System identification through chaotic interrogation

We introduce a method by which the coefficient of viscous damping for a linear ndof system may be estimated. The technique utilises the unique properties of chaos by driving the system with the output of a non-linear oscillator. By tuning the Lyapunov exponents of the driving signal to the eigenvalues of the linear structure, the dimension of the output is effectively controlled. Estimates of the complete Lyapunov spectrum may then be used to extract the real part of the dominant eigenvalue, and hence the damping, for the system. Results are presented for a 2-dof spring-mass-damper driven with the output of the chaotic Lorenz oscillator. The effects of additive noise are also considered.