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New results for model order reduction, for weakly non-linear systems in the frequency domain, are derived based on a parametric modelling approach. [ABSTRACT FROM AUTHOR]

Many real-life systems can be modelled as a periodic structure which is constituted by repeating identical systems which are called elements. The periodic structures have drawn extensive attentions from researchers and engineers. In this study, based on the concept non-linear output frequency response function, a novel method is developed to detect the position of non-linear components in periodic structures. The validity of this method is demonstrated by numerical studies. Although the method assumes that the linear stiffness and damping for multi-degree-of-freedom (MDOF) systems under study are known a priori, the results of the numerical studies indicate that, even if only approximate values of the linear stiffness and damping parameters are used, the method can still correctly detect the position of the non-linear component. Since the position of a non-linear component often corresponds to the location of a defect in a periodic structure, this new method is of great practical significance for fault diagnosis in mechanical and structural systems. Moreover, the method does not involve complicated procedure and can be readily applied in practice. [ABSTRACT FROM AUTHOR]

New results about the bound characteristics of both the generalized frequency response functions (GFRFs) and the output frequency response for the NARX (Non-linear AutoRegressive model with eXogenous input) model are established. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique for the magnitude based analysis of nonlinear systems in the frequency domain, for example, evaluation of the truncation error in a volterra series expression of non-linear systems and the highest order needed in the volterra series approximation. A numerical example is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]