Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Multidisciplinary System Modeling and Optimization Read chapter Read first chapter

2020 | OriginalPaper | Chapter

4. Reliability Analysis

Authors : Jérôme Morio, Loïc Brevault, Mathieu Balesdent

Published in: Aerospace System Analysis and Optimization in Uncertainty

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Assessing the reliability of a complex system with uncertainty propagation consists in estimating its probability of failure. Common sampling strategies for such tasks are notably based on Monte Carlo sampling. This kind of methods is well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. However, for critical systems such as aerospace vehicles, the reliability specifications often induce very low probability of failures (said below 10−4). In this case, Monte Carlo based methods are not efficient inducing unaffordable costs with regard to the available simulation budget. In this chapter, we review the main simulation techniques to estimate low failure probabilities with accuracy.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Uncertainty Propagation and Sensitivity Analysis
next chapter Overview of Problem Formulations and Optimization Algorithms in the Presence of Uncertainty
Literature
Akpan, U., Rushton, P., and Koko, T. (2002). Fuzzy probabilistic assessment of the impact of corrosion on fatigue of aircraft structures. In 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, USA.
Au, S. K. and Beck, J. L. (2001). Estimation of small failure probabilities in high dimensions by subset simulations. Probabilistic Engineering Mechanics, 16(4):263–277.
Balesdent, M., Morio, J., and Brevault, L. (2016). Rare event probability estimation in the presence of epistemic uncertainty on input probability distribution parameters. Methodology and Computing in Applied Probability, 18(1):197–216.MathSciNetMATH
Balesdent, M., Morio, J., and Marzat, J. (2013). Kriging-based adaptive importance sampling algorithms for rare event estimation. Structural Safety, 13:1–10.
Basudhar, A., Missoum, S., and Sanchez, A. (2008). Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains. Probabilistic Engineering Mechanics, 23:1–11.
Bect, J., Ginsbourger, D., Li, L., Picheny, V., and Vazquez, E. (2012). Sequential design of computer experiments for the estimation of a probability of failure. Statistics and Computing, 22(3):773–793.MathSciNetMATH
Bjerager, P. (1988). Probability integration by directional simulation. Journal of Engineering Mechanics, 114(8):1288–1302.
Bjerager, R. (1991). Methods for structural reliability computation, pages 89–136. Springer Verlag, New York.
Botev, Z. I. and Kroese, D. P. (2012). Efficient Monte Carlo simulation via the generalized splitting method. Statistics and Computing, 22(1):1–16.MathSciNetMATH
Bourinet, J.-M., Deheeger, F., and Lemaire, M. (2011a). Assessing small failure probabilities by combined subset simulation and support vector machines. Structural Safety, 33:343–353.
Breitung, K. (1984). Asymptotic approximation for multinormal integrals. Journal of Engineering Mechanics, 110(3):357–366.MATH
Bucklew, J. A. (2004). Introduction to Rare Event Simulation. Springer.MATH
Cannamela, C., Garnier, J., and Iooss, B. (2008). Controlled stratification for quantile estimation. Annals of Applied Stats, 2(4):1554–1580.MathSciNetMATH
Cérou, F., Del Moral, P., Furon, T., and Guyader, A. (2012). Sequential Monte-Carlo for rare event estimation. Statistics and computing, 22(3):795–808.MathSciNetMATH
Cérou, F., Del Moral, P., Le Gland, F., and Lezaud, P. (2006). Genetic genealogical models in rare event analysis. INRIA report, 1797:1–30.
Coles, S. G. (2001). An introduction to statistical modeling of extreme values. Springer, New York.MATH
De Boer, P.-T., Kroese, D. P., Mannor, S., and Rubinstein, R. Y. (2005). A tutorial on the cross-entropy method. Annals of operations research, 134(1):19–67.MathSciNetMATH
Deheeger, F. and Lemaire, M. (2007). Support vector machine for efficient subset simulations: 2SMART method. In 10th International Conference on Application of Statistics and Probability in Civil Engineering, Tokyo, Japan.
Dekkers, A. L. M. and De Haan, L. (1999). On the estimation of the extreme-value index and large quantile estimation. The Annals of Statistics, 17(4):1795–1832.MathSciNetMATH
Dietlevsen, O. and Madsen, H. (1996). Structural Reliability Methods. John Wiley and Sons, New York.
Du, X. (2008). Unified uncertainty analysis by the first order reliability method. Journal of Mechanical Design, 130(9):091401.
Dubourg, V., Deheeger, E., and Sudret, B. (2011). Metamodel-based importance sampling for the simulation of rare events. In Faber, M. J. Kohler and K. Nishilima (Eds.), Proceedings of the 11th International Conference of Statistics and Probability in Civil Engineering (ICASP2011), Zurich, Switzerland.
Echard, B. (2012). Kriging-based reliability assessment of structures submitted to fatigue. PhD thesis, Université Blaise Pascal.
Echard, B., Gayton, N., and Lemaire, M. (2011). AK-MCS : An active learning reliability method combining Kriging and Monte-Carlo Simulation. Structural Safety, 33:145–154.
Echard, B., Gayton, N., Lemaire, M., and Relun, N. (2013). A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models. Reliability Engineering & System Safety, 111:232–240.
Embrechts, P. and Schmidli, H. (1994). Modelling of extremal events in insurance and finance. Zeitschrift für Operations Research, 39(1):1–34.MATH
Finkel, D. E. (2003). DIRECT optimization algorithm user guide. Center for Research in Scientific Computation, North Carolina State University, 2:1–14.
Gerstner, T. and Griebel, M. (2003). Dimension-adaptive tensor-product quadrature. Computing, 71(1):65–87.MathSciNetMATH
Hasofer, A. and Lind, N. (1974). An exact and invariant first-order reliability format. Journal of Engineering Mechanics, 100:111–121.
Hosking, J. and Wallis, J. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics, 29(3):339–349.MathSciNetMATH
Hurtado, J. E. (2013). Assessment of reliability intervals under input distributions with uncertain parameters. Probabilistic Engineering Mechanics, 32:80–92.
Janusevskis, J. and Le Riche, R. (2012). Simultaneous Kriging-based estimation and optimization of mean response. Journal of Global Optimization, 55(2):313–336.MathSciNetMATH
Jiang, C., Zhang, Z., Han, X., and Liu, J. (2013). A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty. Computers & Structures, 129:1–12.
Kiureghian, A. D. and Dakessian, T. (1998). Multiple design points in first and second-order reliability. Structural Safety, 20(1):37–49.
Kiureghian, A. D., Lin, H.-Z., and Hwang, S.-J. (1987). Second-order reliability approximations. Journal of Engineering Mechanics, 113(8):1208–1225.
Kroese, D. P., Brereton, T., Taimre, T., and Botev, Z. I. (2014). Why the Monte Carlo method is so important today. Wiley Interdisciplinary Reviews: Computational Statistics, 6(6):386–392.
Kroese, D. P. and Rubinstein, R. Y. (2012). Monte-Carlo methods. Wiley Interdisciplinary Reviews: Computational Statistics, 4(1):48–58.
Lagnoux, A. (2006). Rare event simulation. Probability in the Engineering and Informational science, 20(1):45–66.MathSciNetMATH
Lassen, T. and Recho, N. (2006). Fatigue Life Analyses of Welded Structures. ISTE Wiley, New York.
Lebrun, R. and Dutfoy, A. (2009a). A generalization of the Nataf transformation to distributions with elliptical copula. Probabilistic Engineering Mechanics, 24(2):172–178.
Lebrun, R. and Dutfoy, A. (2009b). An innovating analysis of the Nataf transformation from the copula viewpoint. Probabilistic Engineering Mechanics, 24(3):312–320.
Li, J. and Xiu, D. (2010). Evaluation of failure probability via surrogate models. Journal of Computational Physics, 229:8966–8980.MathSciNetMATH
Li, L., Bect, J., and Vazquez, E. (2012). Bayesian Subset Simulation: a Kriging-based subset simulation algorithm for the estimation of small probabilities of failure. In 11th International Probabilistic Assessment and Management Conference (PSAM11) and The Annual European Safety and Reliability Conference (ESREL 2012), Helsinki, Finland.
Madsen, H., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Springer-Verlag.
Morio, J. (2012). Extreme quantile estimation with nonparametric adaptive importance sampling. Simulation Modelling Practice and Theory, 27(0):76–89.
