Extrapolation Behavior Comparison of Nonlinear State Space Models

摘要

The extrapolation behavior and its consequences of two different state space models is studied. More specifically, the extrapolation behavior of thelocal model state space network(LMSSN) is compared to thepolynomial nonlinear state space model(PNLSS). Both approaches represent favorable alternatives in the light of their results on recent benchmark studies. The models are compared with regards to their static extrapolation behavior and their tendency to erratic behavior if test amplitudes grow larger than training amplitudes. It is shown on a Hammerstein and Wiener artificial test process that the PNLSS shows severe shortcomings concerning stability when operated close to or outside the boundaries in which it was trained. The LMSSN instead shows more favorable behavior in extrapolation and does only exhibit minor erratic behavior. If the process is inherently polynomial in some way, the PNLSS outperforms other models in extrapolation, as shown on the Silverbox benchmark test.