Non-linear parameter estimation in multi-degree-of-freedom systems using multi-input Volterra series

Functional form input-output representation through Volterra series has been widely used for non-linear system analysis and non-parametric system identification. Recent research work shows that the series representation can be suitably employed for parametric identification also. However, the classical Volterra series is based on a single-input and its application is limited to analysis and identification of single-degree-of-freedom system only. The concept of single-input Volterra series has been extended to multi-input Volterra series by Worden et al. through definition of direct and cross-kernels. The present study employs the multi-input Volterra series and develops a structured response representation of various harmonics under multi-input harmonic excitations. Kernel synthesis formulations are developed for a polynomial form non-linearity with general square and cubic terms. It is shown that higher-order direct and cross-kernel transforms are functions of the first-order kernel transforms and the non-linear parameter vectors. A parameter estimation procedure based on recursive iteration is suggested and illustrated for a two-degree-of-freedom system with square and cubic stiffness non-linearity. Numerical simulations and error analysis are presented for typical rotor-bearing system parameters. (C) 2003 Elsevier Science Ltd. All rights reserved.