Parametric identification of an experimental magneto-elastic oscillator

The identification of parameters in an experimental two-well chaotic system is presented. The method involves the extraction of periodic orbits from a chaotic set. The form of the differential-equation model is assumed, with unknown coefficients appearing linearly on the terms in the model. The harmonic-balance method is applied to these periodic orbits, resulting in a linear set of equations in the unknown parameters, which can then be solved in the least-squares sense. The identification process reveals the non-linear force-displacement characteristic of the oscillator. The results are cross-checked with various sets of extracted periodic orbits. The model is validated by comparing the linearized characteristics, examining simulated responses, and evaluating the vector field.