Technical Papers
Oct 31, 2019

Analytic Probabilistic Safety Analysis under Severe Uncertainty

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6, Issue 1

Abstract

Exact analytic expressions are given to evaluate the reliability of systems consisting of components, connected in parallel or series, subject to imprecise failure distributions. We also proposed a simplified version of the first-order reliability method to deal with imprecision. This development allows engineers to evaluate the reliability of systems without having to resort to optimization techniques and/or Monte Carlo simulation. In addition, this framework does not need to assume a distribution for the epistemic uncertainty, which permits a robust analysis even with limited data. In this way, the approach removes a significant barrier to the modeling of epistemic uncertainties in industrial probabilistic safety analysis workflows.

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Acknowledgments

This research has been generously supported by the EPSRC Centre for Doctoral Training in Nuclear Fission - Next Generation Nuclear (Grant No. EP/L015390/1) which is gratefully acknowledged by the authors. The authors express their gratitude for insightful discussion regarding the industrial application of PSA with Professor Nawal K. Prinja (Technology Director of Clean Energy, Wood plc).

References

Alvarez, D. A., J. E. Hurtado, and J. Ramrez. 2017. “Tighter bounds on the probability of failure than those provided by random set theory.” Comput. Struct. 189 (Sep): 101–113. https://doi.org/10.1016/j.compstruc.2017.04.006.
ASCE. 2005. Seismic design criteria for structures, systems, and components in nuclear facilities. ASCE/SEI 43. Reston, VA: ASCE.
Balch, M. S. 2016. “A corrector for probability dilution in satellite conjunction analysis.” In Proc., 18th AIAA Non-Deterministic Approaches Conf., 1445. Reston, VA: American Institute of Aeronautics and Astronautics.
Balch, M. S., R. Martin, and S. Ferson. 2017. “Satellite conjunction analysis and the false confidence theorem.” Preprint, submitted June 26, 2017. https://arxiv.org/abs/1706.08565.
Beer, M., and E. Patelli. 2015. “Editorial: Engineering analysis with vague and imprecise information.” Struct. Saf. 52 (Part B): 143. https://doi.org/10.1016/j.strusafe.2014.11.001.
Braverman, J., J. Xu, B. Ellingwood, C. Costantino, R. Morante, and C. Hofmayer. 2007. Evaluation of the seismic design criteria in ASCE/SEI standard 43-05 for application to nuclear power plants. Washington, DC: US Nuclear Regulatory Commission.
Budnitz, R. J., P. J. Amico, C. A. Cornell, W. J. Hall, R. P. Kennedy, J. W. Reed, and M. Shinozuka. 1985. Approach to the quantification of seismic margins in nuclear power plants. Livermore, CA: Lawrence Livermore National Laboratory.
Canadian Nuclear Safety Commission. 2005. Probabilistic safety assessment (PSA) for nuclear power plants. Ottawa: Canadian Nuclear Safety Commission.
Collet, J. 1996. “Some remarks on rare-event approximation.” IEEE Trans. Reliab. 45 (1): 106–108. https://doi.org/10.1109/24.488924.
de Angelis, M., E. Patelli, and M. Beer. 2015. “Advanced line sampling for efficient robust reliability analysis.” Struct. Saf. 52 (Jan): 170–182. https://doi.org/10.1016/j.strusafe.2014.10.002.
Faes, M., J. Sadeghi, M. Broggi, M. de Angelis, E. Patelli, M. Beer, and D. Moens. 2019. “On the robust estimation of small failure probabilities for strong non-linear models.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part B: Mech. Eng. 5 (4): 041007. https://doi.org/10.1115/1.4044044.
Feng, G., E. Patelli, M. Beer, and F. P. Coolen. 2016. “Imprecise system reliability and component importance based on survival signature.” Reliab. Eng. Syst. Saf. 150 (Jun): 116–125. https://doi.org/10.1016/j.ress.2016.01.019.
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.
Jiang, C., J. Zheng, and X. Han. 2018. “Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: A review.” Struct. Multidiscip. Optim. 57 (6): 2485–2502. https://doi.org/10.1007/s00158-017-1864-4.
Kaplan, S., V. M. Bier, and D. C. Bley. 1994. “A note on families of fragility curves—Is the composite curve equivalent to the mean curve?” Reliab. Eng. Syst. Saf. 43 (3): 257–261. https://doi.org/10.1016/0951-8320(94)90029-9.
Kapur, K., and L. Lamberson. 1977. Reliability in engineering design. New York: Wiley.
Karanki, D. R., H. S. Kushwaha, A. K. Verma, and S. Ajit. 2009. “Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment.” Risk Anal. 29 (5): 662–675. https://doi.org/10.1111/j.1539-6924.2009.01221.x.
Kennedy, R. P. 2011. “Performance-goal based (risk informed) approach for establishing the sse site specific response spectrum for future nuclear power plants.” Nucl. Eng. Des. 241 (3): 648–656. https://doi.org/10.1016/j.nucengdes.2010.08.001.
