Compact model order reduction of weakly nonlinear systems by associated transform

We advance a recently proposed approach, called the associated transform, for computing slim projection matrices serving high‐order Volterra transfer functions in the context of weakly nonlinear model order reduction (NMOR). The innovation is to carry out an association of multivariate (Laplace) variables in high‐order multiple‐input multiple‐output transfer functions to generate univariate single‐s transfer functions. In contrast to conventional projection‐based NMOR which finds projection subspaces about every s_i in multivariate transfer functions, only that about a single s is required in the proposed approach. This leads to much more compact reduced‐order models without compromising accuracy. Specifically, the proposed NMOR procedure first converts the original set of Volterra transfer functions into a new set of linear transfer functions, which then allows direct utilization of linear MOR techniques for modeling weakly nonlinear systems with either single‐tone or multi‐tone inputs. An adaptive algorithm is also given to govern the selection of appropriate basis orders in different Volterra transfer functions. Numerical examples then verify the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.