Spectral identification of nonlinear structural systems

The paper discusses a spectral method for identification of nonlinear systems encountered in structural applications. The nonlinearity is accounted for by a combination of linear subsystems and known zero-memory nonlinear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a "Gram-Schmidt" type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of a Duffing oscillator with nonlinear damping elucidates the applicability of the proposed method.