Polynomial State-Space Model Decoupling for the Identification of Hysteretic Systems

Hysteresis is a nonlinear effect that shows up in a wide variety of engineering and scientific fields. The identification of hysteretic systems from input-output data is an important but challenging question, which has been studied by using both tailored parametric white-box identification methods as by using black-box identification methods. The white-box modeling approach is by far the most common in identifying hysteretic systems, and has the advantage of resulting into an interpretable model, but it requires to be adjusted to a specific hysteresis model. A black-box approach can be used more universally, but results in models containing many parameters that cannot easily be interpreted. In the current paper, we propose a two-step identification procedure that combines the best of the two approaches. We employ the Bouc-Wen hysteretic model to generate data that is used for identification. The system is identified using a black-box polynomial nonlinear state-space identification procedure. We reduce the number of parameters in this model by applying a polynomial decoupling method that results in a more parsimonious representation. We compare the full black-box model with the decoupled model and show that the proposed method results in a comparable performance, while significantly reducing the number of parameters.