Morio, J. and Balesdent, M. (2015). Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach. Woodhead Publishing.
Mourelatos, Z. P. and Zhou, J. (2005). Reliability estimation and design with insufficient data based on possibility theory. AIAA Journal, 43(8):1696–1705.
Nannapaneni, S. and Mahadevan, S. (2016). Reliability analysis under epistemic uncertainty. Reliability Engineering & System Safety, 155:9–20.
Nataf, A. (1962). Distribution des distributions dont les marges sont données (in French). Comptes rendus de l’ Académie des Sciences, 225:42–43.MATH
Neves, C. and Fraga Alves, M. (2004). Reiss and Thomas’ automatic selection of the number of extremes. Computational Statistics and Data Analysis, 47(4):689–704.MathSciNetMATH
Novak, E. (1988). Deterministic and Stochastic Error Bounds in Numerical Analysis, volume 1349 of Lecture Notes in Mathematics. Springer, Berlin, Germany.
Pei-Ling, L. and Kiureghian, A. D. (1991). Optimization algorithms for structural reliability. Structural Safety, 9(3):161–177.
Penmetsa, R. and Grandhi, R. (2002). Estimating membership response function using surrogate models. In 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, USA.
Rackwitz, R. and Flessler, B. (1978). Structural reliability under combined random load sequences. Computers and Structures, 9(5):489–494.MATH
Robert, C. and Casella, G. (2005). Monte Carlo Statistical Methods. Springer, New York.MATH
Rosenblatt, M. (1952). Remarks on a multivariate transformation. Annals of Mathematical Statistics, 23:470–472.MathSciNetMATH
Schöbi, R. and Sudret, B. (2017). Structural reliability analysis for P-boxes using multi-level meta-models. Probabilistic Engineering Mechanics, 48:27–38.MATH
Schueremans, L. and Van Gemert, D. (2005). Use of Kriging as Meta-model in simulation procedures for structural reliability. In 9th International conference on structural safety and reliability, Rome, pages 2483–2490.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. In Monographs on Statistics and Applied Probability. London: Chapman and Hall.
Smolyak, S. (1963). Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Mathematics, Doklady, 4:240–243.MATH
Sobol, I. M. (1994). A Primer for the Monte Carlo Method. CRC Press, Boca Raton, Fl.MATH
Sudret, B. (2012). Meta-models for structural reliability and uncertainty quantification. In 5th Asian-Pacific Symposium on Structural Reliability and its Applications, Singapore, Singapore.
Thompson, P., Cai, Y., Reeve, D., and Stander, J. (2009). Automated threshold selection methods for extreme wave analysis. Coastal Engineering, 56(10):1013–1021.
Vazquez, E. and Bect, J. (2009). A Sequential Bayesian algorithm to estimate a probability of failure. In 15th IFAC Symposium on System Identification, Saint-Malo, France.
Xiao, M., Gao, L., Xiong, H., and Luo, Z. (2015). An efficient method for reliability analysis under epistemic uncertainty based on evidence theory and support vector regression. Journal of Engineering Design, 26(10–12):340–364.
Yan-Gang, Z. and Tetsuro, O. (1999). A general procedure for first/second-order reliability method (FORM/SORM). Structural Safety, 21(2):95–112.
Yang, X., Liu, Y., Gao, Y., Zhang, Y., and Gao, Z. (2015). An active learning Kriging model for hybrid reliability analysis with both random and interval variables. Structural and Multidisciplinary Optimization, 51(5):1003–1016.MathSciNet
Yao, W., Chen, X., Huang, Y., and van Tooren, M. (2013). An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization. Reliability Engineering & System Safety, 116:28–37.
Zhang, P. (1996). Nonparametric importance sampling. Journal of the American Statistical Association, 91(434):1245–1253.MathSciNetMATH
Zuniga, M. M., Garnier, J., Remy, E., and de Rocquigny, E. (2011). Adaptive directional stratification for controlled estimation of the probability of a rare event. Reliability Engineering & System Safety, 96(12):1691–1712.
Metadata
Title
Reliability Analysis
Authors
Jérôme Morio
Loïc Brevault
Mathieu Balesdent
Copyright Year
2020
Book
Aerospace System Analysis and Optimization in Uncertainty

Print ISBN: 978-3-030-39125-6

Electronic ISBN: 978-3-030-39126-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-39126-3_4