced concrete structures externally bonded with FRP sheets, in: Proceedings, Annu. Conf. - Can. Soc. Civ. Eng., 2008.

M.K. Sharbatdar, S.R. Hoseini Vaez, G. Ghodrati Amiri, H. Naderpour, Seismic response of base-isolated structures with LRB and FPS under near fault ground motions, in: Procedia Eng., 2011.

Mazzoni, Silvia; McKenna, Frank; H.Scott, Michael; L. Fenves, Gregory; et al., OpcnSees Command Language Manual, acific Earthquake Engineering enter, Univ. of Calif., Berkeley., 2007.

N. Maia and J. Silva, Theoretical and Experimental Modal Analysis, England: Research Studies Press Ltd, 1997.

N. Stubbs, J. Kim and K. Topple, "An effect and robust algorithm for damage localization 1 offshore platforms," in ASCE 10th Structural Congress, San Antonio,Texas, 1994.

O. Salawu and C. Williams, "Bridge Assessment Using Forced-Vibration Testing," Journal of Structural Engineering, ASCE, vol. 121, no. 2, pp. 161-173, 1995.

O. Salawu and C. Williams, "Damage Localization Using Vibration Mode Shapes," in The 12 th International Modal Analysis Conference, 1994.

P. Barr, B. Woodward, B. Najera and M. Amin, "Long-term structural health monitoring of the San Ysidro bridge," Journal of performance of Constructed Facilities,ASCE, vol. 20, no. 1, pp. 14-20, 2006.

P. Chang and S. Liu, "Recent research in nondestructive evaluation of civil infrastructures," Journal of Materials in Civil Engineering ,ASCE, vol. 15, no. 3, pp. 298-304, 2003.

P. Hajela and F. Soeiro, "Recent developments in damage detection based on system identification methods," Journal of Structural Optimization, vol. 2, pp. 1-10, 1990.

P. Qiao, K. Luc, W. Lestarid and J. Wang, "Curvature mode shape-based damage detection in composite laminated plates," Composite Structures, vol. 80, no. 3, p. 409–428, 2007.

P. Skjaeraek, S. Nelsen and A. akmak, "Identification of damage in reinforced- concrete structure from earthquake records: Optimal location of sensors," Soil Dynamics and Earthquake Engineering, vol. 15, no. 6, pp. 347-358, 1996.

P. Tsou and M. Shen, "Structural damage detection and identification using neural networks," AIAA Journal, vol. 32, no. 1, pp. 176-183, 1994.

Q. Yang, "A mixed sensitivity method for structural damage detection," Communications in Numerical Methods in Engineering, vol. 25, no. 4, pp. 381-389, 2009.

Q. Yang, "A numerical technique for structural damage detection," Applied Mathematics and Computation, vol. 215, no. 7, pp. 2775-2780, 2009.

R. Adams, P. Cawely, C. Pye and B. Sture, "A Vibration Technique for Non-Destructively Assessing the Integrity of Structures," Journal of Mechanical Engineering Science, vol. 20, no. 2, pp. 93-100, 1978.

R. Cobb and B. Liebst, "Structural damage identification using assigned partial eigenstructure," AIAA Journal, vol. 35, no. 1, pp. 152-158, 1997.

R. Curadelli, J. Rier, D. Ambrosini and M. Amani, "Damage detection by means of structural damping identification," Journal of Engineering Structures, vol. 30, no. 12, pp. 3497-3504, 2008.

R. E. Englekirk, Seismic design of reinforced and precast concrete buildings, Hoboken, New Jersey: John Wiley & Sons, Inc, 2003.

R. Luciana, L. Barroso and R. Rodriguez, "Application of the Damage Index Method to phase liof the Analytical Shm Benchmark Problem," in The 15 th ASCE Engineering Mechanics Conference, Columbia University, NewYork, 2002.

R. Mayes, "Error localization using mode shapes –An application to a two link robot arm," in The 10 th International Modal Analysis Conference, 1992.

R. P. Bandara, "Damage Identification and Condition Assessment of Building Structures Using Frequency Response Functions and Neural Networks," Faculty of Science and Engineering, Queensland University of Technology, Brisbane, 2013.

R. Sanmpiao, N. Maia and J. Silva, "Damage detection using the frequency response function curvature method," Journal of Sound and Vibration, vol. 226, pp. 1029-1042, 1999.

S. Beskhyroun, T. Oshima and S. Mikami, "Wavelet-based technique for structural damage detection," Structural Control and Health Monitoring, vol. 17, no. 5, pp. 73-494, 2010.

S. Doebling, C. Farrar and M. Prime, "A summery review of vibration – based damage identification methods," Shock and Vibration Digest, vol. 30, no. 2, pp. 91-105, 1998.

S. Doebling, C. Ferrar, M. Prime and D. Shevits, "Damage Identification and health monitoring of structural and Mechanical system from changes in their vibration characteristics: A Literature Review," Los Alamos National Laboratory report, New Mexico, 1996.

S. Fang and R. Perea, "Power mode shapes for early damage detection in linear structures," Journal of Sound and Vibration, vol. 324, no. 1-2, p. 40–56, 2009.

S. Mallat, A Wavelet Tour of Signal Processing The Sparse Way, San Diego, CA: Academic Press, 2009.

S. Silva, M. Junior, V. Junior and M. Brennan, "Structural damage detection by fuzzy clustering," Mechanical Systems and Signal Processing, vol. 22, pp. 1636-1649, 2008.

