Nonlinear Parameter Estimation

Abstract

The industrial demand on good dynamical simulation models is increasing. Since most structures show some form of nonlinear behavior, linear models are not good enough to predict the true dynamical behavior. Therefore nonlinear characterization, localization and parameter estimation becomes important issues when building simulation models. This paper presents identification techniques for nonlinear systems based on both random and harmonic excitation signals. The identification technique based on random excitation builds on the well known reverse-path method developed by Julius S. Bendat. This method treats the nonlinearity as a feedback forcing term acting on an underlying linear system and the parameter estimation is performed in the frequency domain by using conventional MISO/MIMO techniques. Although this method provides a straightforward and systematic way of handling nonlinearities, it has been somewhat limited in use due to the complexity of creating uncorrelated inputs to the model. As is shown in this paper, the parameter estimation will not be improved with conditioned inputs and the nonlinear parameters and the underlying linear system can still be estimated with partially correlated inputs. This paper will also describe a parameter estimation method to be used with harmonic input signals. By using the principle of harmonic balance and multi-harmonic balance it is possible to estimate an analytical frequency response function of the studied nonlinear system. This frequency response function can, in conjunction with measured nonlinear transfer functions, be used to estimate the nonlinearity present in the system. This method is also applicable on nonlinear systems with memory, e.g. systems with hysteresis effects. The above mentioned methods are applied to multi-degree-of-freedom and single-degree-of-freedom systems with different types of nonlinearities. Also, techniques for locating nonlinearities are discussed.