Recently, many research works have been published in the area of nonlinear system identification. Up to this year, nonparametric method using functional forms to represent the nonlinear restoring forces is popular since the characteristics of nonlinearity is not known. But, it is difficult to apply the nonparametric method to multi degree-of-freedom system due to such aspects of mathematical complexity and excessive computing time. Now a day, the research to identify the nonlinearity have been doing widely. The main goal of this research area is to investigate the existence of nonlinearity within the system. But the researches to find out nonlinearity positions are rare. And, it is not common that all the system or structural elements have nonlinear characteristics. Mostly, only a few elements have nonlinear properties, and these elements make the whole system be nonlinear. That means it will not be an efficient way to model a locally nonlinear system with the nonparametric identification technique in which it is assumed that nonlinear elements are spread on the whole system. In order to remove the above mentioned inefficiency in the nonparametric identification method, nonlinear elements splitting technique from the whole system is needed.
In this work, an efficient method to identify nonlinear elements' positions and those type within a system or structure is suggested. The positions of nonlinear elements existing locally in a structure can be detected by comparing the equivalent linearized damping and stiffness matrices which are obtained by the process of equivalent linearization for two different input levels. For the detection of nonlinear elements' positions, two different methods are proposed depending on the type of used signal. One is the time domain method in which time domain signal is used to detect positions of nonlinear elements, the other is the frequency domain method in which frequency domain signal is used. In the time domain method, the error matrix method and error vector method are proposed to detect the positions of nonlinear elements while in the frequency domain method only the error matrix method is suggested. By using the error matrix, we can detect the positions of nonlinear elements and by using the error vector, nonlinear elements' connectivities as well as the positions of nonlinear elements can be revealed.
After determining the positions of nonlinear elements, it is furthermore useful if we know the nonlinearity type. In this work, a local identification method is suggested for the identification of nonlinearity type. The information of positions of nonlinear elements is used to group linear and nonlinear parts in the whole system. Then locally existing nonlinear parts are modelled with polynomial series functions of response state vectors as are modelled with polynomial series functions of response state vectors as in the nonparametric method. All the remaining restoring forces related to the linear elements are modelled by linear springs and dampers. And we call such an identification technique as a local nonparametric method. Since the local nonparametric method does not apply the nonparametric technique upon the whole positions but upon only several positions connected with nonlinear elements, it not only reduces calculation efforts drastically but also improves its accuracy. Furthermore, the number of unknown coefficients in the local nonparametric method can be reduced by using the correlation coefficients between the nonlinear restoring force and polynomial terms. Also it is found that these proposed techniques are very effective to identify both the linear and nonlinear joint properties. All the above methods are tested numerically with several models.
