Studies On Experimental Modeling And Frequency Domain Identification Of Nonlinear Systems

In the second chapter, the HBNID method is used to study the experimental modeling of a nonlinear system with parametric excitation. In the modeling, axial static stress is taken into account, which can cause the coefficient of linear stiffness negative. For the data of external excitation, the amplitude and the phase are used, while the amplitude is normalized in the frequency domain to be unit. Since merely the data for acceleration are available, the Fourier coefficients of acceleration are directly computed by numerical calculus while the Fourier coefficients of displacement, velocity, nonliner terms and parametric excitation term are obtained via the differential relationship in the frequency domain, exponential operation and Kronecker function. Finally, the least square method for linear equations in the complex domain is used to identify the unknown parameters. By repeating the modeling, the assumed model is refined and identified for primary resonance and 1/2 subharmonic resonance.In the third chapter, Fast Forier Transform is used to study the modeling and parametric identification of nonlienar systems with parametric exciation by using periodic response, doubling-periodic response and chaotic response. Numerical simulation shows that the coupling of FFT and harmonic balance principle is not only effective in parametric identification by using non-periodic response, such as chaotic response, but also of high identification accuracy. In addition, the effects of measurement noise on parameric identification are analyzed. For the periodic response, higher level of noise and too large harmonic number renders the serious decline in the identificaiton accuracy. However, for the chaotic response, the effect of measurement noise is comparatively slight.In the fourth chapter, a new method, called Incremental Harmonic Balance Nonlinearity Identification:IHBNID, is proposed by using Incremental Harmonic Balance (IHB) inversely to identify parameters. The new method is an iterative method. The initial response of the theoretical model is the experimental response, and the initial values of unknown parameters are arbitrary values, such as zero. In the interation, the Fourier coefficients of large-amplitude and high-SNR are fixed while other Fourier coefficients and the values of unknown parameters are updated to minimize the residue of the model. In the mathematical derivation, the exponential Fourier series is used instead of the usual trigonometrical Fourier series, and therefore a simpler result is achieved by using exponential operation and Kronecker function, which facilitates the computer programming. Finally, the new method is used to study the parametric identification of the theoretical Mathieu-Duffing oscillation by using numerical simulation. Compared to the performance of HBNID, the new method IHBNID is advantageous in terms of identification accuracy and noise resistance.