NEW REGULARIZATION BY TRANSFORMATION FOR NEURAL-NETWORK-BASED INVERSEANALYSES AND ITS APPLICATION TO STRUCTURE IDENTIFICATION

The present authors have been developing an inverse analysis approach using the multilayer neural network and the computational mechanics. T his approach basically consists of the following three subprocesses. F irst, parametrically varying model parameters of a system, their corre sponding responses of the-system are calculated through computational mechanics simulations such as the finite element analyses, each of whi ch is an ordinary direct analysis. Each data pair of model parameters vs. system responses is called training pattern. Second, a neural netw ork is iteratively trained using a number of training patterns. Here t he system responses are given to the input units of the network, while the model parameters to be identified are shown to the network as tea cher data. Finally, some system responses measured are given to the we ll-trained network, which immediately outputs appropriate model parame ters even for untrained patterns. This is an inverse analysis. This pa per proposes a new regularization method suitable for the inverse anal ysis approach mentioned above. This method named the Generalized-Space -Lattice (GSL) transformation transforms original input and/or output data points of all training patterns onto uniformly spaced lattice poi nts over a multi-dimensional space. The topological relationships amon g all the data points are maintained through this transformation. The neural network is then trained using the GSL-transformed training patt erns. Since this method significantly remedies localization of trainin g patterns caused due to strong nonlinearity of problem, the neural ne twork can learn the training patterns efficiently as well as accuratel y. Fundamental performances of the present inverse analysis approach c ombined with the GSL transformation are examined in detail through the identification of a vibrating non-uniform beam in Young's modulus bas ed on the observation of its multiple eigenfrequencies and eigenmodes.