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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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    2. 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.
    3. Oladyshkin, Sergey & Nowak, Wolfgang, 2018. "Incomplete statistical information limits the utility of high-order polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 137-148.
    4. Tang, Zhang-Chun & Zuo, Ming J. & Xiao, Ningcong, 2016. "An efficient method for evaluating the effect of input parameters on the integrity of safety systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 111-123.
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    6. 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.
    7. Verleysen, Kevin & Parente, Alessandro & Contino, Francesco, 2021. "How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)," Energy, Elsevier, vol. 232(C).

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