Detection of nonlinear seismic response of steel moment frames using Frequency Response Functions (FRFs) and Hilbert transforms of FRFs

Document Type : Original Research

Authors
S. S. Majid Zamani 1
H. Movahed 2
1 Faculty member, Structural Engineering Department, Road, Housing and Urban Development Research Center
2 PhD candidateBuilding and Housing FacultyRoad, Housing and Urban Development Research Center
10.22034/21.6.4
Abstract
Occurrence of the nonlinear behavior can be a sign of changes in structural parameters and the presence of damage in systems. This paper presents a method for detecting and quantifying of nonlinearity, as an indication of damage, using the indicators that are extracted from the frequency response functions (FRFs) and Hilbert transform of FRFs, for steel moment frame structural systems. Using time history analysis under selected harmonic ground motions, the results of FRFs for the studied 4-story system are illustrated and discussed.

Nonlinear behavior is a result of formation plastic hinges under earthquake loading. FRFs and Hilbert transform of FRFs are extracted from both the linear and nonlinear behavior of 4, 8, and 12-stories steel moment frames under fifteen different earthquake records with different characteristics in their time histories. Some near and far field well-known earthquakes records have been selected for the present study as the ground motions input in time history analysis. Different levels of nonlinearity are determined based on the maximum rotation of hinges in column members of structures equal to 2θy, 4θy and 6θy, in which θy is yield limit rotation. The indicators of the studied systems are calculated and evaluated for linear and different levels of nonlinearity based on the mathematical power of changes for FRFs and Hilbert transform of FRFs. The presented indicators are extracted based on the frequency response functions (FRFs) and Hilbert transform of FRFs for the responses of absolute acceleration and relative displacement of stories. The indicators are calculated at the location of acceleration sensors (accelerometer) in four levels of the structural systems, while the formation of plastic hinges in the columns of the structures will occur only at the level of the distance between the adjacent sensors.It is shown that the proposed method and calculated indicators have enough accuracy and sensitivity in detecting the “existence”, “location” and “extent” of damage.

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Subjects

[1] Sohn, H. and Farrar, C.R. 2001, Damage diagnosis using time series analysis of vibration signals, Smart Materials and Structures, 10(3):446-451
[2] Farrar, C.R. and Worden, K. 2007, An introduction to structural health monitoring. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 365(1851):303-315.
[3] Fan, W. and Qiao, P. 2010, Vibration-based Damage Identification Methods: A Review and Comparative Study. Structural Health Monitoring, 10(1): p. 83-111.
[4] Das, S., Saha, P. and Patro, S.K. 2016, Vibration-based damage detection techniques used for health monitoring of structures: a review, Journal of Civil Structural Health Monitoring. 6(3):477-507
[5] Hosoya, N., Ozawa, S. and Kajiwara, I. 2019, Frequency response function measurements of rotational degrees of freedom using a non-contact moment excitation based on nanosecond laser ablation, Journal of Sound and Vibration, 456: 239-253.
[6] Shiradhonkar, S.R. and Shrikhande, M. 2011, Seismic damage detection in a building frame via finite element model updating. Comput. Struct., 89(23-24): 2425-2438.
[7] Srinivas, V., Sasmal, S. and Ramanjaneyulu, K. 2014, Damage-sensitive features from non-linear vibration response of reinforced concrete structures, Structural Health Monitoring. 13(3):233-250.
[8] Krishnanunni, C.G., et al. 2019, Sensitivity-based damage detection algorithm for structures using vibration data. Journal of Civil Structural Health Monitoring. 9(1):137-151
[9] Prawin, J. and Rao A.R.M. 2018, A method for detecting damage-induced nonlinearity in structures using weighting function augmented curvature approach. Structural Health Monitoring. 18(4): 1154-1167.
[10] Worden, K. and Tomlinson, G.R. 2001, Nonlinearity in structural dynamics: detection, identification and modelling, UK: Taylor & Francis
[11] Farshadi, M., Esfandiari, A. and Vahedi, M. 2017, Structural model updating using incomplete transfer function and modal data. Structural Control and Health Monitoring. 24(7):1-13.
[12] Bandara, R.P., Chan, T.H.T. and Thambiratnam, D.P. 2014, Frequency response function based damage identification using principal component analysis and pattern recognition technique, Engineering Structures, 66:116-128.
[13] Huynh, D., He, J. and Tran, D. 2005, Damage location vector: A non-destructive structural damage detection technique, Computers & Structures, 83(28):2353-2367.
[14] Araújo dos Santos, J.V., et al. 2005, Structural damage identification in laminated structures using FRF data., Composite Structures, 67(2):239-249.
[15] Cottone, G., Pirrotta, A. and Salamone, S. 2008, Incipient damage identification through characteristics of the analytical signal response, Structural Control and Health Monitoring, 15(8):1122-1142.
[16] Barone, G., Marino, F. and Pirrotta, A. 2008, Low stiffness variation in structural systems: Identification and localization, Structural Control and Health Monitoring, 15(3):450-470.
[17] Mahato, S., Teja, M.V. and Chakraborty, A. 2017, Combined wavelet–Hilbert transform-based modal identification of road bridge using vehicular excitation, Journal of Civil Structural Health Monitoring, 7(1):29-44
[18] Mao, H., et al., 2018, The construction and comparison of damage detection index based on the nonlinear output frequency response function and experimental analysis. Journal of Sound and Vibration. 427:82-94.
[19] Agency, F.E.M. 2000, Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings, in FEMA-356.
[20] Schneider, S.P., Roeder, C.W. and Carpenter, J.E. 1993, Seismic Behavior of Moment‐Resisting Steel Frames: Experimental Study, Journal of Structural Engineering, 119(6):1885-1902.
[21] Naeim, F., et al. 1999, Effect of Hysteretic Deterioration Characteristics on Seismic Response of Moment Resisting Steel Structures, SAC phase II project report, NISEE UC Berkeley.
[22] Krawinkler, H. 2000, SYSTEM PERFORMANCE OF STEEL MOMENT RESISTING FRAME STRUCTURES, in 12th World Conference on Earthquake Engineering: Auckland, New Zealand.
[23] Lee, K. and Foutch, D.A. 2002, Performance evaluation of new steel frame buildings for seismic loads. Earthquake Engineering & Structural Dynamics, 31(3):653-670.
[24] RODGERS, J.E. and MAHIN, S.A. 2004, EFFECTS OF HYSTERETIC DETERIORATION ON SEISMIC RESPONSE OF STEEL MOMENT FRAMES, in 13th World Conference on Earthquake Engineering: Vancouver, B.C., Canada.
[25] Chanpheng, T., et al. 2012, Nonlinear features for damage detection on large civil structures due to earthquakes, Structural Health Monitoring, 11(4):482-488.
[26] SAP-2000 1995, CSI Analysis Reference Manual, Computers and Structures, Inc., University Avenue Berkeley: California.
[27] Clough, R. and Penzin J. 1993 Dynamic of Structures, Mc Graw-Hill Inc
[28] PEER–Pacific Earthquake Engineering Research Center 2018. Strong motion database. Available from: http://peer.berkeley.edu/peer_ground_motion_database, Jun.
Modares Civil Engineering journal
Volume 21, Issue 6
November and December 2021
Pages 55-73