NEW REGULARIZATION BY TRANSFORMATION FOR NEURAL NETWORK BASED INVERSE ANALYSES 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. This approach basically consists of the following three subprocesses. First, parametrically varying model parameters of a system, their corresponding responses of the system are calculated through computational mechanics simulations such as the finite element analyses, each of which is an ordinary direct analysis. Each data pair of model parameters vs. system responses is called training pattern. Second, a neural network is iteratively trained using a number of training patterns. Here the system responses are given to the input units of the network, while the model parameters to be identified are shown to the network as teacher data. Finally, some system responses measured are given to the well-trained network, which immediately outputs appropriate model parameters even for untrained patterns. This is an inverse analysis. This paper proposes a new regularization method suitable for the inverse analysis 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 points over a multi-dimensional space. The topological relationships among all the data points are maintained through this transformation. The neural network is then trained using the GSL-transformed training patterns. Since this method significantly remedies localization of training patterns caused due to strong nonlinearity of problem, the neural network can learn the training patterns efficiently as well as accurately. Fundamental performances of the present inverse analysis approach combined with the GSL transformation are examined in detail through the identification of a vibrating non-uniform beam in Young’s modulus based on the observation of its multiple eigenfrequencies and eigenmodes.