Skip to main content

Response Surface Methodology: A Review of Applications to Risk Assessment

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 136))

Abstract

Risk Analysis has assumed a crucial relevance over the past few years, particularly in dynamical systems with increasing complexity. Thanks to recent technological advances, the use of simulation techniques to estimate models has become the norm rather than the exception. These simulated models are used to predict the behavior of a system, to compute the probability of occurrence of a specific event and to predict the consequence of the said event. Uncertainty associated with the simulation, either in model parameters or in experimental data, requires its quantification as a prerequisite in probabilistic risk assessment. The computational costs of numerical simulations are often very high, thus the use of metamodels arises as a pressing necessity. Response Surface Methodology is known to be a suitable tool, both for the estimation of metamodels for the behaviors of systems and risk assessment, and for the quantification of uncertainty. A review of applications and of various aspects on the use of Response Surface Methodology in Risk Assessment Systems will be presented.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Balakrishnan, S., Roy, A., Ierapetritou, M.G., Flach, G.P., Georgopoulos, P.G.: Uncertainty reduction and characterization for complex environmental fate and transport models: an empirical Bayesian framework incorporating the stochastic response surface method. Water Resour. Res. 39(12), 1350 (2003)

    Article  Google Scholar 

  2. Bauer, K.W., Parnell, G.S., Meyers, D.A.: Response surface methodology as a sensitivity analysis tool in decision analysis. J. Multi-Criteria Decis. Anal. 8(3), 162–180 (1999)

    Article  MATH  Google Scholar 

  3. Baysal, R.E., Nelson, B.L., Staum, J.: Response surface methodology for simulating hedging and trading strategies. In: Simulation Conference, WSC, Winter, December 2008, pp. 629–637. IEEE (2008)

    Google Scholar 

  4. Bouda, M., Rousseau, A.N., Konan, B., Gagnon, P., Gumiere, S.J.: Bayesian uncertainty analysis of the distributed hydrological model HYDROTEL. J. Hydrol. Eng. 17(9), 1021–1032 (2011)

    Article  Google Scholar 

  5. Box, G.E., Draper, N.R.: Empirical Model-Building and Response Surfaces. Wiley, New York (1987)

    MATH  Google Scholar 

  6. Box, G.E., Wilson, K.B.: On the experimental attainment of optimum conditions. J. R. Stat. Soc. Ser. B (Methodological) 13(1), 1–45 (1951)

    MATH  MathSciNet  Google Scholar 

  7. Bucher, C.G., Bourgund, U.: A fast and efficient response surface approach for structural reliability problems. Struct. Saf. 7(1), 57–66 (1990)

    Article  Google Scholar 

  8. Cheung, S.H., Oliver, T.A., Prudencio, E.E., Prudhomme, S., Moser, R.D.: Bayesian uncertainty analysis with applications to turbulence modeling. Reliab. Eng. Syst. Saf. 96(9), 1137–1149 (2011)

    Article  Google Scholar 

  9. Der Kiureghian, A.: Bayesian analysis of model uncertainty in structural reliability. In: Reliability and Optimization of Structural Systems’90, pp. 211–221. Springer, Berlin (1991)

    Google Scholar 

  10. Efron, B.: The Jackknife, The Bootstrap and Other Resampling Plans. Society for Industrial and Applied Mathematics, Philadelphia (1982)

    Book  Google Scholar 

  11. El-Masri, H.A., Reardon, K.F., Yang, R.S.: Integrated approaches for the analysis of toxicologic interactions of chemical mixtures. CRC Crit. Rev. Toxicol. 27(2), 175–197 (1997)

    Article  Google Scholar 

  12. Ernst, O.G., Mugler, A., Starkloff, H.J., Ullmann, E.: On the convergence of generalized polynomial chaos expansions. ESAIM: Math. Model. Numer. Anal. 46(02), 317–339 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. Feraille, M., Marrel, A.: Prediction under uncertainty on a mature field. Oil Gas Sci. Technol.–Rev. IFP Energ. Nouv. 67(2), 193–206 (2012)

    Article  Google Scholar 

  14. Frey, H.C., Mokhtari, A., Zheng, J.: Recommended practice regarding selection, application, and interpretation of sensitivity analysis methods applied to food safety process risk models. US Department of Agriculture. http://www.ce.ncsu.edu/risk/Phase3Final.pdf (2004)

