Machine learning-based predictive models for equivalent damping ratio of RC shear walls
Tóm tắt
Energy-based seismic design is being rapidly developed and suggests that the seismic demands are met by the energy dissipation capacity of the structural members. Equivalent damping ratio is a measure of energy dissipation in structural members that accounts for the post-elastic behavior of the member and provides insight regarding the dynamic response reduction during a seismic event. The present study implements a machine learning algorithm to estimate the equivalent damping ratio in reinforced concrete shear walls at displacements corresponding to a 1.0% lateral drift ratio. Five different machine learning models, namely, Robust Linear Regression, K-Nearest Neighbor Regression, Kernel Ridge Regression, Support Vector Regression, and Gaussian process regression were evaluated in order to choose the model with the highest accuracy. Among all models, Gaussian process regression, a machine learning method with successful implementation experiences in civil/structural engineering related problems, is selected to identify the equivalent damping ratio. The developed GPR-based algorithm uses a database of 161 rectangular shear walls subjected to quasi-static reversed cyclic loading with geometry and mechanical properties commonly found in building stocks of many earthquake-prone countries. The proposed algorithm estimates the equivalent damping ratio for each specimen by predicting the cyclic dissipated energy and lateral force values as two dependent variables. The model validation results show a mean coefficient of determination (R2) of about 0.89; a relative root mean square error of about 0.14 and a mean absolute percentage error of 10.44%, which is considered a substantially accurate prediction for such a complex problem. An open-source model and the entire database are provided which can be used by researchers and also design engineers. The proposed predictive model enables comparing the damping capacity of shear walls and the outcomes of this study are believed to contribute to the energy-based design or performance evaluation procedures in terms of predicting the energy capacity of shear walls.
Tài liệu tham khảo
ACI Committee 318 (2011) Building code requirements for structural concrete (ACI 318-11) and commentary. Farmington Hills: American Concrete Institute
ACI Committee 318 (2014) Building code requirements for structural concrete (ACI 318-14) and Commentary (ACI 318R-14). Farmington Hills: American Concrete Institute
Akiyama H (1985) Earthquake-resistant limit-state design for buildings. The University of Tokyo Press, Tokyo
American Society of Civil Engineers (ASCE) (2000) FEMA 356 prestandard and commentary for the seismic rehabilitation of buildings, prepared for the SAC joint venture. Washington, D.C.: Federal Emergency Management Agency
American Society of Civil Engineers (2016) ASCE/SEI 7-16, minimum design loads and associated criteria for buildings and other structures. Reston, Virginia
Applied Technology Council (1985) ATC-13, earthquake damage evaluation data for California. Redwood City, CA
Arciszewski T (1994) Machine learning in engineering design. In: Intelligent information systems III, pp 40–54. Wigry, Poland
Arciszewski T, Mustafa M, Zairko W (1987) A methodology of design knowledge acquisition for use in learning expert systems. Int J Man Mach Stud 27:23–32
Aristizabal-Ochoa JD (1983) Cracking and shear effects on structural walls. J Struct Eng 109(5):1267–1277
Arroyo O, Barros J, Ramos L (2018) Comparison of the reinforced-concrete seismic provisions of the design codes of the United States, Colombia, and ecuador for low-rise frames. Earthq Spectra 34(2):441–458
Belmouden Y, Lestuzzi P (2007) Analytical model for predicting nonlinear reversed cyclic behaviour of reinforced concrete structural walls. Eng Struct 29:1263–1276
Benavent-Climent A, López-Almansa F, Bravo-González DA (2010) Design energy input spectra for moderate-to-high seismicity regions based on Colombian earthquakes. Soil Dyn Earthq Eng 30:1129–1148
Benavent-Climent A, Escolano-Margarit D, Klenke A, Pujol S (2012) Failure mechanism of reinforced concrete structural walls with and without confinement. In: 15th world conference on earthquake engineering 2012. Lisboa, Portugal
Blandon CA, Priestley MJ (2005) Equivalent viscous damping equations for direct displacement based design. J Earthq Eng 9(2):257–278
Buttmann P (1983) Experimental determination of damping factors for walls of masonry and reinforced concrete. In: Transactions of the 7th international conference on structural mechanics in reactor technology, pp 507–511. Chicago: Amsterdam : North-Holland Physics Publishing for the Commission of the European Communities
Chopra AK (2020) Dynamics of structures: theory and applications to earthquake engineering (Fifth Edition in SI Units). Harlow: Pearson Education Limited
Chou J-S, Pham T-P-T, Nguyen T-K, Pham A-D, Ngo N-T (2020) Shear strength prediction of reinforced concrete beams by baseline, ensemble, and hybrid machine learning models. Soft Comput 24:3393–3411
Consuegra F, Irfanoglu A (2008) Variation of dynamic properties with displacement in a 3-story reinforced concrete flat plate structure. In: The 14th world conference on earthquake engineering. Beijing, China
CSA A23.3-19 (2019) Design of concrete structures. Toronto: CSA Group
Curadelli R, Riera J, Ambrosini D, Amani M (2008) Damage detection by means of structural damping identification. Eng Struct 30:3497–3504
Deger ZT, Basdogan C (2019) Empirical expressions for deformation capacity of reinforced concrete structural walls. ACI Struct J 2:53–61
Deger ZT, Basdogan C (2021) Empirical equations for shear strength of conventional reinforced concrete shear walls. ACI Struct J 118(2):61–71
Deger ZT, Taskin G (2022a) A novel GPR-based prediction model for cyclic backbone curves of reinforced concrete shear walls. Eng Struct 255:1–10
Deger Z, Taskin G (2022b) Glass-box model representation of seismic failure mode prediction for conventional reinforced concrete shear walls. Neural Comput Appl 34(8):1–13
Dindar AACY, Yüksel E, Özkaynak H, Büyüköztürk O (2015) Development of earthquake energy demand spectra. Earthq Spectra 31(3):1667–1689
Dwairi H (2004) Equivalent damping in support of direct displacement-based design with applications to multi-span bridges. (Doctorate thesis). North Carolina State University
Dwairi H, Kowalsky M (2004) Investigation of Jacobsen's equivalent viscous damping approach as applied to displacement-based seismic design. In: 13th world conference on earthquake engineering. Vancouver, Canada
Ebden M (2008) Gaussian processes for regression: a quick introduction. Retrieved from http://ftp.tuebingen.mpg.de/pub/ebio/chrisd/GPtutorial.pdf
Erberik M, Sucuoğlu H, Acun B (2012) Inelastic displacement response of RC systems with cyclic deterioration-an energy approach. J Earthq Eng 16(7):937–962
European Committee for Standardization (2004) Eurocode 8: design of structures for earthquake resistance-part 1: general rules, seismic actions and rules for buildings (EN 1998-1). Brussels: CEN
European Committee for Standardization (2005) Eurocode 8: design of structures for earthquake resistance-part 3: assessment and retrofitting of buildings (EN 1998-3). Brussels: CEN
Faraone G, Hutchinson T, Piccinin R, Silva J (2020) Damage patterns in squat and flexural RC shear walls. In: Structures congress 2020, pp 687–696. Reston: American Society of Civil Engineers
Fardis M, Panagiotakos T (1996) Hysteretic damping of reinforced concrete elements. In: Eleventh world conference on earthquake engineering. Acapulco: Elsevier Science Ltd, Paper No 464
Farrar CR, Baker WE (1995) Damping in low-aspect-ratio, reinforced concrete shear walls. Earthq Eng Struct Dyn 24:439–455
Fayyad U, Piatetsky-Shapiro G, Smyth P (1996) From data mining to knowledge discovery in databases. AI Mag 17(3):37–54
Filliben JJ (1975) The probability plot correlation coefficient test for normality. Technometrics 17(1):111–117
Ghobarah A (2004) On drift limits associated with different damage levels. In: International workshop on performance-based seismic design. Ontario: Department of Civil Engineering, McMaster University
Gulec C, Whittaker AS (2011) Empirical equations for peak shear strength of low aspect ratio reinforced concrete walls. ACI Struct J 108(1):80–89
Gulkan P, Sozen M (1974) Inelastic responses of reinforced concrete structures to earthquake motions. J Am Concr Inst 2:604–610
Hoang N-D, Pham A-D, Nguyen Q-L, Pham Q-N (2016) Estimating compressive strength of high performance concrete with gaussian process regression model. Adv Civil Eng 2:7744
Housner G (1956) Limit design of structures to resist earthquakes. In: Proceedings of the 1st world conference on earthquake engineering, pp 186–198. Berkeley: IAEE
Huang Y, Li J, Fu J (2019) Review on application of artificial intelligence in civil engineering. Comput Model Eng Sci 121(3):845–875
Hudson DE (1965) Equivalent viscous friction for hysteretic systems with earthquake-like excitations. In: 3rd world conference on earthquake engineering, pp II-185/II-201. New Zealand
Hwang SJ, Fang WH, Lee HJ, Yu HW (2001) Analytical model for predicting shear strengthof squat walls. J Struct Eng 127(1):43–50
Iwan WD (1980) Estimating inelastic response spectra from elastic spectra. Earthq Eng Struct Dyn 8:375–388
Jacobsen LS (1930) Steady forced vibrations as influenced by damping. ASME Trans 52(1):169–181
Jacobsen LS (1960) Damping in composite structures. In: Proceedings of second world conference on earthquake engineering, vol 2, pp 1029–1044. Tokyo and Kyoto
Jeon J-S, Shafieezadeh A, DesRoches R (2014) Statistical models for shear strength of RC beam-column joints using machine-learning techniques. Earthq Eng Struct Dyn 43:2075–2095
Jiang Y, Cukic B, Menzies T (2008) Can data transformation help in the detection of fault-prone modules? In: Proceedings of the 2008 workshop on defects in large software systems-DEFECTS '08, pp 16–20. Seattle: ACM Press
Kassem W, Elsheikh A (2010) Estimation of shear strength of structural shear walls. J Struct Eng 136(10):1215–1224
Kowalsky MJ, Priestley MJ, Macrae GA (1995) Displacement-based design of RC bridge columns in seismic regions. Earthq Eng Struct Dyn 24:1623–1643
Looi D, Su R (2017) Predictive seismic shear capacity model of rectangular squat RC shear walls in flexural and shear zones. In: 16th world conference on earthquake engineering. Santiago, Chile
Lu NW, Noori M, Liu Y (2017) Fatigue reliability assessment of welded steel bridge decks under stochastic truck loads via machine learning. J Bridg Eng 22:04016105
Luo H, Paal SG (2018) Machine learning-based backbone curve model of reinforced concrete columns subjected to cyclic loading reversals. J Comput Civil Eng 32(5):04018042
Mangalathu S, Jang H, Hwang S-H, Jeon J-S (2020) Data-driven machine-learning-based seismic failure mode identification of reinforced concrete shear walls. Eng Struct 208:555
Ministerio de Ambiente V and NSR-10 DT (2010) Reglamento Colombiano De Construcción Sismo Resistente. Bogota
Ministry of Interior, Disaster and Emergency Management Authority (AFAD) (2018) TBSC-2018: Turkish Building Seismic Code-2018
Miranda E, Ruiz-Garcia J (2002) Evaluation of approximate methods to estimate maximum inelastic displacement demands. Earthq Eng Struct Dyn 31:539–560
Momeni E, Dowlatshahi MB, Omidinasab F, Maizir H, Armaghani DJ (2020) Gaussian process regression technique to estimate the pile bearing capacity. Arab J Sci Eng 3:8255–8267
Montáns FJ, Chinesta F, Gómez-Bombarelli R, Kutz JN (2019) Data-driven modeling and learning in science and engineering. CR Mec 347:845–855
National Research Council of Canada (NRCC) (2015) NBC 2015, National Building Code of Canada. Ottawa, ON, Canada: Associate Commission on the National Building Code
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(4):308–313
Nie X, Wang J-J, Tao M-X, Fan J-S, Mo YL, Zhang Z-Y (2020) Experimental study of shear-critical reinforced-concrete shear walls under tension-bending shear-combined cyclic load. J Struct Eng 146(5):04020047
Oh Y-H, Han SW, Lee L-H (2002) Effect of boundary element details on the seismic deformation capacity of structural walls. Earthq Eng Struct Dyn 31:1583–1602
Orakcal K, Massone LM, Wallace JW (2009) Shear strength of lightly reinforced wall piers and spandrels. ACI Struct J 106(4):455–466
Özkaynak H (2010) The earthquake behavior of RC frames with fiber polymer confined infill walls and their structural damping properties. (Doctorate thesis). Istanbul Technical University, (in Turkish)
Ozkaynak H, Yuksel E, Yalcin C, Dindar AA, Buyukozturk O (2014) Masonry infill walls in reinforced concrete frames as a source of structural damping. Earthq Eng Struct Dyn 43:949–968
Pan H, Azimi M, Yan F, Lin ZB (2018) Time-frequency-based data-driven structural diagnosis and damage detection for cable-stayed bridges. J Bridg Eng 23(6):04018033
