Development of a Modular Broad Learning System Model for Dynamic Hysteresis Effects

The Hammerstein model, comprising a nonlinear static subsystem in series with a linear dynamic subsystem, is widely employed to characterize various dynamic hysteresis effects. However, its serial structure poses challenges in simultaneously identifying the parameters of both subsystems. To address this limitation, a modular broad learning system (MBLS) model is proposed. In the MBLS model, different hysteresis modules are interconnected in parallel to the output layer. This design divides the complex task of modeling comprehensive dynamic hysteresis effects into subtasks assigned to individual modules. The MBLS model comprises a static hysteresis module and several dynamic hysteresis modules. The static hysteresis module employs an operator-based hysteresis model to delineate the static hysteresis phenomenon. The dynamic hysteresis modules are subsequently incorporated by adding module increments to the static foundation. Experiments are conducted on a dielectric elastomer actuator (DEA) system to validate the effectiveness of the proposed MBLS model.