Kennedy, R. P., C. Cornell, R. Campbell, S. Kaplan, and H. Perla. 1980. “Probabilistic seismic safety study of an existing nuclear power plant.” Nucl. Eng. Des. 59 (2): 315–338. https://doi.org/10.1016/0029-5493(80)90203-4.
Kim, J. H., I.-K. Choi, and J.-H. Park. 2010. “Seismic evaluation by using composite standard deviation.” In Proc., Transactions of the Korean Nuclear Society Autumn Meeting. Daejeon, Republic of Korea: Korean Nuclear Society.
Le Duy, T. D., D. Vasseur, L. Dieulle, C. Bérenguer, and M. Couplet. 2010. “Representation of parameter uncertainty with evidence theory in probabilistic risk assessment.” In Proc., Workshop on the Theory of Belief Functions. Siena, Italy: Belief Functions and Applications Society.
Modarres, M., M. P. Kaminskiy, and V. Krivtsov. 2016. Reliability engineering and risk analysis: A practical guide. New York: CRC Press.
Modarres, M., and I. S. Kim. 2010. Handbook of nuclear engineering, 1739–1812. Boston: Springer.
Moore, R. E., R. B. Kearfott, and M. J. Cloud. 2009. Introduction to interval analysis. Philadelphia: Society for Industrial and Applied Mathematics.
Patelli, E. 2016. “Chapter COSSAN: A multidisciplinary software suite for uncertainty quantification and risk management.” In Handbook of uncertainty quantification, 1–69. Cham: Springer. https://doi.org/10.1007/978-3-319-11259-6_59-1.
Patelli, E., D. A. Alvarez, M. Broggi, and M. de Angelis. 2014. “An integrated and efficient numerical framework for uncertainty quantification: Application to the NASA Langley multidisciplinary uncertainty quantification challenge.” In Proc., 16th AIAA Non-Deterministic Approaches Conf. (SciTech 2014), AIAA SciTech. Reston, VA: American Institute of Aeronautics and Astronautics.
Patelli, E., D. A. Alvarez, M. Broggi, and M. de Angelis. 2015. “Uncertainty management in multidisciplinary design of critical safety systems.” J. Aerosp. Inf. Syst. 12: 140–169. https://doi.org/10.2514/1.I010273.
Patelli, E., M. Broggi, S. Tolo, and J. Sadeghi. 2017a. “Cossan software: A multidisciplinary and collaborative software for uncertainty quantification.” In Proc., 2nd ECCOMAS Thematic Conf. on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2017. Rhodes Island, Greece: ECCOMAS Proceedia.
Patelli, E., G. Feng, F. Coolen, and T. Coolen-Maturi. 2017b. “Simulation methods for system reliability using survival signature.” Reliab. Eng. Syst. Saf. 167 (Nov): 327–337. https://doi.org/10.1016/j.ress.2017.06.018.
Patelli, E., H. J. Pradlwarter, and G. I. Schuëller. 2011. “On multinormal integrals by importance sampling for parallel system reliability.” Struct. Saf. 33 (1): 1–7. https://doi.org/10.1016/j.strusafe.2010.04.002.
Pellissetti, M., H. Keßler, F. Laudarin, D. Altieri, and E. Patelli. 2017. “Statistical analysis of impact forces and permanent deformations of fuel assembly spacer grids in the context of seismic fragility.” In Proc., 24th Conf. on Structural Mechanics in Reactor Technology. Raleigh, NC: International Association for Structural Mechanics in Reactor Technology.
Prinja, N. K., A. Ogunbadejo, J. Sadeghi, and E. Patelli. 2017. “Structural reliability of prestressed concrete containments.” Nucl. Eng. Des. 323 (Nov): 235–244. https://doi.org/10.1016/j.nucengdes.2016.11.036.
Qiu, Z., D. Yang, and I. Elishakoff. 2008. “Probabilistic interval reliability of structural systems.” Int. J. Solids Struct. 45 (10): 2850–2860. https://doi.org/10.1016/j.ijsolstr.2008.01.005.
Rüschendorf, L. 1991. “Fréchet-bounds and their applications.” In Advances in probability distributions with given marginals, 151–187. Dordrecht, Netherlands: Springer.
Samaniego, F. J. 2007. Vol. 110 of System signatures and their applications in engineering reliability. New York: Springer.
Sun, H.-L., and W.-X. Yao. 2008. “The basic properties of some typical systems’ reliability in interval form.” Struct. Saf. 30 (4): 364–373. https://doi.org/10.1016/j.strusafe.2007.05.003.
Sundararajan, C. R. 2012. Probabilistic structural mechanics handbook: Theory and industrial applications. New York: Springer.

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6Issue 1March 2020

History

Received: Nov 30, 2018
Accepted: May 3, 2019
Published online: Oct 31, 2019
Published in print: Mar 1, 2020
Discussion open until: Mar 31, 2020

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Jonathan Sadeghi
Ph.D. Candidate, Institute for Risk and Uncertainty, Univ. of Liverpool, Chadwick Bldg., Peach St., Liverpool L69 7ZF, UK.
Marco de Angelis
Postdoctoral Researcher, Institute for Risk and Uncertainty, Univ. of Liverpool, Chadwick Bldg., Peach St., Liverpool L69 7ZF, UK.
Professor, Dept. of Civil and Environmental Engineering, Univ. of Strathclyde, James Weir Bldg., 75 Montrose St., Glasgow G1 1XJ, UK; Senior Lecturer, Institute for Risk and Uncertainty, Univ. of Liverpool, Chadwick Bldg., Peach St., Liverpool L69 7ZF, UK (corresponding author). ORCID: https://orcid.org/0000-0002-5007-7247. Email: [email protected]

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