Browse > Article
http://dx.doi.org/10.12989/eas.2022.23.6.549

Nonlinear structural finite element model updating with a focus on model uncertainty  

Mehrdad, Ebrahimi (Department of Civil Engineering, K.N. Toosi University of Technology)
Reza Karami, Mohammadi (Department of Civil Engineering, K.N. Toosi University of Technology)
Elnaz, Nobahar (Department of Civil Engineering, K.N. Toosi University of Technology)
Ehsan Noroozinejad, Farsangi (Faculty of Civil and Surveying Engineering, Graduate University of Advanced Technology)
Publication Information
Earthquakes and Structures / v.23, no.6, 2022 , pp. 549-580 More about this Journal
Abstract
This paper assesses the influences of modeling assumptions and uncertainties on the performance of the non-linear finite element (FE) model updating procedure and model clustering method. The results of a shaking table test on a four-story steel moment-resisting frame are employed for both calibrations and clustering of the FE models. In the first part, simple to detailed non-linear FE models of the test frame is calibrated to minimize the difference between the various data features of the models and the structure. To investigate the effect of the specified data feature, four of which include the acceleration, displacement, hysteretic energy, and instantaneous features of responses, have been considered. In the last part of the work, a model-based clustering approach to group models of a four-story frame with similar behavior is introduced to detect abnormal ones. The approach is a composition of property derivation, outlier removal based on k-Nearest neighbors, and a K-means clustering approach using specified data features. The clustering results showed correlations among similar models. Moreover, it also helped to detect the best strategy for modeling different structural components.
Keywords
EDP; hysteretic models; kmeans clustering; modeling uncertainty; nonlinear finite element model updating; OpenSees; panel zone;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Van Overschee, P. and De Moor, B. (1996), Subspace Identification for Inear Systems: Theory-ImplementationApplications, Kluwer Academic Publishers, Dordrecht, Netherlands.
2 Wang, S.J. (1989), "Seismic response of steel building frames with inelastic joint deformation", Ph.D. Dissertation, Lehigh University, Bethlehem, Pennsylvania, USA.
3 Wang, Z.C., Ren, W.X. and Chen, G.D. (2013), "Time-varying linear and nonlinear structural identification with analytical mode decomposition and Hilbert transform", J. Struct. Eng., 139(12), 06013001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000832.   DOI
4 Wang, Z.C., Xin, Y. and Ren, W.X. (2015), "Nonlinear structural model updating based on instantaneous frequencies and amplitudes of the decomposed dynamic responses", Eng. Struct., 100, 189-200. https://doi.org/10.1016/j.engstruct.2015.06.002.   DOI
5 Wang, Z.C., Xin, Y. and Ren, W.X. (2016), "Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses", Mech. Syst. Signal Pr., 76, 476-496. https://doi.org/10.1016/j.ymssp.2016.01.024.   DOI
6 Weng, J.H. and Loh, C.H. (2011), "Recursive subspace identification for on-line tracking of structural modal parameter", Mech. Syst. Signal Pr., 25(8), 2923-2937. https://doi.org/10.1016/j.ymssp.2011.05.013.   DOI
7 EN 1993-1-1 (2005), Eurocode 3: Design of Steel Structures-Part 1-1: General Rules and Rules for Buildings, CEN, Brussels, Belgium.
8 BS10210 (2006), British Standard: Hot Finished Structural Hollow Sections of Non-Alloy and Fine Grain Steels-Part 2: Tolerances, Dimensions, and Sectional Properties, British Standard Institute, London, England.
