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

Abstract—This paper presents a parameterized reduction tech-nique 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 ana-lyzed. In addition, we propose a training scheme which automat-ically 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 microelectromechanical switch, and a pulse-narrowing nonlinear transmission line. In most cases, we are able to accurately capture the parameter dependence over the parameter ranges of ±50 % from the nominal values and to achieve an average simulation speedup of about 10×. Index Terms—Model-order reduction (MOR), nonlinear systems, parameterized reduced-order models (PROMs)