Linear and nonlinear ARMAX modeling approach in nonlinearity identification

Abstract

Nonlinear ARMAX models and generalized frequency response functions(FRFs) are good tools for identification of a nonlinear system as well as for control of it. The NARMAX model not only enlarges applicable input range, which is often restricted to very narrow one when a linear model is used, but enables spectral analysis of the system in terms of the generalized FRFs, which are very difficult by other methods. Once determined, the generalized FRFs give good descriptions of various nonlinearities such as harmonics, gain variation and intemodulations. With all the strong advantages of the NARMAX model, there are several obstacles to be solved first. The main objective of the dissertation is to develope a nonlinear time series modeling approach for the purpose of the identification of nonlinearities contained in linear-based nonlinear systems. To achieve the purpose, the work has done about the following topics: i) testing of existence of nonlinearity, ii) investigating the several problems of the NARMAX modeling and, as a solution to them, developing a new modeling technique so as to fit the aim, iii) confirming the feasibilities of the method through applications to simulations and experiments. As a start of the identification of nonlinear systems, an existence of any nonlinearity is tested using kurtosis or 4th moment, which has been widely used for analyzing signal patterns. By inputting a harmonic input to the nonlinear system and investigating distortions of the output signal from a harmonic pattern, which are due to violations of the proportionality between the input and the output, it is judged whether the output is generated from a linear system or not. Most of nonlinearities in mechanical systems are often regarded as to be dependent upon amplitudes of responses. In case of a linear-based nonlinear system, which is regarded as linear for responses of small amplitudes and as nonlinear for large ones, linear characteristics of the system are found to do...