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Sensitivity study of dynamic systems using polynomial chaos

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  • Haro Sandoval, Eduardo
  • Anstett-Collin, Floriane
  • Basset, Michel

Abstract

Global sensitivity has mainly been analyzed in static models, though most physical systems can be described by differential equations. Very few approaches have been proposed for the sensitivity of dynamic models and the only ones are local. Nevertheless, it would be of great interest to consider the entire uncertainty range of parameters since they can vary within large intervals depending on their meaning. Other advantage of global analysis is that the sensitivity indices of a given parameter are evaluated while all the other parameters can be varied. In this way, the relative variability of each parameter is taken into account, revealing any possible interactions. This paper presents the global sensitivity analysis for dynamic models with an original approach based on the polynomial chaos (PC) expansion of the output. The evaluation of the PC expansion of the output is less expensive compared to direct simulations. Moreover, at each time instant, the coefficients of the PC decomposition convey the parameter sensitivity and then a sensitivity function can be obtained. The PC coefficients are determined using non-intrusive methods. The proposed approach is illustrated with some well-known dynamic systems.

Suggested Citation

  • Haro Sandoval, Eduardo & Anstett-Collin, Floriane & Basset, Michel, 2012. "Sensitivity study of dynamic systems using polynomial chaos," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 15-26.
    • Handle: RePEc:eee:reensy:v:104:y:2012:i:c:p:15-26
    DOI: 10.1016/j.ress.2012.04.001
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    References listed on IDEAS

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    1. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    2. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    3. Dirk J.W. De Pauw & Peter A. Vanrolleghem, 2006. "Practical aspects of sensitivity function approximation for dynamic models," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 12(5), pages 395-414, October.
    4. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    5. Crestaux, Thierry & Le Maıˆtre, Olivier & Martinez, Jean-Marc, 2009. "Polynomial chaos expansion for sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1161-1172.
    6. Jacques, Julien & Lavergne, Christian & Devictor, Nicolas, 2006. "Sensitivity analysis in presence of model uncertainty and correlated inputs," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1126-1134.
    7. Marco Ratto & Andrea Pagano, 2010. "Using recursive algorithms for the efficient identification of smoothing spline ANOVA models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(4), pages 367-388, December.
    8. Rahman, Sharif, 2011. "Global sensitivity analysis by polynomial dimensional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 825-837.
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    Cited by:

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    2. Cao, Jiaokun & Du, Farong & Ding, Shuiting, 2013. "Global sensitivity analysis for dynamic systems with stochastic input processes," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 106-117.
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    5. Oladyshkin, S. & Nowak, W., 2012. "Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 179-190.
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    7. Zhai, Qingqing & Yang, Jun & Zhao, Yu, 2014. "Space-partition method for the variance-based sensitivity analysis: Optimal partition scheme and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 66-82.

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