No abstract

This paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended to nonlinear systems with time delay. The proposed algorithm combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation for preprocessing signals to filter the noise and for removing the dependence on initial conditions. We further integrate the bootstrapping resampling technique with the sparse regression to obtain the statistical properties of estimation. We use Taylor expansion to parameterize time delay. The proposed algorithm in this paper is computationally efficient and robust to noise. A nonlinear Duffing oscillator is simulated to demonstrate the efficiency and accuracy of the proposed technique. An experimental example of a nonlinear rotary flexible joint is presented to further validate the proposed method.

This paper proposes a nonparametric system identification technique to discover the governing equation of nonlinear dynamic systems with the focus on practical aspects. The algorithm builds on Brunton's work in 2016 and combines the sparse regression with an algebraic calculus to estimate the required derivatives of the measurements. This reduces the required derivative data for the system identification. Furthermore, we make use of the concepts of K-fold cross validation from machine learning and information criteria for model selection. This allows the system identification with less measurements than the typically required data for the the sparse regression. The result is an optimal model for the underlining system of the data with a minimum number of terms. The proposed nonparametric system identification method is applicable for multiple-input-multiple-output systems. Two examples are presented to demonstrate the proposed method. The first one makes use of the simulated data of a nonlinear oscillator to show the effectiveness and accuracy of the proposed method. The second example is a nonlinear rotary flexible beam. Experimental responses of the beam are used to identify the underlining model. The Coulomb friction in the servo motor together with other nonlinear terms of the system variables are found to be important components of the model. These are, otherwise, not available in the theoretical linear model of the system.

No abstract

No abstract