Resilience Assessment under Imprecise Probability
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 2
Abstract
Resilience analysis of civil structures and infrastructure systems is a powerful approach to quantifying an object’s ability to prepare for, recover from, and adapt to disruptive events. The resilience is typically measured probabilistically by the integration of the time-variant performance function, which is by nature a stochastic process as it is affected by many uncertain factors such as hazard occurrences and posthazard recoveries. Resilience evaluation could be challenging in many cases with imprecise probability information on the time-variant performance function. In this paper, a novel method for the assessment of imprecise resilience is presented, which deals with resilience problems with nonprobabilistic performance function. The proposed method, producing lower and upper bounds for imprecise resilience, has benefited from that for imprecise reliability as documented in the literature, motivated by the similarity between reliability and resilience. Two types of stochastic processes, namely log-Gamma and lognormal processes, are employed to model the performance function, with which the explicit form of resilience is derived. Moreover, for a planning horizon within which the hazards may occur for multiple times, the incompletely informed performance function results in “time-dependent imprecise resilience,” which is dependent on the duration of the service period (e.g., life cycle) and can also be handled by applying the proposed method. Through examining the time-dependent resilience of a strip foundation in a coastal area subjected to groundwater intrusion in a changing climate, the applicability of the proposed resilience bounding method is demonstrated. The impact of imprecise probability information on resilience is quantified through sensitivity analysis.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research described in this paper was supported by the Career Development Fellowship for Cao Wang from the University of Wollongong. This support is gratefully acknowledged.
References
Alvarez, D. A., and J. E. Hurtado. 2014. “An efficient method for the estimation of structural reliability intervals with random sets, dependence modeling and uncertain inputs.” Comput. Struct. 142 (Sep): 54–63. https://doi.org/10.1016/j.compstruc.2014.07.006.
Attoh-Okine, N. O., A. T. Cooper, and S. A. Mensah. 2009. “Formulation of resilience index of urban infrastructure using belief functions.” IEEE Syst. J. 3 (2): 147–153. https://doi.org/10.1109/JSYST.2009.2019148.
Augustin, T., F. P. Coolen, G. De Cooman, and M. C. Troffaes. 2014. Introduction to imprecise probabilities. New York: Wiley.
Beer, M., S. Ferson, and V. Kreinovich. 2013. “Imprecise probabilities in engineering analyses.” Mech. Syst. Signal Process. 37 (1–2): 4–29. https://doi.org/10.1016/j.ymssp.2013.01.024.
Bocchini, P., D. M. Frangopol, T. Ummenhofer, and T. Zinke. 2014. “Resilience and sustainability of civil infrastructure: Toward a unified approach.” J. Infrastruct. Syst. 20 (2): 04014004. https://doi.org/10.1061/(ASCE)IS.1943-555X.0000177.
Bruneau, M., S. E. Chang, R. T. Eguchi, G. C. Lee, T. D. O’Rourke, A. M. Reinhorn, M. Shinozuka, K. Tierney, W. A. Wallace, and D. Von Winterfeldt. 2003. “A framework to quantitatively assess and enhance the seismic resilience of communities.” Earthquake Spectra 19 (4): 733–752. https://doi.org/10.1193/1.1623497.
Cimellaro, G. P., A. M. Reinhorn, and M. Bruneau. 2010. “Framework for analytical quantification of disaster resilience.” Eng. Struct. 32 (11): 3639–3649. https://doi.org/10.1016/j.engstruct.2010.08.008.
Coolen, F. 2004. “On the use of imprecise probabilities in reliability.” Qual. Reliab. Eng. Int. 20 (3): 193–202. https://doi.org/10.1002/qre.560.
Dang, C., P. Wei, M. G. Faes, and M. Beer. 2022. “Bayesian probabilistic propagation of hybrid uncertainties: Estimation of response expectation function, its variable importance and bounds.” Comput. Struct. 270 (Oct): 106860. https://doi.org/10.1016/j.compstruc.2022.106860.
