Non-linear model updating of a three-dimensional portal frame based on Wiener series

Abstract

The common metrics used in linear finite element (FE) model updating using vibration test data are generally functions of relationships based on unidimensional convolution, for example, distances involving natural frequencies, frequency response or impulse response functions, modal shapes, etc. When a structure has local elements or geometry, like joints, bolts, gaps, backlash, etc., these approaches can fail once it could to induce non-linear behavior. Thus, the methods for FE model updating, when considering the existence of localized non-linear parameters, have been receiving much attention in the last years. In this sense, the present paper proposes the use of a strategy through objective functions based on multiples convolutions described by the first order and second order discrete-time Volterra kernels. These kernels are effective metrics for a model updating into large FE model with local non-linearity. In order to improve the non-linear coefficient identification, an orthogonal basis involving Kautz filter is used to expand the kernels, called by Wiener kernel. To exemplify in full details the steps of the updating procedure, an FE model of a three-dimensional portal frame with commons non-linearities is simulated with different excitation forces and used to identify the non-linear parameters. These results allow us to characterize the practical applicability and the drawbacks of the proposed method with suggestions and remarks for further use in industrial structures.