  15. Ghanem, R.G., Spanos, P.D.: Stochastic Finite Elements: A Spectral Approach. Springer, New York (1991)

    Book  MATH  Google Scholar 

  16. Groten, J.P., Feron, V.J., Sühnel, J.: Toxicology of simple and complex mixtures. Trends Pharmacol. Sci. 22(6), 316–322 (2001)

    Article  Google Scholar 

  17. Gupta, S., Manohar, C.S.: An improved response surface method for the determination of failure probability and importance measures. Struct. Saf. 26(2), 123–139 (2004)

    Article  Google Scholar 

  18. Ha, T., Garland, W.J.: Loss of coolant accident (LOCA) analysis for mcmaster nuclear reactor through probabilistic risk assessment (PRA). In: Proceedings of 27th Annual Conference of the Canadian Nuclear Society Toronto, Ontario, Canada, 11–14 June 2006

    Google Scholar 

  19. Helton, J.C.: Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliab. Eng. Syst. Saf. 42(2), 327–367 (1993)

    Article  MathSciNet  Google Scholar 

  20. Hoffman, F.O., Miller, C.W., Ng, Y.C.: Uncertainties in radioecological assessment models (No. IAEA-SR-84/4; CONF-831032-1). Oak Ridge National Laboratory, TN (USA); Lawrence Livermore National Laboratory, CA, USA (1983)

    Google Scholar 

  21. Hosmer Jr, D.W., Lemeshow, S., Sturdivant, R.X.: Applied Logistic Regression, 3rd edn. Wiley, New York (2013)

    Book  MATH  Google Scholar 

  22. Iervolino, I., Fabbrocino, G., Manfredi, G.: Fragility of standard industrial structures by a response surface based method. J. Earthq. Eng. 8(06), 927–945 (2004)

    Google Scholar 

  23. Iooss, B., Van Dorpe, F., Devictor, N.: Response surfaces and sensitivity analyses for an environmental model of dose calculations. Reliab. Eng. Syst. Saf. 91(10), 1241–1251 (2006)

    Article  Google Scholar 

  24. Isukapalli, S.S., Georgopoulos, P.G.: Computational Methods for Sensitivity and Uncertainty Analysis for Environmental and Biological Models. Environmental and Occupational Health Sciences Institute, New Jersey (2001)

    Google Scholar 

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

    Article  Google Scholar 

  26. Kennedy, A.B., Westerink, J.J., Smith, J.M., Hope, M.E., Hartman, M., Taflanidis, A.A., Dawson, C.: Tropical cyclone inundation potential on the Hawaiian Islands of Oahu and Kauai. Ocean Model. 52, 54–68 (2012)

    Article  Google Scholar 

  27. Kleijnen, J.P., van Ham, G., Rotmans, J.: Techniques for sensitivity analysis of simulation models: a case study of the \(\mathit{CO}_2\) greenhouse effect. Simulation 58(6), 410–417 (1992)

    Google Scholar 

  28. Liel, A.B., Haselton, C.B., Deierlein, G.G., Baker, J.W.: Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings. Struct. Saf. 31(2), 197–211 (2009)

    Article  Google Scholar 

  29. Myers, R.H., Montgomery, D.C., Anderson-Cook, C.M.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, New York (2009)

    Google Scholar 

  30. Oladyshkin, S., Nowak, W.: Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. Reliab. Eng. Syst. Saf. 106, 179–190 (2012)

    Article  Google Scholar 

  31. Oladyshkin, S., Class, H., Helmig, R., Nowak, W.: Highly efficient tool for probabilistic risk assessment of CCS joint with injection design. Comput. Geosci. 13, 451–467 (2009)

    Article  Google Scholar 

  32. Oladyshkin, S., Class, H., Helmig, R., Nowak, W.: An integrative approach to robust design and probabilistic risk assessment for \(\mathit{CO}_2\) storage in geological formations. Comput. Geosci. 15(3), 565–577 (2011)

    Google Scholar 

  33. Oladyshkin, S., Class, H., Helmig, R., Nowak, W.: A concept for data-driven uncertainty quantification and its application to carbon dioxide storage in geological formations. Adv. Water Resour. 34(11), 1508–1518 (2011)

    Google Scholar 

  34. Oladyshkin, S., Class, H., Nowak, W.: Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations. Comput. Geosci. 17, 1–17 (2013)