Dubois, D., and H. Prade. 1989. “Fuzzy sets, probability and measurement.” Eur. J. Oper. Res. 40 (2): 135–154. https://doi.org/10.1016/0377-2217(89)90326-3.
Ellingwood, B. R. 2005. “Risk-informed condition assessment of civil infrastructure: State of practice and research issues.” Struct. Infrastruct. Eng. 1 (1): 7–18. https://doi.org/10.1080/15732470412331289341.
El Maaddawy, T., and K. Soudki. 2007. “A model for prediction of time from corrosion initiation to corrosion cracking.” Cem. Concr. Compos. 29 (3): 168–175. https://doi.org/10.1016/j.cemconcomp.2006.11.004.
Faes, M. G., M. Broggi, G. Chen, K.-K. Phoon, and M. Beer. 2022. “Distribution-free p-box processes based on translation theory: Definition and simulation.” Probab. Eng. Mech. 69 (Jul): 103287. https://doi.org/10.1016/j.probengmech.2022.103287.
Faes, M. G., M. Daub, S. Marelli, E. Patelli, and M. Beer. 2021a. “Engineering analysis with probability boxes: A review on computational methods.” Struct. Saf. 93 (Nov): 102092. https://doi.org/10.1016/j.strusafe.2021.102092.
Faes, M. G., M. A. Valdebenito, D. Moens, and M. Beer. 2020. “Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading.” Comput. Struct. 239 (Oct): 106320. https://doi.org/10.1016/j.compstruc.2020.106320.
Faes, M. G., M. A. Valdebenito, D. Moens, and M. Beer. 2021b. “Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities.” Mech. Syst. Signal Process. 152 (May): 107482. https://doi.org/10.1016/j.ymssp.2020.107482.
Faes, M. G., M. A. Valdebenito, X. Yuan, P. Wei, and M. Beer. 2021c. “Augmented reliability analysis for estimating imprecise first excursion probabilities in stochastic linear dynamics.” Adv. Eng. Software 155 (Mar): 102993. https://doi.org/10.1016/j.advengsoft.2021.102993.
Ferson, S., V. Kreinovich, L. Ginzburg, D. S. Myers, and K. Sentz. 2003. Constructing probability boxes and Dempster-Shafer structures. Albuquerque, NM: Sandia National Laboratories.
Kahle, W., S. Mercier, and C. Paroissin. 2016. Chap. 2 in Gamma processes, 49–148. New York: Wiley.
Kahraman, C., B. Öztayşi, and S. Çevik Onar. 2016. “A comprehensive literature review of 50 years of fuzzy set theory.” Supplement, Int. J. Comput. Intell. Syst. 9 (S1): 3–24. https://doi.org/10.1080/18756891.2016.1180817.
Li, Q., and X. Ye. 2018. “Surface deterioration analysis for probabilistic durability design of RC structures in marine environment.” Struct. Saf. 75 (Nov): 13–23. https://doi.org/10.1016/j.strusafe.2018.05.007.
Limbourg, P., and E. De Rocquigny. 2010. “Uncertainty analysis using evidence theory–confronting level-1 and level-2 approaches with data availability and computational constraints.” Reliab. Eng. Syst. Saf. 95 (5): 550–564. https://doi.org/10.1016/j.ress.2010.01.005.
Melchers, R. E., and A. T. Beck. 2018. Structural reliability analysis and prediction. New York: Wiley.
National Research Council. 2012a. Disaster resilience: A national imperative. Washington, DC: The National Academies Press.
National Research Council. 2012b. Sea-level rise for the coasts of California, Oregon, and Washington: Past, present, and future. Washington, DC: The National Academies Press.
Oberguggenberger, M., and W. Fellin. 2008. “Reliability bounds through random sets: Non-parametric methods and geotechnical applications.” Comput. Struct. 86 (10): 1093–1101. https://doi.org/10.1016/j.compstruc.2007.05.040.
