Parameter estimation on nonlinear systems using orthogonal and algebraic techniques

Abstract

High displacements, geometrical restrictions and complex behavior are now common in modern mechanical structures involving new materials with inherent nonlinear phenomena (e.g., stiffness, damping and excitation). In this work, we propose a novel parameter identification scheme based on signal approximation via orthogonal functions. A Hilbert transform based nonlinearity index is calculated in order to evaluate possible nonlinearities appearing into the system dynamics and then we compute the algebraic estimation of the most important parameters into the nonlinear system.We use algebraic identification techniques based on the Mikusinski’s approach to operational calculus, The proposed approach is first developed for single degree-of-freedom systems and then this is generalized for some case studies considering multiple degrees-of-freedom, by using information obtained from variations in the initial conditions (free response) to get the so-called eigenstructure. The approach is validated by means of numerical simulations and experimental results.