CHARACTERIZATION AND DETECTION OF PARAMETER VARIATIONS OF NONLINEAR MECHANICAL SYSTEMS

The present study applies the recently developed ideas in experimental system modeling to both characterize the behavior of simple mechanica l systems and detect variations in their parameters. First, an experim ental chaotic time series was simulated from the solution of the diffe rential equation of motion of a mechanical system with clearance. From the scalar time series, a strange attractor was reconstructed optimal ly by the method of delays. Optimal reconstructions of the attractors can be achieved by simultaneously determining the minimal necessary em bedding dimension and the proper delay time. Periodic saddle orbits we re extracted from the chaotic orbit and their eigenvalues were calcula ted. The eigenvalues associated with the saddle orbits are used to est imate the Lyapunov exponents for the steady state motion. An analysis of the associated one dimensional delay map, obtained from the chaotic time series, is made to determine the allowable periodic orbits and t o yield an estimate of the topological entropy for the positive Lyapun ov exponent. Sensitivity of the positions of the low order unstable pe riodic orbits (orbits of short period) of a chaotic attractor is used as a basis for detection of parameter variations in another unsymmetri c bilinear system. For the experimental scalar time series generated b y the dynamical system as a parameter varies, the chaotic attractors w ere again optimally reconstructed using the method of delays. The para meter variations were detected by the changes in location of the unsta ble periodic orbits extracted from the reconstructed attractors of the experimental scalar time series.