Algebraic Parameter Identification of Nonlinear Vibrating Systems and Non Linearity Quantification Using the Hilbert Transformation

Abstract

A novel algebraic scheme for parameters’ identification of a class of nonlinear vibrating mechanical systems is introduced. A nonlinearity index based on the Hilbert transformation is applied as an effective criterion to determine whether the system is dominantly linear or nonlinear for a specific operating condition. The online algebraic identification is then performed to compute parameters of mass and damping, as well as linear and nonlinear stiffness. The proposed algebraic parametric identification techniques are based on operational calculus of Mikusiński and differential algebra. In addition, we propose the combination of the introduced algebraic approach with signals approximation via orthogonal functions to get a suitable technique to be applied in embedded systems, as a digital signals’ processing routine based on matrix operations. A satisfactory dynamic performance of the proposed approach is proved and validated by experimental case studies to estimate significant parameters on the mechanical systems. The presented online identification approach can be extended to estimate parameters for a wide class of nonlinear oscillating electric systems that can be mathematically modelled by the Duffing equation.