Skip to main content
SpringerLink
Log in

Uncertainty Quantification for Decision-Making in Engineered Systems

  • Conference paper
  • First Online:
Proceedings of the International Symposium on Engineering under Uncertainty: Safety Assessment and Management (ISEUSAM - 2012)

Abstract

This chapter discusses current research and opportunities for uncertainty quantification in performance prediction and risk assessment of engineered systems. Model-based simulation becomes attractive for systems that are too large and complex for full-scale testing. However, model-based simulation involves many approximations and assumptions, and thus, confidence in the simulation result is an important consideration in risk-informed decision-making. Sources of uncertainty are both aleatory and epistemic, stemming from natural variability, information uncertainty, and modeling approximations. The chapter draws on illustrative problems in aerospace, mechanical, civil, and environmental engineering disciplines to discuss (1) recent research on quantifying various types of errors and uncertainties, particularly focusing on data uncertainty and model uncertainty (both due to model form assumptions and solution approximations); (2) framework for integrating information from multiple sources (models, tests, experts), multiple model development activities (calibration, verification, validation), and multiple formats; and (3) using uncertainty quantification in risk-informed decision-making throughout the life cycle of engineered systems, such as design, operations, health and risk assessment, and risk management.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The current observation can be expressed as a linear function of past observations.

  2. 2.

    A process is said to be nonstationary if its probability structure varies with the time or space coordinate.

  3. 3.

    Bootstrapping is a data-based simulation method for statistical inference by resampling from an existing data set [7].

References

  1. Barford NC (1985) Experimental measurements: precision, error, and truth. Wiley, New York

    Google Scholar 

  2. Bichon, BJ, Eldred, MS, Swiler, LP, Mahadevan, S, McFarland, JM (2007) Multimodal reliability assessment for complex engineering applications using efficient global optimization. In: Proceedings of 9th AIAA non-deterministic approaches conference, Waikiki, HI

    Google Scholar 

  3. Blischke WR, Murthy DNP (2000) Reliability: modeling, prediction, and optimization. Wiley, New York

    Book  MATH  Google Scholar 

  4. Box GEP, Hunter WG, Hunter JS (1978) Statistics for experimenters, an introduction to design, data analysis, and model building. Wiley, New York

    MATH  Google Scholar 

  5. Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis forecasting and control, 3rd edn. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  6. Campolongo F, Saltelli A, Sorensen T, Tarantola S (2000) Hitchhiker’s guide to sensitivity analysis. In: Saltelli A, Chan K, Scott EM (eds) Sensitivity analysis. Wiley, New York, pp 15–47

    Google Scholar 

  7. Efron B, Tibshirani RJ (1994) An introduction to the bootstrap. Chapman & Hall/CRC, New York/Boca Raton

    Google Scholar 

  8. Farrar CR, Sohn H, Hemez FM, Anderson MC, Bement MT, Cornwell PJ, Doebling SW, Schultze JF, Lieven N, Robertson AN (2003) Damage prognosis: current status and future needs. Technical report LA–14051–MS, Los Alamos National Laboratory, Los Alamos, New Mexico

    Google Scholar 

  9. Ferson S, Kreinovich V, Hajagos J, Oberkampf W, Ginzburg L (2007) Experimental uncertainty estimation and statistics for data having interval uncertainty. Sandia National Laboratories technical report, SAND2003-0939, Albuquerque, New Mexico

    Google Scholar 

  10. Ghanem R, Spanos P (2003) Stochastic finite elements: a spectral approach. Springer, New York

    Google Scholar 

  11. Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov Chain Monte Carlo in practice, Interdisciplinary statistics series. Chapman and Hall, Boca Raton

    MATH  Google Scholar 

  12. Goktepe AB, Inan G, Ramyar K, Sezer A (2006) Estimation of sulfate expansion level of pc mortar using statistical and neural approaches. Constr Build Mater 20:441–449

    Article  Google Scholar 

  13. Gurley KR (1997) Modeling and simulation of non-Gaussian processes. Ph.D. thesis, University of Notre Dame, April

    Google Scholar 

  14. Haldar A, Mahadevan S (2000) Probability, reliability and statistical methods in engineering design. Wiley, New York

    Google Scholar 

  15. Haldar A, Mahadevan S (2000) Reliability analysis using the stochastic finite element method. Wiley, New York

    Google Scholar 

  16. Helton JC, Sallabery CJ (2009) Conceptual basis for the definition and calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada. Reliab Eng Syst Saf 94:677–698

