Parameter estimation of Duffing oscillator using Volterra series and multi-tone excitation

Use of Volterra series in nonlinear system identification is well established now. The series represents response of a nonlinear system in a functional series form consisting of convolution integrals involving higher-order impulse response functions known as Volterra kernels. Multi-dimensional Fourier transforms of these Volterra kernels give the higher-order frequency response functions (FRFs). The measurement of these FRFs under harmonic excitation and their relationship with the first-order FRFs provide a basis for estimation of the nonlinear parameters. However, most of the methods employ single-tone excitation, which provide limited FRF measurement in a single experiment. In the present study, a novel procedure based on multi-tone excitation is presented for a typical Duffing oscillator and it is demonstrated that accurate estimation of both nonlinear and linear parameters is possible with fewer number of experiments.

Research highlights
► Nonlinear parameter estimation of a Duffing oscillator using Volterra series is proposed.
► Response amplitudes under multi-tone excitation are computed using Higher Order FRFs.
► Higher order FRFs are extracted from the measured response harmonic amplitudes.
► Synthesis of higher order FRFs from First order FRFs provides estimation of the nonlinear parameter.