Park H, Eom T (2004) Energy dissipation capacity of reinforced concrete members. In: CTBUH 2004 Seoul conference, pp 378–384. Seoul, South Korea: Council on Tall Buildings and Urban Habitat
Park R (2003) Earthquake resistant structures. In: Milne I, Ritchie R, Karihaloo B (eds) Comprehensive structural integrity. Elsevier Science Ltd., London, pp 271–303
Priestley MJ (2003) Myths and fallacies in earthquake engineering, revisited: the Ninth Mallet Milne Lecture, 2003. IUSS press, Pavia
Priestley MJ, Calvi GM, Kowalsky MJ (2007) Displacement based seismic design of structures, 1st edn. IUSS Press, Pavia
Rasmussen CE (2004) Gaussian processes in machine learning. In: Bousquet O, Luxburg UV, Rätsch G (eds) Advanced lectures on machine learning. Springer, Berlin, pp 67–75
Rasmussen CE, Nickisch H (2010) Gaussian processes for machine learning (GPML) toolbox. J Mach Learn Res 11:3011–3015
Reich Y (1996) Machine learning techniques for civil engineering problems. Comput-Aided Civil Infrastruct Eng 6:5555
Rosenblueth E, Herrera I (1964) On a kind of hysteretic damping. J Eng Mech Div 90(EM4):37–49
Rossetto T, Elnashai A (2003) Derivation of vulnerability functions for European-type RC structures based on observational data. Eng Struct 25:1241–1263
Salonikios TN, Kappos AJ, Tegos IA, Penelis GG (1999) Cyclic load behavior of low-slenderness reinforced concrete walls: design basis and test results. ACI Struct J 96(4):649–661
Schulz E, Speekenbrink M, Krause A (2018) A tutorial on gaussian process regression: modelling, exploring, and exploiting functions. J Math Psychol 85:1–16
Sengupta P, Li B (2014) Hysteresis behavior of reinforced concrete walls. J Struct Eng 5:04014030
Shegay A, Motter C, Henry R, Elwood K (2015) A database for investigating NZS3101 structural wall provisions. In: Proceedings of the tenth Pacific conference on earthquake engineering. Sydney, Australia
Sheibani M, Ou G (2020) The development of Gaussian process regression for effective regional post-earthquake building damage inference. Comput-Aided Civil Infrastruct Eng 2:1–24
Siam A, Ezzeldin M, El-Dakhakhni W (2019) Machine learning algorithms for structural performance classifications and predictions: application to reinforced masonry shear walls. Structures 22:252–265
Song I, Cho IH, Wong RK (2020) An advanced statistical approach to data-driven earthquake engineering. J Earthq Eng 24(8):1245–1269
Song JK, Chun YS, Song JW, Yang KH, Chang KK (2019) Seismic performance of special structural walls using overlapping hoops instead of closed hoops. J Concrete Struct Mater 13:1–17
Su RK, Wong SM (2007) Seismic behaviour of slender reinforced concrete shear walls under high axial load ratio. Eng Struct 29:1957–1965
Sullivan TJ (2018) Highlighting differences between force-based and displacement-based design solutions for reinforced concrete frame structures. Struct Eng Int 2:122–131
Trifunac M, Brady A (1975) A study on the duration of strong earthquake ground motion. Bull Seismol Soc Am 65:581–626
Tseranidis S, Brown NC, Mueller CT (2016) Data-driven approximation algorithms for rapid performance evaluation and optimization of civil structures. Autom Constr 72:279–293
Vu D-T, Hoang N-D (2016) Punching shear capacity estimation of FRP-reinforced concrete slabs using a hybrid machine learning approach. Struct Infrastruct Eng 12(9):1153–1161
Wallace JW (2012) Performance of structural walls in recent earthquakes and tests and implications for US building codes. In: 15th world conference on. earthquake engineering. Lisbon, Portugal
Yan S, Zhang LF, Zhang, YG (2008) Seismic performances of high-strength concrete shear walls reinforced with high-strength rebars. In: 11th Biennial ASCE aerospace division international conference on engineering, science, construction, and operations in challenging environments, pp 1–8. Long Beach, California, USA
Yang H-K, Park H-G (2021) Damping ratio of RC squat wall with limited damage under high-frequency earthquake. J Struct Eng 147(1):04020295
Zaharia R, Taucer F (2008) Equivalent period and damping for EC8 spectral response of SDOF ring-spring hysteretic models. Italy
Zhang WG, Goh AT, Zhang YM (2016) Multivariate adaptive regression splines application for multivariate geotechnical problems with big data. Geotech Geol Eng 34:193–204