Abstract
Seismic fragility curves provide a powerful tool to assess the reliability of structures. However, conventional fragility analysis of structures comprising a large number of components requires enormous computational efforts. In this paper, the application of probabilistic support vector machines (PSVM) for the system fragility analysis of existing structures is proposed. It is demonstrated that support vector machine based fragility curves provide accurate predictions compared to rigorous methodologies such as component based fragilities developed by Monte Carlo simulations. The proposed method is applied to an existing bridge structure in order to develop fragility curves for serviceability and collapse limit states. In addition, the efficiency of using the PSVM method in the application of vector-valued ground motion intensity measures (IM) as well as traditional single-valued IM are investigated. The results obtained from an incremental dynamic analysis of the structure are used to train PSVMs. The application of PSVM in binary and multi-class classifications is used for the fragility analysis and reliability assessment of the bridge structure.
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References
Atkinson GM, Boore DM (2006) Earthquake ground-motion prediction equations for eastern North America. Bull Seismol Soc Am 96:2181–2205
Baker JW (2011) Conditional mean spectrum: tool for ground motion selection. J Struct Eng 137(3):322–331
Baker JW, Cornell CA (2005) A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 34:1193–1217
Baker JW, Cornell CA (2006) Spectral shape, epsilon and record selection. Earthq Eng Struct Dyn 34(10):1193–1217
Baker JW, Jayaram N (2008) Correlation of spectral acceleration values from NGA ground motion models. Earthq Spectra 24(1):299–317
Bignell JL, Lafave JM, Wilkey JP, Hawkins NM (2004) Seismic evaluation of vulnerable highway bridges with wall piers on emergency routes in southern illinois. In: 13th world conference on eartquake engineering, Vancouver, BC, Canada
Boore DM, Atkinson GM (2008) Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s. Earthqu Spectra 24:99–138
Breiman L, Spector P (1992) Submodel selection and evaluation in regression. The X-random case. Int Stat Rev (revue internationale de Statistique) 60(3):291–319
Bucher CG, Bourgund UA (1990) Fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57–66
Cherkassky V, Mulier F (2007) Learning from data: concepts, theory, and methods. Wiley, New York
Choi E, DesRoches R, Nielson B (2004) Seismic fragility of typical bridges in moderate seismic zones. Eng Struct 26(2):187–199
Cornell AC, Jalayer F, Hamburger RO (2002) Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. J Struct Eng 128(4):526–532
Cortes C, Vapnik VN (1995) Support vector networks. Mach Learn 20(3):273–297
Duan KB, Keerthi SS (2005) Which is the best multiclass SVM method? An empirical study. In: Oza NC, Polikar R, Kittler J, Roli F (eds) Multiple classifier systems, vol 3541. Springer, Berlin, pp 278–285
Ge M, Du R, Zhang G, Xu Y (2004) Fault diagnosis using support vector machine with an application in sheet metal stamping operations. Mech Syst Signal Process 18:143–159
Guan XL, Melchers RE (2001) Effect of response surface parameter variation on structural reliability estimates. Struct Saf 23:429–444
Guo Z, Bai G (2009) Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut 22(2):160–166
Hastie T, Tibshirani R (1998) Classification by pairwise coupling. In: Jordan MI, Kearns MJ, Solla AS (eds) Advances in neural information processing systems 10. MIT Press, Cambridge
Hurtado JE (2004) An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory. Struct Saf 26(3):271–293
Hurtado JE, Alvarez DA (2003) A classification approach for reliability analysis with stochastic finite element modelling. J Struct Eng 129:1141–1149
Hwang H, Huo JR (1998) Probabilistic seismic damage assessment of highway bridges. In: The 6th U.S. National conference on earthquake engineering, Seattle, Washington, June, 1998