9 Aggarwal, C.C. (2017), Proximity-Based Outlier Detection, Springer, New York, New York, USA.
10 Altman, N.S. (1992), "An introduction to kernel and nearestneighbor nonparametric regression", Am. Stat., 46(3), 175-185. https://doi.org/10.1080/00031305.1992.10475879.   DOI
11 Asgarieh, E., Moaveni, B., Barbosa, A.R. and Chatzi, E. (2017), "Nonlinear model calibration of a shear wall building using time and frequency data features", Mech. Syst. Signal Pr., 85, 236-251. https://doi.org/10.1016/j.ymssp.2016.07.045.   DOI
12 Astroza, R., Ebrahimian, H. and Conte, J.P. (2019), "Performance comparison of Kalman- based filters for nonlinear structural finite element model updating", J. Sound Vib., 438, 520-542. https://doi.org/10.1016/j.jsv.2018.09.023.   DOI
13 Beck, J.L. and Katafygiotis, L.S. (1998), "Updating models and their uncertainties. I: Bayesian statistical framework", J. Eng. Mech., 124(4), 455-461. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:4(455).   DOI
14 Behmanesh, I. and Moaveni, B. (2015), "Probabilistic identification of simulated damage on the dowling hall footbridge through Bayesian finite element model updating", Struct. Control Health Monit., 22(3), 463-483. https://doi.org/10.1002/stc.1684.   DOI
15 Bertero, R.D. and Bertero, V.V. (2002), "Performance-based seismic engineering: the need for a reliable conceptual comprehensive approach", Earthq. Eng. Struct. Dyn., 31(3), 627-652. https://doi.org/10.1002/eqe.146.   DOI
16 Bouc, R. (1967), "Forced vibrations of mechanical systems with hysteresis", Proceedings of the Fourth Conference on Nonlinear Oscillations, Prague, Czech Republic, September.
17 Wong, K.C. and Temple, M.C. (1982), "Stayed column with initial imperfection", J. Struct. Div., 108(7), 1623-1640. https://doi.org/10.1061/JSDEAG.0005992.   DOI
18 Wu, W., Xiong, H. and Shekhar, S. (2003), Clustering and Information Retrieval, Kluwer Academic Publishers, Amsterdam, Netherlands.
19 Yamada, S., Suita, K., Tada, M., Kasai, K., Matsuoka, Y. and Shimada, Y. (2008). "Collapse experiment on 4-story steel moment frame: Part 1 outline of test results", Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, October.
20 Yamada, S., Kasai, K., Shimada, Y., Suita, K., Tada, M. and Matsuoka, Y. (2009), "Full scale shaking table collapse experiment on 4-story steel moment frame: Part 1 outline of the experiment", Proceedings of Behaviour of Steel Structures in Seismic Areas: STESSA 2009, Philadelphia, Pennsylvania, USA, August.
21 Yang, J.N., Xia, Y. and Loh, C.H. (2014), "Damage detection of hysteretic structures with a pinching effect", J. Eng. Mech., 140(3), 462-472. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000581.   DOI
22 Yu, L., Zhu, J.H. and Yu, L.L. (2013), "Structural damage detection in a truss bridge model using fuzzy clustering and measured FRF data reduced by principal component projection", Adv. Struct. Eng., 16(1), 207-217. https://doi.org/10.1260/1369-4332.16.1.207.   DOI
23 Yuen, K.V. and Katafygiotis, L.S. (2001), "Bayesian time-domain approach for modal updating using ambient data", Probab. Eng. Mech., 16(3), 219-231. https://doi.org/10.1016/S0266-8920(01)00004-2.   DOI
24 Zhou, Y.L., Maia, N.M., Sampaio, R.P. and Wahab, M.A. (2017), "Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure", Struct. Health Monit., 16(6), 711-731. https://doi.org/10.1177/1475921716680849.   DOI
25 Campione, G., Cavaleri, L., Macaluso, G., Amato, G. and Di Trapani, F. (2015), "Evaluation of infilled frames: An updated in-plane-stiffness macro-model considering the effects of vertical loads", Bull. Earthq. Eng., 13(8), 2265-2281. https://doi.org/10.1007/s10518-014-9714-x.   DOI
26 Castaldo, P., Gino, D., Marano, G.C. and Mancini, G. (2022), "Aleatory uncertainties with global resistance safety factors for non-linear analyses of slender reinforced concrete columns", Eng. Struct., 255, 113920. https://doi.org/10.1016/j.engstruct.2022.113920.   DOI
27 Cao, G. and Bouman, C.A. (2008), "Covariance estimation for high dimensional data vectors using the sparse matrix transform", Proceedings of the 21st International Conference on Neural Information Processing Systems, Vancouver, Canada, December.
28 Castaldo, P. and Amendola, G. (2021), "Optimal sliding friction coefficients for isolated viaducts and bridges: A comparison study", Struct. Control Health Monit., 28(12), e2838. https://doi.org/10.1002/stc.2838.   DOI
29 Castaldo, P., Gino, D., Bertagnoli, G. and Mancini, G. (2020), "Resistance model uncertainty in non-linear finite element analyses of cyclically loaded reinforced concrete systems", Eng. Struct., 211, 110496. https://doi.org/10.1016/j.engstruct.2020.110496.   DOI
30 Castro, J., Elghazouli, A. and Izzuddin, B. (2005), "Modelling of the panel zone in steel and composite moment frames", Eng. Struct., 27(1), 129-144. https://doi.org/10.1016/j.engstruct.2004.09.008.   DOI
31 Ching, J. and Beck, J.L. (2004), "New Bayesian model updating algorithm applied to a structural health monitoring benchmark", Struct. Health Monit., 3(4), 313-332. https://doi.org/10.1177/1475921704047499.   DOI
32 AISC (2010), Specification for Structural Steel Buildings (ANSI/AISC 360-10), American Institute of Steel Construction, Chicago-Illinois, USA.