    Article  Google Scholar 

  17. Helton JC, Sallabery CJ (2009) Computational implementation of sampling-based approaches to the calculation of expected dose in performance assessments for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada. Reliab Eng Syst Saf 94:699–721

    Article  Google Scholar 

  18. Huang S, Mahadevan S, Rebba R (2007) Collocation-based stochastic finite element analysis for random field problems, Probab Eng Mech 22:194–205

    Article  Google Scholar 

  19. Isukapalli SS, Roy A, Georgopoulos PG (1998) Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems. Risk Anal 18(3):351–363

    Article  Google Scholar 

  20. Jeffreys H (1961) Theory of probability, 3rd edn. Oxford University Press, London

    MATH  Google Scholar 

  21. Jensen FV, Jensen FB (2001) Bayesian networks and decision graphs. Springer, New York

    MATH  Google Scholar 

  22. Jiang X, Mahadevan S (2007) Bayesian risk-based decision method for model validation under uncertainty. Reliab Eng Syst Saf 92(6):707–718

    Article  Google Scholar 

  23. Jiang X, Mahadevan S (2008) Bayesian validation assessment of multivariate computational models. J Appl Stat 35(1):49–65

    Article  MathSciNet  MATH  Google Scholar 

  24. Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models (with discussion). JR Stat Soc Ser B 63(3):425–464

    Article  MathSciNet  MATH  Google Scholar 

  25. Langley RS (2000) A unified approach to the probabilistic and possibilistic analysis of uncertain systems. ASCE J Eng Mech 126:1163–1172

    Article  Google Scholar 

  26. Liang B, Mahadevan S (2011) Error and uncertainty quantification and sensitivity analysis of mechanics computational models. Int J Uncertain Quantif 1:147–161

    Article  MathSciNet  Google Scholar 

  27. Ling Y, Mahadevan S (2012) Intepretations, relationships, and application issues in model validation. In: Proceedings, 53rd AIAA/ASME/ASCE Structures, Dynamics and Materials (SDM) conference, paper no. AIAA-2012-1366, Honolulu, Hawaii, April 2012

    Google Scholar 

  28. Mahadevan S, Raghothamachar P (2000) Adaptive simulation for system reliability analysis of large structures. Comput Struct 77(6):725–734

    Article  Google Scholar 

  29. Mahadevan S, Rebba R (2005) Validation of reliability computational models using Bayes networks. Reliab Eng Syst Saf 87(2):223–232

    Article  Google Scholar 

  30. Mathelin L, Hussaini MY, Zang TA (2005) Stochastic approaches to uncertainty quantification in CFD simulations. Numer Algorithm 38:209–236

    MathSciNet  MATH  Google Scholar 

  31. McFarland JM (2008) Uncertainty analysis for computer simulations through validation and calibration. Ph.D. dissertation, Vanderbilt University, Nashville, TN

    Google Scholar 

  32. Mckay MD, Conover WJ, Beckman RJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21:239–245

    MathSciNet  MATH  Google Scholar 

  33. Rebba R (2005) Model validation and design under uncertainty. Ph.D. dissertation, Vanderbilt University, Nashville, TN, USA

    Google Scholar 

  34. Rebba R, Mahadevan S (2006) Model predictive capability assessment under uncertainty. AIAA J 44(10):2376–2384

    Article  Google Scholar 

  35. Rebba R, Mahadevan S (2008) Computational methods for model reliability assessment. Reliab Eng Syst Saf 93:1197–1207

    Article  Google Scholar 

  36. Rebba R, Mahadevan S, Huang S (2006) Validation and error estimation of computational models. Reliab Eng Syst Saf 91(10–11):1390–1397

    Article  Google Scholar 

  37. Red-Horse JR, Benjamin AS (2004) A probabilistic approach to uncertainty quantification with limited information. Reliab Eng Syst Saf 85:183–190

