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

Research paper by Zhuang-Zhuang Liu, Tian-Shu Wang, Jun-Feng Li

Indexed on: 16 Sep '15Published on: 16 Sep '15Published in: Acta Mechanica Sinica


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 10.1007/s10409-015-0500-z.gif