Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics

Abstract

A parametric identification procedure is proposed that combines

the method of multiple scales and higher-order statistics to

efficiently and accurately model nonlinear

systems. A theoretical background for the method of

multiple scales and higher-order

statistics is given.

Validation of the procedure is performed

through applying it to numerical simulations of two

nonlinear systems. The results show how the procedure can

successfully characterize the system damping and nonlinearities and

determine the corresponding parameters.

The procedure is then applied to experimental measurements from

two structural systems, a

cantilevered beam and a three-beam frame. The results show that

quadratic damping should be accounted for in both systems.

Moreover, for the three-beam frame, the parametric excitation is

much more important than the direct excitation.

To show the flexibility of the

procedure, numerical simulations of ship motion under parametric

excitation are used to determine nonlinear parameters govening the

relation between pitch, heave, and roll motions. The results show

a high level of agreement between the numerical simulation and the

mathematical model with the identified parameters.