33 Cover, T. and Hart, P. (1967), "Nearest neighbor pattern classification", IEEE Trans. Inf. Theory, 13(1), 21-27. https://doi.org/10.1109/TIT.1967.1053964.   DOI
34 Diez, A., Khoa, N.L.D., Alamdari, M.M., Wang, Y., Chen, F. and Runcie, P. (2016), "A clustering approach for structural health monitoring on bridges", J. Civil Struct. Health Monit., 6(3), 429-445. https://doi.org/10.1007/s13349-016-0160-0.   DOI
35 Crisafulli, F.J. and Carr, A.J. (2007), "Proposed macro-model for the analysis of infilled frame structures", Bull. N.Z. Soc. Earthq. Eng., 40(2), 69-77. https://doi.org/10.5459/bnzsee.40.2.69-77.   DOI
36 Decanini, L., Mollaioli, F., Mura, A. and Saragoni, R. (2004). "Seismic performance of masonry infilled R/C frames", 13th World Conference on Earthquake Engineering, Vancouver, British Columbia, Canada, August.
37 Der Kiureghian, A. and Ditlevsen, O. (2009), "Aleatory or epistemic? Does it matter?", Struct. Saf., 31(2), 105-112. https://doi.org/10.1016/j.strusafe.2008.06.020.   DOI
38 Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review", Report No. LA13070-MS, Los Alamos National Laboratory.
39 Dolsek, M. and Fajfar, P. (2008), "The effect of masonry infills on the seismic response of a four-storey reinforced concrete frame-a deterministic assessment", Eng. Struct., 30(7), 1991-2001. https://doi.org/10.1016/j.engstruct.2008.01.001.   DOI
40 Ebrahimi, M. and Karami Mohammadi, R. (2020), "Damage detection of steel moment frames under earthquake excitation", Struct. Control Health Monit., 27(10), e2599. https://doi.org/10.1002/stc.2599.   DOI
41 El-Dakhakhni, W.W., Hamid, A.A. and Elgaaly, M. (2004). "Strength and stiffness prediction of masonry infill panels", Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, British Columbia, Canada, August.
42 Gupta, A. and Krawinkler, H. (1998), "Seismic demands for the performance evaluation of steel moment resisting frame structures", Report No. 132, Stanford University.
43 Fan, C.L. (2021), "Detection of multidamage to reinforced concrete using support vector machine-based clustering from digital images", Struct. Control Health Monit., 28(12), e2841. https://doi.org/10.1002/stc.2841.   DOI
44 Feldman, M. (1997), "Non-linear free vibration identification via the Hilbert transform", J. Sound Vib., 208(3), 475-489. https://doi.org/10.1006/jsvi.1997.1182.   DOI
45 Fielding, D. and Huang, J. (1971), "Shear in steel beam-to-column connections", Weld. J., 50(7), 313-326.
46 Filippou, F.C., Popov, E.P. and Bertero, V.V. (1983), "Modeling of R/C joints under cyclic excitations", J. Struct. Eng., 109(11), 2666-2684. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:11(2666).   DOI
47 Gino, D., Castaldo, P., Giordano, L. and Mancini, G. (2021), "Model uncertainty in non-linear numerical analyses of slender reinforced concrete members", Struct. Concrete, 22(2), 845-870. https://doi.org/10.1002/suco.202000600.   DOI
48 Kim, K. and Engelhardt, M.D. (1995), "Development of analytical models for earthquake analysis of steel moment frames", Ph.D. Dissertation, University of Texas at Austin, Austin, Texas, USA.
