Linear Bounds on an Uncertain Non-Linear Oscillator: An Info-Gap Approach

  • Yakov Ben-Haim
  • Scott Cogan
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 27)


We study a 1-dimensional cubic non-linear oscillator in the frequency domain, in which the non-linearity is roughly estimated but highly uncertain. The task is to choose a suite of linear computational models at different excitation frequencies whose responses are useful approximations to, or upper bounds of, the real non-linear system. These model predictions must be robust to uncertainty in the non-linearity. A worst case for the uncertain non-linearity is not known. The central question in this paper is: how to choose the linear computational models when the magnitude of error of the estimated non-linearity is unknown. A resolution is proposed, based on the robustness function of info-gap decision theory. We also prove that the non-probabilistic info-gap robustness is a proxy for the probability of success.


Middle Curve Load Uncertainty Robustness Function Life Cycle Design Uncertain Load 
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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Yitzhak Moda’i Chair in Technology and Economics, Faculty of Mechanical EngineeringTechnion — Israel Institute of TechnologyHaifaIsrael

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