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

作　　者：Zhuang-Zhuang Liu Tian-ShuWang Jun-Feng Li 

机构地区：[1]School of Aerospace,Tsinghua University

出　　处：《Acta Mechanica Sinica》2016年第1期170-180,共11页力学学报（英文版）

摘　　要：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 arith- metic 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 ＂wrap- ping 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 effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.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 arith- metic 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 ＂wrap- ping 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 effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

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

分 类 号：O175[理学—数学]