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.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering