An interval uncertainty propagation method using polynomial chaos expansion and its application in complicated multibody dynamic systems

Abstract

This paper is devoted to the construction of a nonintrusive interval uncertainty propagation approach for the response bounds evaluation of multibody systems. The motivation for this effort is twofold. First, the traditional methods using the Taylor inclusion function and interval arithmetic usually lead to the wrapping effect. Second, the real-life multibody dynamics models are mostly large systems, which are highly rigid, nonlinear, and discontinuous; however, many conventional, intrusive interval analysis methods are not suitable for such large, complicated multibody systems. To end these, a polynomial chaos inclusion function using Legendre orthogonal basis is presented for analyzing such multibody dynamics models with interval uncertainty, where the Galerkin projection method is adopted to compute the Legendre polynomial coefficients. The capacity of the Legendre polynomial inclusion function to alleviate the wrapping effect is proved by a mathematical example. Through sampling, the nonintrusive algorithm expresses the original multibody dynamics system with interval uncertainty as the deterministic differential algebraic equations, followed by calculation using the general numerical integration method. The response bounds at each time step are predicted using the truncated Legendre polynomial expansion. A benchmark test based on three methods is analyzed to demonstrate the effectiveness of this approach. Moreover, an artillery multibody dynamics model created in ADAMS/Solver can reproduce a suite of experimental results, and is then specifically investigated to illustrate the superiority of this method in large, complicated multibody dynamic systems.