Keywords: recurrent neural networks, fuzzy data, model-free material description, fuzzy structural analysis, finite element method, alpha-level optimization.

The behaviour of engineering structures is influenced by a multiplicity of structural actions, e.g. mechanical, thermal and hygric loads, which result in structural responses such as displacements and stresses. The realistic description of dependencies between structural actions and responses requires adequate structural models. This includes descriptions, e.g. for geometry, loads and the material behaviour. Numerical tools are available to evaluate the structural models in order to compute the structural response. The finite element method (FEM) with its different element formulations is a widespread numerical technology for structural analyses.

Models and their parameters are required for the structural analysis. Often, only imprecise information is available for the selection of adequate structural models and parameters. Imprecise structural parameters can be described as fuzzy data. The consideration of fuzzy data within the structural analysis results in the fuzzy structural analysis [1]. For computations based on the FEM, the fuzzy finite element method (FFEM) can be used.

Typically, the material behaviour is described by specific material models within the FFEM. As an alternative, a new generalized model-free material description based on soft computing methods is presented. It can be applied to identify dependencies between time-varying loads and responses from uncertain data series obtained by experimental investigations. Imprecise data series representing time-varying stresses and strains are treated as fuzzy processes. Recurrent neural networks for fuzzy data have been developed to map fuzzy or deterministic input processes onto fuzzy response processes. In [2], fuzzy arithmetic is applied to compute the fuzzy response processes. However, another signal computation is required using recurrent neural networks for fuzzy data instead of material models within the FFEM. For network training and prediction, the alpha-level optimization presented in [1] is utilized.

An algorithm is presented for the signal computation with alpha-level optimization. It is developed for the identification of the fuzzy network parameters (i.e. training) and the application of the network as material description for uncertain stress-strain-time dependencies within the FFEM. A Newton-Raphson method is used for an incremental iterative numerical solution. In order to compute the tangential stiffness matrix, the partial derivatives of the network outputs with respect to the network inputs are formulated.

The developed recurrent neural network approach is verified with a model based solution. Application capabilities for model-free material descriptions within the FFEM are demonstrated by a numerical investigation of a pavement construction.

1

B. Möller, W. Graf, M. Beer, "Fuzzy structural analysis using alpha-level optimization", Computational Mechanics, 26, 547-565, 2000.

2

W. Graf, S. Freitag, M. Kaliske, J.-U. Sickert, "Recurrent Neural Networks for Uncertain Time-Dependent Structural Behaviour", Computer-Aided Civil and Infrastructure Engineering, 25, 322-333, 2010. doi:10.1111/j.1467-8667.2009.00645.x

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