Skip to main content
SpringerLink
Log in

Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems

  • Conference paper
  • First Online:
Scientific Computing in Electrical Engineering SCEE 2008

Part of the book series: Mathematics in Industry ((TECMI,volume 14))

Abstract

Numerical simulation of electric circuits uses systems of differential algebraic equations (DAEs) in general. We examine forced oscillators, where the DAE models involve periodic solutions. Uncertainties in physical parameters can be described by random variables. We apply the strategy of the generalised polynomial chaos (gPC) to resolve the stochastic model. In particular, failure probabilities are determined using the approximation from gPC. We present results of numerical simulations for a system of DAEs modelling a Schmitt trigger.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kampowsky, W., Rentrop, P., Schmitt, W.: Classification and numerical simulation of electric circuits. Surv. Math. Ind. 2, 23–65 (1992).

    MATH  Google Scholar 

  2. Augustin, F., Gilg, A., Paffrath, M., Rentrop, P., Wever, U.: Polynomial chaos for the approximation of uncertainties: chances and limits. Euro. Jnl. of Applied Mathematics 19, 149–190 (2008).

    MATH  MathSciNet  Google Scholar 

  3. Xiu, D.: Fast numerical methods for stochastic computations: a review. Comm. Comput. Phys. 5 (2-4), 242–272 (2009).

    MathSciNet  Google Scholar 

  4. Günther, M., Feldmann, U., ter Maten, E.J.W.: Modelling and discretization of circuit problems. In: Schilders, W.H.A., ter Maten, E.J.W. (eds.), Handbook of Numerical Analysis, Vol. XIII: Numerical Methods in Electromagnetics, pp. 523-659, Elsevier, N. Holland (2005).

    Google Scholar 

  5. Lucor, D., Karniadakis, G.E.: Adaptive generalized polynomial chaos for nonlinear random oscillators. SIAM J. Sci. Comput. 26 (2), 720–735 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  6. Lucor, D., Su, C.H., Karniadakis, G.E.: Generalized polynomial chaos and random oscillators. Int. J. Numer. Meth. Engng. 60, 571–596 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  7. Pulch, R.: Polynomial chaos for analysing periodic processes of differential algebraic equations with random parameters. To appear in: Proc. Appl. Math. Mech.

    Google Scholar 

  8. Paffrath, M., Wever, U.: Adapted polynomial chaos expansion for failure detection. J. Comput. Phys. 226, 263–281 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  9. Xiu, D., Hesthaven, J.S.: High order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27 (3), 1118–1139 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  10. Pulch, R.: Polynomial chaos for linear DAEs with random parameters. Preprint, Bergische Universität Wuppertal (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik und Numerische Mathematik, Bergische Universität Wuppertal, Gaußstr. 20, 42119, Wuppertal, Germany

    Roland Pulch

Authors
  1. Roland Pulch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roland Pulch .

Editor information

Editors and Affiliations

  1. , Faculty of Electronics, Communications a, Aalto University School of Science and T, AALTO, 00076, Finland

    Janne Roos

  2. , Faculty of Electronics, Communications a, Aalto University School of Science and T, AALTO, 00076, Finland

    Luis R.J. Costa

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pulch, R. (2010). Polynomial Chaos for the Computation of Failure Probabilities in Periodic Problems. In: Roos, J., Costa, L. (eds) Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry(), vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12294-1_25

Download citation

Publish with us

Policies and ethics

Search

Navigation