An Optimal Model Identification Algorithm of Nonlinear Dynamical Systems With the Algebraic Method

Abstract

Abstract This article 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 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.