  In this paper we aim to apply an adaptation of the recently developed
technique of sparse identification of nonlinear dynamical systems on a Duffing
experimental setup with cubic feedback of the output. The Duffing oscillator
described by nonlinear differential equation which demonstrates chaotic
behavior and bifurcations, has received considerable attention in recent years
as it arises in many real-world engineering applications. Therefore its
identification is of interest for numerous practical problems. To adopt the
existing identification method to this application, the optimization process
which identifies the most important terms of the model has been modified. In
addition, the impact of changing the amount of regularization parameter on the
mean square error of the fit has been studied. Selection of the true model is
done via balancing complexity and accuracy using Pareto front analysis. This
study provides considerable insight into the employment of sparse
identification method on the real-world setups and the results show that the
developed algorithm is capable of finding the true nonlinear model of the
considered application including a nonlinear friction term.
