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Sensitivity analysis and model order reduction for random linear dynamical systems

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  • Pulch, Roland
  • ter Maten, E. Jan W.
  • Augustin, Florian

Abstract

We consider linear dynamical systems defined by differential algebraic equations. The associated input–output behaviour is given by a transfer function in the frequency domain. Physical parameters of the dynamical system are replaced by random variables to quantify uncertainties. We analyse the sensitivity of the transfer function with respect to the random variables. Total sensitivity coefficients are computed by a nonintrusive and by an intrusive method based on the expansions in series of the polynomial chaos. In addition, a reduction of the state space is applied in the intrusive method. Due to the sensitivities, we perform a model order reduction within the random space by changing unessential random variables back to constants. The error of this reduction is analysed. We present numerical simulations of a test example modelling a linear electric network.

Suggested Citation

  • Pulch, Roland & ter Maten, E. Jan W. & Augustin, Florian, 2015. "Sensitivity analysis and model order reduction for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 111(C), pages 80-95.
    • Handle: RePEc:eee:matcom:v:111:y:2015:i:c:p:80-95
    DOI: 10.1016/j.matcom.2015.01.003
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    References listed on IDEAS

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    1. Villegas, M. & Augustin, F. & Gilg, A. & Hmaidi, A. & Wever, U., 2012. "Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 805-817.
    2. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    3. Pulch, Roland, 2011. "Modelling and simulation of autonomous oscillators with random parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1128-1143.
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    1. Pulch, Roland, 2018. "Model order reduction and low-dimensional representations for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 1-20.
    2. Pulch, Roland, 2019. "Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 76-92.

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