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Analytical global sensitivity analysis with Gaussian processes

Published online by Cambridge University Press:  03 August 2017

Ankur Srivastava ,
Arun K. Subramaniyan  and
Liping Wang
Ankur Srivastava*
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
Arun K. Subramaniyan
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
Liping Wang
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
*
Reprint requests to: Ankur Srivastava, GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309, USA. E-mail: [email protected]
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Abstract

Methods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

Keywords

Bayesian QuadratureEffect FunctionsGaussian ProcessesSobol Indices
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 3: Uncertainty Quantification for Engineering Design , August 2017 , pp. 235 - 250
Copyright
Copyright © Cambridge University Press 2017 

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References

REFERENCES

Caniou, Y., & Sudret, B. (2010). Distribution-based global sensitivity analysis using polynomial chaos expansion. Proc. 6th Int. Conf. Sensitivity Analysis of Model Output, pp. 7625–7626, Milan, Italy, July 19–22.CrossRefGoogle Scholar
Chastaing, G., Gamboa, F., & Prieur, C. (2014). Generalized Sobol sensitivity indices for dependent variables: numerical methods. Journal of Statistical Computation and Simulation 85(7), 1306–1333.CrossRefGoogle Scholar
Chennimalai Kumar, N., Subramaniyan, A.K., & Wang, L. (2012). Improving high-dimensional physics models through Bayesian calibration with uncertain data. Proc. ASME Turbo Expo 2012, Copenhagen, June 11–15.CrossRefGoogle Scholar
Chennimalai Kumar, N., Subramaniyan, A.K., & Wang, L. (2013). Calibrating transient models with multiple responses using Bayesian inverse techniques. Proc. ASME Turbo Expo 2013, San Antonio, TX, June 5–10.CrossRefGoogle Scholar
Hastie, T., Tibshirani, R., & Friedman, J. (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer.CrossRefGoogle Scholar
Haylock, R.G., & O'Hagan, A. (1996). On inference for outputs of computationally expensive algorithms with uncertainty on the inputs. In Bayesian Statistics (Bernardo, J.M., Berger, J.O., Dawid, A.P., & Smith, A.F.M., Eds.), Vol. 5, pp. 629–637. Oxford: Oxford University Press.CrossRefGoogle Scholar
Iooss, B., & Lemaître, P. (2015). A review on global sensitivity analysis methods. In Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications (Meloni, C., & Dellino, G., Eds.). New York: Springer.Google Scholar
Kennedy, M., & O'Hagan, A. (2001). Bayesian calibration of computer models (with discussion). Journal of the Royal Statistical Society (Series B) 68, 425–464.CrossRefGoogle Scholar
Kennedy, M.C., & O'Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society (Part B) 63(3), 425–464.CrossRefGoogle Scholar
Li, G., & Rabitz, H. (2012). General formulation of HDMR component functions with independent and correlated variables. Journal of Mathematical Chemistry 50(1), 99–130.CrossRefGoogle Scholar
Li, G., Rabitz, H., Yelvington, P.E., Oluwole, O.O., Bacon, F., Kolb, C.E., & Schoendorf, J. (2010). Global sensitivity analysis for systems with independent and/or correlated inputs. Journal of Physical Chemistry: Part A 114, 6022–6032.CrossRefGoogle ScholarPubMed
Munoz Zuniga, M., Kucherenko, S., & Shah, N. (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications 184, 1570–1580.CrossRefGoogle Scholar
Oakley, J.E., & O'Hagan, A. (2004). Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Part B 66(3), 751–769.CrossRefGoogle Scholar
Reuter, U., Mehmood, Z., Gebhardt, C., Liebscher, M., Müllerschön, H., & Lepenies, I. (2011). Using LS-OPT for meta-model based global sensitivity analysis. Proc. 8th European LS-Dyna Conf., Session 4, Strasbourg, France.Google Scholar
Saltelli, S., & Tarantola, S. (2002). On the relative importance of input factors in mathematical models. Journal of the American Statistical Association 97(459), 2002.CrossRefGoogle Scholar
Saltelli, S., Tarantola, S., & Campolongo, F. (2000). Sensitivity analysis as an ingradient of modeling. Statistical Science 15(4), 377–395.Google Scholar
Subramaniyan, A.K., Kumar, N., Wang, L., Beeson, D., & Wiggs, G. (2012). Enhancing high-dimensional physics models for accurate predictions with Bayesian calibration. Proc. 2012 Propulsion-Safety and Affordable Readiness Conf., Jacksonville, FL, March 20–22.Google Scholar
Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety 93(7), 964–979.CrossRefGoogle Scholar
Wang, L., Fang, X., Subramaniyan, A., Jothiprasad, G., Gardner, M., Kale, A., Akkaram, S., Beeson, D., Wiggs, G., & Nelson, J. (2011). Challenges in uncertainty, calibration, validation and predictability of engineering analysis models. Proc. ASME Turbo Expo 2011: Power for Land, Sea and Air GT2011, Paper No. GT2011-46554, Vancouver, CA, June 6–10.Google Scholar
Xu, C., & Gertner, G.Z. (2008). Uncertainty and sensitivity analysis for models with correlated parameters. Reliability Engineering and System Safety 93, 1563–1573.CrossRefGoogle Scholar