Position of non-linear elements and identification of their type by a local non-parametric method

Abstract

In this paper, an efficient method of identifying non-linear element positions and their type within a system or structure is suggested. Allowing for the non-proportional relationship between input excitation force and resulting output responses, time domain excitation and response signals are used to detect the non-linear element positions. When two different levels of excitation force are imposed on a testing system, the resulting responses at n points are measured and analysed. Assuming the system is linear, the equivalent linearised damping and stiffness matrices for each input force level are determined with the corresponding input and output time domain signals. An error matrix is then defined and obtained from the linearised matrices for each different force level. By examining the error matrix, it is possible to detect the positions of non-linear damping and/or stiffness elements within the structure. The non-linear element connectivity information can be judged with an error vector which is defined as the difference between the linearised force and the non-linear restoring force. Since the magnitude of each element of the error vector represents the degree of non-linearity, the degrees of freedom connected with non-linear elements can be approximately identified by examining the error vector plot. After determining the positions of non-linear elements, it is additionally useful to know the non-linearity type. In this work, a local identification method is suggested for that purpose. First, each non-linear restoring force is modeled with polynomial series functions of response state vectors. Then all the coefficients of those series functions are determined with the least square error minimisation method. Since the local identification method does not apply the non-parametric technique upon all the positions but only on several connected with non-linear elements, it not only reduces calculation efforts drastically but also improves accuracy. In order to show the effectiveness of these methods, several numerical examples are tested and discussed. Noise effects on both position detection and type identification are also analysed and discussed. © 1991.