Interval analysis method based on Legendre polynomial approximation for uncertain multibody systems

Abstract An interval analysis method termed as Legendre interval model is presented to solve multibody dynamic systems with interval parameters. The implementation of Legendre interval model involves two steps. The first step is to approximate the original multibody model using Legendre polynomial approximation. Then take the interval parameters into consideration, and the Legendre interval model with interval parameters is obtained. The second step is to calculate the bounds of Legendre interval model using interval arithmetic or scanning. Legendre interval model using interval arithmetic, Legendre interval model using scanning, Chebyshev inclusion function method and scanning method are applied into typical multibody systems with interval parameters and compared in terms of efficiency and accuracy. The Legendre interval model using scanning shows high accuracy and efficiency.