49 Ibarra, L.F., Medina, R.A. and Krawinkler, H. (2005), "Hysteretic models that incorporate strength and stiffness deterioration", Earthq. Eng. Struct. Dyn., 34(12), 1489-1511. https://doi.org/10.1002/eqe.495.   DOI
50 Kerschen, G., Worden, K., Vakakis, A.F. and Golinval, J.C. (2006), "Past, present and future of nonlinear system identification in structural dynamics", Mech. Syst. Signal Pr., 20(3), 505-592. https://doi.org/10.1016/j.ymssp.2005.04.008.   DOI
51 Kim, K.D. and Engelhardt, M.D. (2002), "Monotonic and cyclic loading models for panel zones in steel moment frames", J. Constrete Steel Res., 58(5-8), 605-635. https://doi.org/10.1016/S0143-974X(01)00079-7.   DOI
52 Kitayama, S. and Constantinou, M.C. (2018), "Collapse performance of seismically isolated buildings designed by the procedures of ASCE/SEI 7", Eng. Struct., 164, 243-258. https://doi.org/10.1016/j.engstruct.2018.03.008.   DOI
53 Krawinkler, H. (1971), "Inelastic behavior of steel beam-tocolumn subassemblages", Report No. UCB/EERC-71/07, University of California, Berkeley.
54 Krawinkler, H. (1978), "Shear in beam-column joints in seismic design of steel frames", Eng. J., 15(3), 82-91.
55 Krawinkler, H., Popov, E.P. and Bertero, V.V. (1975), "Shear behavior of steel frame joints", J. Struct. Div., 101(11), 2317-2336. https://doi.org/10.1061/JSDEAG.0004206.   DOI
56 Lederman, G., Wang, Z., Bielak, J., Noh, H., Garrett, J.H., Chen, S., Kovacevic, J., Cerda, F. and Rizzo, P. (2014), "Damage quantification and localization algorithms for indirect SHM of bridges", Proceedings of the 7th International Conference on Bridge Maintenance, Safety and Management, Shanghai, China, July.
57 Ma, Z.S., Liu, L., Zhou, S.D., Yu, L., Naets, F., Heylen, W. and Desmet, W. (2018), "Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach", Mech. Syst. Signal. Pr., 98, 684-701. https://doi.org/10.1016/j.ymssp.2017.05.013.   DOI
58 Li, P., Wadee, M.A., Yu, J., Christie, N.G. and Wu, M. (2016), "Stability of prestressed stayed steel columns with a three branch crossarm system", J. Constrete Steel Res., 122, 274-291. https://doi.org/10.1016/j.jcsr.2016.03.007.   DOI
59 Lui, E.M. (1986), "Effects of connection flexibility and panel zone deformation on the behavior of plane steel frames", Ph.D Dissertation, Purdue University, West Lafayette, Indiana.
60 Lui, E.M. and Wai-Fah, C. (1986), "Frame analysis with panel zone deformation", Int. J. Solid. Struct., 22(12), 1599-1627. https://doi.org/10.1016/0020-7683(86)90065-X.   DOI
61 Marwala, T. and Sibisi, S. (2005), "Finite element model updating using Bayesian framework and modal properties", J. Aircr., 42(1), 275-278. https://doi.org/10.2514/1.11841.   DOI
62 Mazzoni, S., McKenna, F., Scott, M.H. and Fenves, G.L. (2006), Open System for Earthquake Engineering Simulation User Command-Language Manual.
63 Moaveni, B. and Asgarieh, E. (2012), "Deterministic-stochastic subspace identification method for identification of nonlinear structures as time-varying linear systems", Mech. Syst. Signal. Pr., 31, 40-55. https://doi.org/10.1016/j.ymssp.2012.03.004.   DOI
64 Mulas, M.G. (2004), "A structural model for panel zones in non linear seismic analysis of steel moment-resisting frames", Eng. Struct., 26(3), 363-380. https://doi.org/10.1016/j.engstruct.2003.10.009.   DOI
65 Pence, B.L., Fathy, H.K. and Stein, J.L. (2011), "Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory", Automatica, 47(11), 2420-2424. https://doi.org/10.1016/j.automatica.2011.08.014.   DOI
66 Nicola, T., Leandro, C., Guido, C. and Enrico, S. (2015), "Masonry infilled frame structures: state-of-the-art review of numerical modelling", Earthq. Struct., 8(3), 733-759. https://doi.org/10.12989/eas.2015.8.1.225.   DOI
67 Panagiotakos, T. and Fardis, M. (1996). "Seismic response of infilled RC frames structures", Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, January.
68 Paulay, T. and Priestley, M.N. (1992), Seismic Design of Reinforced Concrete and Masonry Buildings, Wiley, New York, New York, USA.
