Nonlinear Model Order Reduction Using Remainder Functions

This paper describes a novel approach to the problem of model order reduction (MOR) of very large nonlinear systems. We consider the behavior of a dynamic nonlinear system as having two fundamental characteristics: a global behavioral "envelope" that describes major transformations to the state of the system under external stimuli and a local behavior that describes small perturbation responses. The nonlinear low order envelope function is generated by using the remainders from the coalescence of projection bases taken through a space-state sample. A behavioral model can then be expressed as the superposition of these two descriptions, operating according to the input stimuli and the current state value. The global behavior describes major transformations to the state of the system under external stimuli and the local behavior describes small perturbation responses. Local effects are captured by regions through a set of linear projections to a reduced state-space while global effects are captured by examining the non-commonalty among these projections. These "remainders" are used to build a modulation function that will generate the required dynamic changes in the common linear projection. The advantage of the envelope representation for strongly nonlinear systems is that it simplifies the complexity of the model into a two-part problem. Depending on the complexity or cost of the behavioral separation procedure, it can be repeated recursively