Physical-Inspired State Space Structure for Nonlinear Gray-Box Modeling
Hermann Klein, Max Schüssler, Oliver Nelles · 2024
Nonlinear models in state space representation are powerful architectures for system identification. Modern blackbox state space models have shown high modeling performance, but comprehending the meaning of their parameters is often difficult. The goal is to increase the interpretability of a datadriven model. For that purpose, this paper presents a modeling strategy that applies a gray-box specific state space structure based on an arbitrary linear differential equation from frist-principles, which is provided by the user as prior knowledge. Furthermore, we use the applied structure to transport the prior knowledge from the linear differential equation to a nonlinear state space model with the help of the Local Model State Space Network (LMSSN). The gray-box modeling concept is demonstrated on a simulated system identification problem, where we show that the resulting gray-box structured model allows detailed physical insights.