69 Priestley, M.N. and Calvi, G.M. (1991), "Towards a capacitydesign assessment procedure for reinforced concrete frames", Earthq. Spectra, 7(3), 413-437. https://doi.org/10.1193/1.1585635.   DOI
70 Qiu, L., Yuan, S., Mei, H. and Fang, F. (2016), "An improved Gaussian mixture model for damage propagation monitoring of an aircraft wing spar under changing structural boundary conditions", Sensors, 16(3), 291. https://doi.org/10.3390/s16030291.   DOI
71 Saneinejad, A. and Hobbs, B. (1995), "Inelastic design of infilled frames", J. Struct. Eng., 121(4), 634-650. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:4(634).   DOI
72 Santos, A., Figueiredo, E. and Costa, J. (2015). "Clustering studies for damage detection in bridges: A comparison study", Proceeding of 10th International Workshop on Structural Health Monitoring, Stanford, California, USA, September.
73 Shi, Y. and Eberhart, R. (1998), "A modified particle swarm optimizer", 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360), Anchorage, AK, USA, May.
74 Santos, A., Silva, M., Santos, R., Figueiredo, E., Sales, C. and Costa, J. (2016). "Output-only structural health monitoring based in mean shift clustering for vibration-based damage detection", Proceeding of 8th European Workshop on Structural Health Monitoring, Bilbao, Spain, July.
75 Sattar, S. and Liel, A.B. (2016), "Seismic performance of nonductile reinforced concrete frames with masonry infill wallsI: development of a strut model enhanced by finite element models", Earthq. Spectra, 32(2), 795-818. https://doi.org/10.1193/90914eqs139m.   DOI
76 Schneider, S.P. and Amidi, A. (1998), "Seismic behavior of steel frames with deformable panel zones", J. Struct. Eng., 124(1), 35-42. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:1(35).   DOI
77 Sivaselvan, M.V. and Reinhorn, A.M. (2000), "Hysteretic models for deteriorating inelastic structures", J. Eng. Mech., 126(6), 633-640. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(633).   DOI
78 Sohn, H. and Farrar, C.R. (2001), "Damage diagnosis using time series analysis of vibration signals", Smart Mater. Struct., 10(3), 446. https://doi.org/10.1088/0964-1726/10/3/304.   DOI
79 Sohn, H. and Law, K.H. (1997), "A Bayesian probabilistic approach for structure damage detection", Earthq. Eng. Struct. Dyn., 26(12), 1259-1281. https://doi.org/10.1002/(SICI)1096-9845(199712)26:12<1259::AID-EQE709>3.0.CO,2-3.   DOI
80 Song, M., Astroza, R., Ebrahimian, H., Moaveni, B. and Papadimitriou, C. (2020), "Adaptive Kalman filters for nonlinear finite element model updating", Mech. Syst. Signal Pr., 143, 106837. https://doi.org/10.1016/j.ymssp.2020.106837.   DOI
81 Taghipour, A. (2016), "Seismic behavior of vertical reinforced autoclaved aerated concrete (AAC) panel walls", Master's thesis, Middle East Technical University, Ankara, Turkey.
82 Song, M., Renson, L., Moaveni, B. and Kerschen, G. (2022), "Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes", Mech. Syst. Signal Pr., 165, 108337. https://doi.org/10.1016/j.ymssp.2021.108337.   DOI
83 EN 1998-1 (2005), Eurocode 8: Design of Structures for Earthquake Resistance-Part 1: General Rules, Seismic Actions and Rules for Buildings, CEN, Brussels, Belgium.
84 Suita, K., Yamada, S., Tada, M., Kasai, K., Matsuoka, Y. and Shimada, Y. (2008), "Collapse experiment on 4-story steel moment frame: Part 2 detail of collapse behavior", Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, October.
85 Tibaduiza, D.A., Mujica, L.E. and Rodellar, J. (2013), "Damage classification in structural health monitoring using principal component analysis and self-organizing maps", Struct. Control Health Monit., 20(10), 1303-1316. https://doi.org/10.1002/stc.1540.   DOI
86 Tsai, K.C. and Popov, E.P. (1988), "Steel beam-column joints in seismic moment resisting frames", Ph.D. Dissertation, University of California, Berkeley, CA, USA.
87 Tuan-Nam, T. and Kasai, K. (2012). "Study on shaking-table experiment of a full-scale four-story steel building", Proceeding of 15th World Conference on Earthquake Engineering, Lisbon, Portugal, September.
88 Uva, G., Raffaele, D., Porco, F. and Fiore, A. (2012), "On the role of equivalent strut models in the seismic assessment of infilled RC buildings", Eng. Struct., 42, 83-94. https://doi.org/10.1016/j.engstruct.2012.04.005.   DOI