Estimation of Volterra kernel coefficients of a nonlinear dynamic system

초록

The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by Volterra series, provided that the Volterra kernels of different order is known. This study presents the methodology on the direct estimation of Volterra kernel coefficients up to second order using prepared data which is obtained by running time domain analysis of the system of interest. To avoid potential problems during kernel estimation, Volterra kernel was expanded into the polynomial series using Laguerre polynomials then the coefficients of Laguerre polynomial were estimated via least square method. A nonlinear oscillator with quadratic stiffness term was introduced and the methodology was applied to check the applicability and accuracy. Also, the methodology was applied to the more realistic engineering problem which modeled a simplified riser under irregular wave excitation.

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