Extended and Generalized Fragility Functions
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
Fragility functions indicate the probability of a system exceeding certain damage states given some appropriate measures that characterize recorded or simulated data series. Presented in two main parts, this paper develops fragility functions in their utmost generality, accounting for both (1) multivariate intensity measures with multiple damage states and (2) longitudinal damage state dependencies in time. Without adopting the limiting assumption of common variance to avoid improper function crossings, the first part presents what is here compactly termed as extended fragility functions. As shown, these are best supported by the softmax function for any arbitrary distribution of the exponential family to which the intensity measures of different states may belong, including the typically used normal distribution in the logarithmic scale of intensity measures. In the second part, generalized fragility functions are introduced for cases where multiple system state transitions need to be captured. To that end, dependent Markov and hidden Markov models are employed because they are able to portray longitudinal data dependencies and reveal intrinsic deterioration trends for multiple sequential events. Numerical results are presented, together with underlying implementation details, statistical properties, and practical suggestions.
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References
Agresti, A., and M. Kateri. 2011. Categorical data analysis. Heidelberg, Germany: Springer.
Andriotis, C. P., I. Gkimousis, and V. Koumousis. 2015. “Modeling reinforced concrete structures using smooth plasticity and damage models.” J. Struct. Eng. 142 (2): 04015105. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001365.
Baker, J. W. 2007. “Probabilistic structural response assessment using vector-valued intensity measures.” Earthquake Eng. Struct. Dyn. 36 (13): 1861–1883. https://doi.org/10.1002/eqe.700.
Baker, J. W. 2015. “Efficient analytical fragility function fitting using dynamic structural analysis.” Earthquake Spectra 31 (1): 579–599. https://doi.org/10.1193/021113EQS025M.
Barbato, M., F. Petrini, V. U. Unnikrishnan, and M. Ciampoli. 2013. “Performance-based hurricane engineering (PBHE) framework.” Struct. Saf. 45: 24–35. https://doi.org/10.1016/j.strusafe.2013.07.002.
Bengio, Y., and P. Frasconi. 1996. “Input-output HMMs for sequence processing.” IEEE Transact. Neural Networks 7 (5): 1231–1249. https://doi.org/10.1109/72.536317.
Bishop, C. M. 1995. Neural networks for pattern recognition. Oxford, UK: Oxford University Press.
Cornell, C. A., and H. Krawinkler. 2000. “Progress and challenges in seismic performance assessment.” PEER Center News 3 (2): 1–3.
Domingos, P., and M. Pazzani. 1997. “On the optimality of the simple Bayesian classifier under zero-one loss.” Mach. Learn. 29 (2): 103–130. https://doi.org/10.1023/A:1007413511361.
Gardoni, P., A. Der Kiureghian, and K. M. Mosalam. 2002. “Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations.” J. Eng. Mech. 128 (10): 1024–1038. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1024).
Ghahramani, Z. 2001. “An introduction to hidden Markov models and Bayesian networks.” Int. J. Pattern Recogn. Artif. Intell. 15 (1): 9–42. https://doi.org/10.1142/S0218001401000836.
Grigoriu, M. 2010. “To scale or not to scale seismic ground-acceleration records.” J. Eng. Mech. 137 (4): 284–293. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000226.
Jalayer, F. 2003. “Direct probabilistic seismic anaysis: Implementing non-linear dynamic assessments.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Stanford Univ.
Jalayer, F., and C. A. Cornell. 2009. “Alternative non-linear demand estimation methods for probability-based seismic assessments.” Earthquake Eng. Struct. Dyn. 38 (8): 951–972. https://doi.org/10.1002/eqe.876.
Jalayer, F., P. Franchin, and P. E. Pinto. 2007. “A scalar damage measure for seismic reliability analysis of RC frames.” Earthquake Eng. Struct. Dyn. 36 (13): 2059–2079. https://doi.org/10.1002/eqe.704.
Kafali, C., and M. Grigoriu. 2007. “Seismic fragility analysis: Application to simple linear and nonlinear systems.” Earthquake Eng. Struct. Dyn. 36 (13): 1885–1900. https://doi.org/10.1002/eqe.726.
Lallemant, D., A. Kiremidjian, and H. Burton. 2015. “Statistical procedures for developing earthquake damage fragility curves.” Earthquake Eng. Struct. Dyn. 44 (9): 1373–1389. https://doi.org/10.1002/eqe.2522.
Luco, N., and P. Bazzurro. 2007. “Does amplitude scaling of ground motion records result in biased nonlinear drift responses?” Earthquake Eng. Struct. Dyn. 36 (13): 1813–1835. https://doi.org/10.1002/eqe.695.
McCullagh, P., and J. A. Nedler. 1989. Generalized linear models. London: Chapman and Hall.
Murphy, K. P. 2012. Machine learning: A probabilistic perspective. Cambridge, MA: MIT Press.
Papakonstantinou, K. G., C. P. Andriotis, and M. Shinozuka. 2018. “POMDP and MOMDP solutions for structural life-cycle cost minimization under partial and mixed observability.” Struct. Infrastruct. Eng. 14 (7): 869–882. https://doi.org/10.1080/15732479.2018.1439973.
Papakonstantinou, K. G., and M. Shinozuka. 2013. “Probabilistic model for steel corrosion in reinforced concrete structures of large dimensions considering crack effects.” Eng. Struct. 57: 306–326. https://doi.org/10.1016/j.engstruct.2013.06.038.
Papakonstantinou, K. G., and M. Shinozuka. 2014a. “Optimum inspection and maintenance policies for corroded structures using partially observable Markov decision processes and stochastic, physically based models.” Probab. Eng. Mech. 37: 93–108. https://doi.org/10.1016/j.probengmech.2014.06.002.
Papakonstantinou, K. G., and M. Shinozuka. 2014b. “Planning structural inspection and maintenance policies via dynamic programming and Markov processes. Part I: Theory.” Reliab. Eng. Syst. Saf. 130: 202–213. https://doi.org/10.1016/j.ress.2014.04.005.
Papakonstantinou, K. G., and M. Shinozuka. 2014c. “Planning structural inspection and maintenance policies via dynamic programming and Markov processes. Part II: POMDP implementation.” Reliab. Eng. Syst. Saf. 130: 214–224. https://doi.org/10.1016/j.ress.2014.04.006.
Porter, K., R. Kennedy, and R. Bachman. 2007. “Creating fragility functions for performance-based earthquake engineering.” Earthquake Spectra 23 (2): 471–489. https://doi.org/10.1193/1.2720892.
Rabiner, L. R. 1989. “A tutorial on hidden Markov models and selected applications in speech recognition.” Proc. IEEE 77 (2): 257–286. https://doi.org/10.1109/5.18626.
Sanchez-Silva, M., D. M. Frangopol, J. Padgett, and M. Soliman. 2016. “Maintenance and operation of infrastructure systems: Review.” J. Struct. Eng. 142 (9): F4016004. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001543.
Shinozuka, M., M. Q. Feng, H. Kim, T. Uzawa, and T. Ueda 2003. Statistical analysis of fragility curves. Buffalo, NY: State Univ. of New York at Buffalo.
Shinozuka, M., M. Q. Feng, J. Lee, and T. Naganuma. 2000. “Statistical analysis of fragility curves.” J. Eng. Mech. 126 (12): 1224–1231. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:12(1224).
Straub, D., and A. Der Kiureghian. 2008. “Improved seismic fragility modeling from empirical data.” Struct. Saf. 30 (4): 320–336. https://doi.org/10.1016/j.strusafe.2007.05.004.
Vamvatsikos, D. 2015. “Analytic fragility and limit states [P(EDP|IM)]: Nonlinear dynamic procedures.” In Encyclopedia of earthquake engineering, 87–94. Berlin, Germany: Springer.
Vamvatsikos, D., and C. A. Cornell. 2002. “Incremental dynamic analysis.” Earthquake Eng. Struct. Dyn. 31 (3): 491–514. https://doi.org/10.1002/eqe.141.
Visser, I., and M. Speekenbrink. 2010. “depmixS4: An R-package for hidden Markov models.” J. Stat. Software 36 (7): 1–21. https://doi.org/10.18637/jss.v036.i07.
Vlachos, C., K. G. Papakonstantinou, and G. Deodatis. 2016. “A multi-modal analytical non-stationary spectral model for characterization and stochastic simulation of earthquake ground motions.” Soil Dyn. Earthquake Eng. 80: 177–191. https://doi.org/10.1016/j.soildyn.2015.10.006.
Vlachos, C., K. G. Papakonstantinou, and G. Deodatis. 2018. “Predictive model for site specific simulation of ground motions based on earthquake scenarios.” Earthquake Eng. Struct. Dyn. 47 (1): 195–218. https://doi.org/10.1002/eqe.2948.
Yang, T. Y., J. Moehle, B. Stojadinovic, and A. Der Kiureghian. 2009. “Seismic performance evaluation of facilities: Methodology and implementation.” J. Struct. Eng 135 (10): 1146–1154. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:10(1146).
Yazdi, A. J., T. Haukaas, T. Yang, and P. Gardoni. 2016. “Multivariate fragility models for earthquake engineering.” Earthquake Spectra 32 (1): 441–461. https://doi.org/10.1193/061314EQS085M.
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©2018 American Society of Civil Engineers.
History
Received: Jul 16, 2017
Accepted: Jan 18, 2018
Published online: Jul 4, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 4, 2018
ASCE Technical Topics:
- Arbitration
- Business management
- Deterioration
- Dispute resolution
- Engineering fundamentals
- Legal affairs
- Markov process
- Materials characterization
- Materials engineering
- Mathematics
- Measurement (by type)
- Methodology (by type)
- Numerical methods
- Practice and Profession
- Probability
- Statistics
- Stochastic processes
- Time dependence
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