    Article  Google Scholar 

  38. Richards SA (1997) Completed Richardson extrapolation in space and time. Commun Numer Methods Eng 13(7):558–573

    Article  MathSciNet  Google Scholar 

  39. Robert CP, Casella G (2004) Monte Carlo statistical methods, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  40. Ross TJ, Booker JM, Parkinson WJ (2002) Fuzzy logic and probability applications: bridging the gap. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  41. Rubinstein RY (1981) Simulation and the Monte Carlo method. Wiley, New York

    Book  MATH  Google Scholar 

  42. Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis. Wiley, West Sussex

    MATH  Google Scholar 

  43. Sankararaman S, Mahadevan S (2011) Likelihood-based representation of epistemic uncertainty due to sparse point data and interval data. Reliab Eng Syst Saf 96:814–824

    Article  Google Scholar 

  44. Sankararaman S, Mahadevan S (2012) Roll-up of calibration and validation results towards system-level QMU. In: Proceedings of 15th AIAA non-deterministic approaches conference, Honolulu, Hawaii

    Google Scholar 

  45. Tatang MA, Pan W, Prinn RG, McRae GJ (1997) An efficient method for parametric uncertainty analysis of numerical geophysical models. J Geophys Res 102(D18):21925–21932

    Article  Google Scholar 

  46. Trucano TG, Easterling RG, Dowding KJ, Paez TL, Urbina A, Romero VJ, Rutherford BM, Hills RG (2001) Description of the Sandia validation metrics project. Sandia National Laboratories technical report, SAND2001-1339, Albuquerque, New Mexico

    Google Scholar 

  47. Xiu D, Karniadakis GE (2003) Modeling uncertainty in flow simulations via generalized polynomial chaos. J Comput Phys 187(1):137–167

    Article  MathSciNet  MATH  Google Scholar 

  48. Zaman K, McDonald M, Mahadevan S (2011) A probabilistic approach for representation of interval uncertainty. Reliab Eng Syst Saf 96(1):117–130

    Article  Google Scholar 

  49. Zhang R, Mahadevan S (2003) Bayesian methodology for reliability model acceptance. Reliab Eng Syst Saf 80(1):95–103

    Article  Google Scholar 

  50. Zou T, Mahadevan S, Mourelatos Z (2003) Reliability-based evaluation of automotive wind noise quality. Reliab Eng Syst Saf 82(2):217–224

    Article  Google Scholar 

Download references

Acknowledgement

The research described in this chapter by the author and his students/colleagues has been funded by many sources during the past decade. A partial listing of the recent sources includes the following: (1) National Science Foundation (IGERT project on Reliability and Risk Assessment and Management at Vanderbilt University), (2) Sandia National Laboratories (Bayesian framework for model validation, calibration, and error estimation), (3) US Department of Energy (uncertainty quantification in micro-electro-mechanical systems (MEMS) reliability prediction, long-term durability of cementitious barriers), (4) National Aeronautics and Space Administration (space vehicle performance uncertainty quantification, uncertainty quantification in diagnosis and prognosis, Bayesian network development for testing resource allocation), (5) US Air Force Office of Scientific Research (multidisciplinary uncertainty analysis of aircraft components), and (6) Federal Aviation Administration (uncertainty quantification in fracture mechanics simulation of rotorcraft components). The support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. John R. Murray Sr. Professor of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, USA

    Sankaran Mahadevan

Authors
  1. Sankaran Mahadevan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sankaran Mahadevan .

Editor information

Editors and Affiliations

  1. , Civil Engineering, Bengal Engineering and Science Univ., Botanic Garden, Howrah, India

    Subrata Chakraborty

  2. Bengal Engineering and Science Univ., Howrah, India

    Gautam Bhattacharya

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer India

About this paper

Cite this paper

Mahadevan, S. (2013). Uncertainty Quantification for Decision-Making in Engineered Systems. In: Chakraborty, S., Bhattacharya, G. (eds) Proceedings of the International Symposium on Engineering under Uncertainty: Safety Assessment and Management (ISEUSAM - 2012). Springer, India. https://doi.org/10.1007/978-81-322-0757-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-0757-3_5

  • Published:

  • Publisher Name: Springer, India

  • Print ISBN: 978-81-322-0756-6

  • Online ISBN: 978-81-322-0757-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation