A piecewise-linear moment-matching approach to parameterized model-order reduction for highly nonlinear systems

This paper presents a parameterized reduction technique for highly nonlinear systems. In our approach, we first approximate the nonlinear system with a convex combination of parameterized linear models created by linearizing the nonlinear system at points along training trajectories. Each of these linear models is then projected using a moment matching scheme into a low order subspace, resulting in a parameterized reduced order nonlinear system. Several options for selecting the linear models and constructing the projection matrix are presented and analyzed. In addition, we propose a training scheme which automatically selects parameter-space training points by approximating parameter sensitivities. Results and comparisons are presented for three examples which contain distributed strong nonlinearities: a diode transmission line, a Micro-Electro-Mechanical switch and a pulse narrowing nonlinear transmission line. In most cases we are able to accurately capture the parameter dependence over parameter ranges of ±50% from the nominal values, and to achieve an average simulation speedup of about 10×. Copyright © 2007 IEEE.