Fast simulation of nonlinear dynamical systems for application in reduced order modelling

Abstract

The Trajectory piecewise linear (TPWL) representation of nonlinear dynamical systems requires an a-priori solution of the nonlinear system trajectory. This paper proposes a new algorithm for finding an approximate nonlinear system trajectory to reduce the computational burden of the TPWL process. Additionally, the new algorithm has an error assessment feature that provides a less heuristic alternative to the conventional methods. It is shown that the TPWL model can be obtained with lesser user intervention using the new algorithm and also comprises of a smaller number of constituent linear systems.