Determination of the polynomial restoring force of a one DoF bistable Duffing oscillator by linear regression

A large class of energy-harvesting systems includes a bistable magnetoelastic oscillator. Due to the high complexity of the inherent magnetic field forces, those systems are commonly represented as a combination of physical and phenomenological, low-dimensional models. Therein occurring three free parameters of dissipation and restoring force are determined by the decay rate as well as constraints for the position of the equilibria and the frequency of small amplitude oscillations. As will be shown in this paper, one major disadvantage of this procedure is that high amplitude oscillations, which are most relevant in context of energy harvesting, yield the poorest consistency with experimental observations. To overcome the problem, a regression-based nonlinear system identification is performed using system responses under harmonic excitation. Models with cubic as well as quintic restoring forces are identified and compared with the experimental observations as well as a model that was built with the commonly used identification procedure. As a result, it is found that both models from the regression show a higher agreement with the experimental data. Furthermore, the quintic model is found to be more accurate than the cubic model. This shows the necessity to be able to include more than three free parameters in the model. The advantage of the applied procedure lies in the raised flexibility of model adaptation resulting in improved agreement of simulation and experimental results.