Identification of structured nonlinear state–space models for hysteretic systems using neural network hysteresis operators

• Published in: Measurement : journal of the International Measurement Confederation Vol. 224; p. 113966
• Main Authors: Krikelis, Konstantinos, Pei, Jin-Song, van Berkel, Koos, Schoukens, Maarten
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2024
• Subjects: Artificial neural networks; Hysteresis; Linear fractional representation; Nonlinear state space; Nonlinear system identification; Prandtl–Ishlinskii; Prandtl–Ishlinskii; Nonlinear state space; Hysteresis; Nonlinear system identification; Artificial neural networks; Linear fractional representation
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2023.113966

Hysteretic system behavior is ubiquitous in science and engineering fields including measurement systems and applications. In this paper, we put forth a nonlinear state–space system identification method that combines the state–space equations to capture the system dynamics with a compact and exact artificial neural network (ANN) representation of the classical Prandtl–Ishlinskii (PI) hysteresis. These ANN representations called PI hysteresis operator neurons employ recurrent ANNs with classical activation functions, and thus can be trained with classical neural network learning algorithms. The structured nonlinear state–space model class proposed in this paper, for the first time, offers a flexible interconnection of PI hysteresis operators with a linear state–space model through a linear fractional representation. This results in a comprehensive and flexible model structure. The performance is validated both on numerical simulation and on measurement data. •Exact recurrent ANN representations of the stop, play & generalized play PI operators•Simultaneous identification of hysteretic & system dynamics using state–space models•The use of rich signals allows to capture the system dynamics and hysteretic effects