Acta Mechanica Sinica

, Volume 32, Issue 1, pp 170–180 | Cite as

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

  • Zhuang-Zhuang Liu
  • Tian-Shu WangEmail author
  • Jun-Feng Li
Research Paper


This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arithmetic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the “wrapping effect” of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

Graphical Abstract


Non-intrusive hybrid interval method Dynamic response analysis Uncertain nonlinear systems Polynomial approximation Interval arithmetic  Derivative information 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of AerospaceTsinghua UniversityBeijingChina

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