    Google Scholar 

  35. Patel, T., Telesca, D., George, S., Nel, A.: Toxicity profiling of engineered nanomaterials via multivariate dose response surface modeling (2011)

    Google Scholar 

  36. Que, J.: Response surface modelling of Monte-Carlo fire data. Doctoral dissertation, Victoria University (2003)

    Google Scholar 

  37. Risso, F., Schiozer, D.: Risk analysis of petroleum fields using Latin hypercube, Monte carol and derivative tree techniques. J. Pet. Gas Explor. 1(1), 014–021 (2011)

    Google Scholar 

  38. Rohmer, J., Bouc, O.: A response surface methodology to address uncertainties in cap rock failure assessment for \(\mathit{CO}_2\) geological storage in deep aquifers. Int. J. Greenh. Gas Control 4(2), 198–208 (2010)

    Google Scholar 

  39. Rossetto, T., Elnashai, A.: A new analytical procedure for the derivation of displacement-based vulnerability curves for populations of RC structures. Eng. Struct. 27(3), 397–409 (2005)

    Article  Google Scholar 

  40. Royal Society: Risk: Analysis, Perception and Management. Report of a Royal Society Study Group, London, The Royal Society, pp. 89–134 (1992)

    Google Scholar 

  41. Song, X., Zhan, C., Xia, J., Kong, F.: An efficient global sensitivity analysis approach for distributed hydrological model. J. Geogr. Sci. 22(2), 209–222 (2012)

    Article  Google Scholar 

  42. Steffen, O.K.H., Contreras, L.F., Terbrugge, P.J., Venter, J.: A risk evaluation approach for pit slope design. 42nd US rock mechanics symposium and 2nd U.S.-Canada Rock Mechanics Symposium, held in San Francisco, 29 June–2 July 2008

    Google Scholar 

  43. Taflanidis, A.A., Kennedy, A.B., Westerink, J.J., Smith, J., Cheung, K.F., Hope, M., Tanaka, S.: Probabilistic hurricane surge risk estimation through high fidelity numerical simulation and response surface approximations. ASCE April 2011

    Google Scholar 

  44. Tanase, F.N.: Seismic performance assessment using response surface methodology. Constr.: J. Civ. Eng. Res. 2, 13 (2012)

    Google Scholar 

  45. Wang, X., Song Z.: Reliability analysis of evacuation B improved response surface method. In: 2nd International Conference on Electronic and Mechanical Engineering and Information Technology (EMEIT-2012). Published by Atlantis Press, Paris, France (2012)

    Google Scholar 

  46. Wiener, N.: The homogeneous chaos. Am. J. Math. 60(4), 897–936 (1938)

    Article  MathSciNet  Google Scholar 

  47. Wilde, M.L., Kümmerer, K., Martins, A.F.: Multivariate optimization of analytical methodology and a first attempt to an environmental risk assessment of \(\beta \)-\(blockers\) in hospital wastewater. J. Braz. Chem. Soc. 23(9), 1732–1740 (2012)

    Article  Google Scholar 

  48. Xiu, D., Karniadakis, G.E.: Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Comput. Methods Appl. Mech. Eng. 191(43), 4927–4948 (2002)

    Google Scholar 

  49. Xiu, D., Karniadakis, G.E.: The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619–644 (2002)

    Google Scholar 

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

    Google Scholar 

  51. Xiu, D., Karniadakis, G.E.: A new stochastic approach to transient heat conduction modeling with uncertainty. Int. J. Heat Mass Transf. 46(24), 4681–4693 (2003)

    Google Scholar 

Download references

Acknowledgments

The authors are very grateful to the referees for their useful comments and suggestions. This research was partially sponsored by national founds through the Fundação Nacional para a Ciência e Tecnologia, Portugal - FCT under the projects: (PEst-OE/MAT/UI0006/2011 and PEst-OE/MAT/UI0006/2014).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Teresa A. Oliveira .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Oliveira, T.A., Leal, C., Oliveira, A. (2015). Response Surface Methodology: A Review of Applications to Risk Assessment. In: Kitsos, C., Oliveira, T., Rigas, A., Gulati, S. (eds) Theory and Practice of Risk Assessment. Springer Proceedings in Mathematics & Statistics, vol 136. Springer, Cham. https://doi.org/10.1007/978-3-319-18029-8_29

Download citation

Publish with us

Policies and ethics