Nonlinear bearing stiffness parameter estimation in flexible rotor–bearing systems using Volterra and Wiener approach

Higher order frequency response functions based on Volterra and Wiener series are explored for the inverse problem of stiffness estimation of a flexible rotor supported in nonlinear bearings. The Volterra series has been employed by researchers earlier for the identification of higher order kernels of nonlinear systems through a non-parametric approach. The present study investigates the possibility of employing these kernels for parameter estimation of the system. Numerical simulation has been carried out for a system with three degrees of freedom and with cubic nonlinearity in stiffness. A frequency domain has been adopted for the identification of higher order kernels. The procedure involves extraction of Wiener kernels from the response of the system to a Gaussian white noise excitation. Volterra kernels are in turn synthesised from the Wiener kernels. In addition to direct kernels, the system under consideration, requires definitions of cross-kernels and their estimation. Expressions for the cross and direct kernels are constructed in the frequency domain. A set of third-order kernel factors are algebraically and graphically synthesised from the measured first-order kernels. These third-order kernel factors are then processed with the measured third-order kernels for nonlinear parameter estimation. Damping is taken to be linear in the analysis. The procedure is illustrated through numerical simulation. The assumptions involved and the approximations are discussed.