Hwang H, Jernigan JB, Lin Y (2000) Evaluation of seismic damage to memphis bridges and highway systems. J Bridge Eng 5(4):322–330
Jack LB, Nandi AK (2002) Fault detection using support vector machines and artificial neural networks, augmented by genetic algorithms. Mech Syst Signal Process 16(2–3):373–390
Kennedy RP, Cornell CA, Campbell RD, Kaplan S, Perla HF (1980) Probabilistic seismic safety study of an existing nuclear power plant. Nucl Eng Des 59:315–338
Li HS, Lu ZZ, Yue ZF (2006) Support vector machine for structural reliability analysis. Appl Math Mech 27:1295–1303
Lin HT, Lin CJ, Weng RC (2003) A note on Platt’s probabilistic outputs for support vector machines. http://www.csie.ntu.edu.tw/˜cjlin/papers/plattprob.ps
Mackie K, Stojadinovic B (2002) Relation between probabilistic seismic demand analysis and incremental dynamic analysis. In: 7th US National Conference on earthquake engineering, Boston, MA
Mahmoudi SN (2015) Seismic fragility assessment of highway bridges. PhD thesis, McGill University, Montreal, Canada
Mahmoudi SN, Chouinard L (2013) Bayesian updating and structural model validation of bridges based on ambient vibration tests. In: 3rd specialty conference on material engineering and applied mechanics, CSCE, Montreal, Canada
Mander JB, Priestley MJN, Park R (1988) Theoretical stress-strain model of confined concrete. J Struct Eng 114(8):1804–1826
Nielson BG, DesRoches R (2007) Seismic fragility methodology for highway bridges using a component level approach. Earthq Eng Struct Dyn 36:823–839
Platt JC (1998) Sequential minimal optimization: a fast algorithm for training support vector machines. In: Microsoft research technical report, MSR-TR-98-14, Microsoft, Redmond, Washington
Platt JC (1999) Probabilistic outputs for support vector machines and comparison to regularized likelihood methods. In: Smola AJ, Bartlett P, Schölkopf B, Schuurmans D (eds) Advances in large margin classifiers. MIT Press, Cambridge, pp 61–74
Priestley MJN, Calvi GM, Kowalsky MJ (2007) Direct displacement-based seismic design of structures. In: 2007 NZSEE conference
Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220
Rocco CM, Moreno JA (2002) Fast Monte Carlo reliability evaluation using support vector machine. Reliab Eng Syst Saf 76(3):237–243
SAP2000 (1996) Integrated finite element analysis and design of structures: analysis reference. Computers and Structures, Inc., Berkeley
Shamsabadi A, Rollins KM, Kapuskar M (2007) Nonlinear soil-abutment-bridge structure interaction for seismic performance-based design. J Geotech Geoenviron Eng 133(6):707–720
Shinozuka M, Constantinou MC (1998) Development of bridge fragility curves. Technical Report, No. 98-0015. US Muticisplinary Center for Earthquake Engineering Research, pp 249–256
Shinozuka M, Feng MQ, Kim H, Uzawa T, Ueda T (2003) Statistical analysis of fragility curves. Report No. MCEER-03-0002, MCEER
Song J, Kang WH (2009) System reliability and sensitivity under statistical dependence by matrix-based system reliability method. Struct Saf 31(2):148–156
Unnikrishnan VU, Prasad AM, Rao BN (2013) Development of fragility curves using high-dimensional model representation. Earthq Eng Struct Dyn 42(3):419–430
Vamvatsikos D, Cornell AC (2002) Incremental dynamic analysis. Earthq Eng Struct Dyn 31:491–514
Vapnik VN (1995) The nature of statistical learning theory. Springer, New York
Widodo A, Yang B (2007) Support vector machine in machine condition monitoring and fault diagnosis. Mech Syst Signal Process 21:2560–2574
Wu TF, Lin CJ, Weng RC (2004) Probability estimates for multi-class classification by pairwise coupling. J Mach Learn Res 5:975–1005
Zhu L (2005) Probabilistic drift capacity model for reinforced concrete columns. MSc Thesis, University of British Columbia, Canada
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Mahmoudi, S.N., Chouinard, L. Seismic fragility assessment of highway bridges using support vector machines. Bull Earthquake Eng 14, 1571–1587 (2016). https://doi.org/10.1007/s10518-016-9894-7
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DOI: https://doi.org/10.1007/s10518-016-9894-7