The experiment of chaotic exponent extraction is carried out on the basis of nonlinear vibration system, and the responses under different conditions are processed with the improved algorithm. Firstly, the weighted wavelet denoise method is applied to filter the contaminated noise. Then, on the basis of fast search technology i.e. space grid hiberarchy inquiry method, the chaos characteristic exponent extraction algorithm is modified and applied to LE and fractal dimension calculation. Finally the piece-wise vibration system is designed, and the nonlinear dynamics under different harmonic frequencies excitation are analyzed. The comprehensive chaos judgment program is developed, in which the time domain diagram, phase space reconstruction attractor, Lyapunov exponent, fractal dimension curve of the measured data are obtained. The interesting phenomena such as AM modulation, limited cycle, and strange attractor are observed.

<p>The characteristics of quasi-zero stiffness(QZS) system with nonlinear positive and negative stiffness is researched. A modified QZS model with nonlinear spring element is established and the stiffness curves are obtained based on the analysis of relationship between spring force and displacement. A non-dimensional form of QZS is deduced to discover its essential laws, and simulation is presented with different nonlinear springs. Then the force transmissibility of QZS is verified with the experiment, which shows that the QZS isolation performance is better than the linear one in the low frequency band, and there exists no resonant peak in this system.</p>

For the purpose of improving adaptive performance of chaotic signals de-noising with wavelet transform, a method of Memetic-algorithm-based adaptive wavelet de-noising (MAWD) is presented. The MAWD based on generalized cross validation (GCV) is competent to obtain the global optimum thresholds and to raise the efficiency of adaptive searching computation. The de-noising results of simulative Lorenz time series are presented. The results show that the chaotic signals de-noised by MAWD can remove the white noise more effectively than the signals de-noised by using standard soft threshoding method (STM) and genetic-algorithm-based adaptive wavelet de-noising (GAWD), and the advantages are more apparent under the condition of lower SNR. The Lorenz time series with lower SNR de-noised by MAWD and GAWD respectively are predicted by Volterra adaptive filters, and the results show that the prediction absolute error of Lorenz time series de-noised by MAWD is nearly nine times smaller than that by GAWD. This method has a promising prospect in practical Chaotic signals de-noising.