Penmetsa, R. C., and R. V. Grandhi. 2002. “Efficient estimation of structural reliability for problems with uncertain intervals.” Comput. Struct. 80 (12): 1103–1112. https://doi.org/10.1016/S0045-7949(02)00069-X.
Ross, S. M. 2014. Introduction to probability models. Cambridge, MA: Academic Press.
Shinozuka, M. 1971. “Simulation of multivariate and multidimensional random processes.” J. Acoust. Soc. Am. 49 (1B): 357–368. https://doi.org/10.1121/1.1912338.
Utkin, L. V., and F. P. Coolen. 2007. Imprecise reliability: An introductory overview, 261–306. New York: Springer.
Vidal, T., A. Castel, and R. François. 2004. “Analyzing crack width to predict corrosion in reinforced concrete.” Cem. Concr. Res. 34 (1): 165–174. https://doi.org/10.1016/S0008-8846(03)00246-1.
Walley, P. 2000. “Towards a unified theory of imprecise probability.” Int. J. Approx. Reason. 24 (May): 125–148. https://doi.org/10.1016/S0888-613X(00)00031-1.
Wang, C. 2021a. “Explicitly assessing the durability of RC structures considering spatial variability and correlation.” Infrastructures 6 (11): 156. https://doi.org/10.3390/infrastructures6110156.
Wang, C. 2021b. Structural reliability and time-dependent reliability. New York: Springer.
Wang, C. 2023. “A generalized index for functionality-sensitive resilience quantification.” Resilient Cities Struct. 2 (1): 68–75. https://doi.org/10.1016/j.rcns.2023.02.001.
Wang, C., and B. M. Ayyub. 2022. “Time-dependent resilience of repairable structures subjected to nonstationary load and deterioration for analysis and design.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 8 (3): 04022021. https://doi.org/10.1061/AJRUA6.0001246.
Wang, C., B. M. Ayyub, and W. G. P. Kumari. 2023. “Resilience model for coastal-building foundations with time-variant soil strength due to water intrusion in a changing climate.” Rock Soil Mech. 44 (1): 67–74.
Wang, C., H. Zhang, and M. Beer. 2018. “Computing tight bounds of structural reliability under imprecise probabilistic information.” Comput. Struct. 208 (Oct): 92–104. https://doi.org/10.1016/j.compstruc.2018.07.003.
Wei, P., J. Song, S. Bi, M. Broggi, M. Beer, Z. Lu, and Z. Yue. 2019. “Non-intrusive stochastic analysis with parameterized imprecise probability models: I. Performance estimation.” Mech. Syst. Signal Process. 124 (Jun): 349–368. https://doi.org/10.1016/j.ymssp.2019.01.058.
Wu, D., W. Gao, F. Tin-Loi, and Y. Pi. 2016. “Probabilistic interval limit analysis for structures with hybrid uncertainty.” Eng. Struct. 114 (May): 195–208. https://doi.org/10.1016/j.engstruct.2016.02.015.
Wu, W.-Z., Y. Leung, and W.-X. Zhang. 2002. “Connections between rough set theory and Dempster-Shafer theory of evidence.” Int. J. Gen. Syst. 31 (4): 405–430. https://doi.org/10.1080/0308107021000013626.
Zhang, H. 2012. “Interval importance sampling method for finite element-based structural reliability assessment under parameter uncertainties.” Struct. Saf. 38 (Sep): 1–10. https://doi.org/10.1016/j.strusafe.2012.01.003.
Zhang, H., R. L. Mullen, and R. L. Muhanna. 2010. “Interval Monte Carlo methods for structural reliability.” Struct. Saf. 32 (3): 183–190. https://doi.org/10.1016/j.strusafe.2010.01.001.
Zhang, J., and M. D. Shields. 2019. “Efficient monte carlo resampling for probability measure changes from Bayesian updating.” Probab. Eng. Mech. 55 (Jan): 54–66. https://doi.org/10.1016/j.probengmech.2018.10.002.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 2 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Sep 26, 2023
Accepted: Jan 11, 2024
Published online: Mar 28, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 28, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.