S. Smith and C. Beattie, "Optimal Identification Inconsistent Modal Data," in The 32 th AIAA/ASME/ASCE/AHS/ASC Strutructures,Structural Dynamics, and Materials Conference, 1991.

S. Yang and G. Lee, "Effects of Modeling Error on Structure Damage Diagnosis by Two – Stage Optimization," Structural Heaith Monitorig, pp. 817-880, 1999.

S.R. Hoseini Vaez, A. Kheyroddin, H. Naderpour, 3D finite element simulation of slab-column connections strengthened with CFRP, in: Proc. 4th Int. Conf. FRP Compos. Civ. Eng. CICE 2008, 2008.

S.R. Hoseini Vaez, M.K. Sharbatdar, G. Ghodrati Amiri, H. Naderpour, A. Kheyroddin, Dominant pulse simulation of near fault ground motions, Earthq. Eng. Eng. Vib. 12 (2013).

S.R.H. Vaez, H. Naderpour, R.C. Barros, Influence of equivalent pulses of near fault ground motions on base-isolated RC structures, in: Proc. Int. Conf. Struct. Dyn. , EURODYN, 2014.

T. Lim, "A Submatrix Approach to Stiffness Matrix Correction Using Modal Test Data," Journal of AIAA, vol. 28, pp. 1123-1130, 1990.

T. Lim, "Structural Damage Detection of a Planar Truss Structure Using a Constrained Eigenstructure Assignmen," in The 35th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference, 1994.

T. Marwala, "Fault Identification using Neural Network and vibration Data Ph.D. Dissertation," John s Collegs, university of Cambridge, 2000.

T. R. Fasel, H. Sohn, G. Park and C. R. Farrar, "Active sensing using impedance-based ARX models and extreme value statistics for damage detection," Earthquake Engineering & Structural Dynamics, vol. 34, no. 7, pp. 763-785, 2005.

T. W. Lim, "Structural Damage Detection Using Constrained Eigenstructure Assignment," Journal of Guidance, Control, and Dynamics, vol. 18, no. 3, pp. 411-418, 1995.

U. Lee and J. Shin, "A Frequency Response Function Based Structural Damage Identification Method," Computers and Structures, vol. 80, pp. 117-132, 2002.

V. Pakrashi, B. Basu and A. O'Connor, "Structural damage detection and calibration using a wavelet-kurtosis technique," Engineering structures, vol. 29, no. 9, pp. 2097-2108, 2007.

W. Biemans, W. Staszewski, J. Boller and G. Tomlinson, "Crack Detection in Metallic Structures Using Broadband Excitation of Acousto-Ultrasonics," Journal of Intelligent Material Systems and Structures, vol. 12, no. 8, pp. 589-597, 2001.

W. Ren and Z. Sun, "Structural damage identification by using wavelet entropy," Engineering structures, vol. 30, no. 10, pp. 2840-2849, 2008.

W. West, "Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen . in Proc," Air Force Conference on Aircraft Structural Integrity, 1984.

X. Jiang and S. Mahadevan, "Bayesian wavelet methodology for structural damage detection," Structural Control and Health Monitoring, vol. 15, no. 7, pp. 974-991, 2008.

Y. Diao, H. Li and Y. Wang, "A two-step structural damage detection approach based on wavelet packet analysis and neural network. in Machine Leaming and Cybernetics," International Conference on .. IEEE, 2006.

Y. Ding, A. Li and T. Liu, "A study on the WPT-based structural damage alarming of the ASCE benchmark experiments," Advances in Structural Engineering, vol. 11, no. 1, pp. 12-127, 2008.

Y. Dong, R. Song and H. Liu, "Bridges Structural Health Monitoring and Deterioration Detection- Synthesis of Knowledge and Technology," Final Report Prepared for Alaska University Transportation Center, 2010.

Y. Ni, X. Zhou and J. Ko, "Experimental investigation of seisimic damage identification using PCA- compressed frequency response functions and neural network," Journal of Sound and Vibration, vol. 290, pp. 242-263, 2006.

Z. Hou, A. Hera and A. Shinde, "Wavelet-Based Structural Health Monitoring of Earthquake Excited Structures," Computer-Aided Civil and Infrastructure Engineering, vol. 21, no. 4, pp. 268-279, 2006.

Z. Kıral, B. M. İçten and B. G. Kıral, "Effect of impact failure on the damping characteristics of beam – like composite structure," Journal of Composite Part B: Engineering, vol. 43, no. 8, pp. 3053-3060, 2012.

Z. Sun and C. Chang, "Structural damage assessment based on wavelet packet transform," Journal of Structural Engineering, vol. 128, no. 10, pp. 1345-1361, 2002.

Z. Wang, R. Lin and M. Lin, "Structural damage detection using measured FRF data," Computer Method in Applied Mechanics and Engineering, vol. 147, pp. 187-197, 1997.

Z. Zhang and A. Aktan, "The damage indices for constructed facilities," in The 13 th International Modal Analysis Conference, Nashville ,TN, 1995.

Z. Zhou, "Vibration-Based Damage Detection of Simple Bridge Superstructures," In Department of Civil and Geological Engineering, University of Saskatchewan, 2006.