Keywords: recurrent neural network, fuzzy process, model-free prediction, time-dependent structural behaviour, fractional rheological model, textile reinforced concrete.

The long-term behaviour of civil engineering structures depends on a variety of environmental influences such as applied loadings, temperature and weathering. This results in uncertain time-dependent deformations and stress rearrangements inside the structure. These phenomena can be incorporated into a time-dependent structural analysis. A clear separation of long-term effects with respect to individual environmental influences and the formulation of an associated mechanical model are difficult due to the limited amount of experiments and not yet complete physical-mechanical insight. As an alternative, a novel method for the numerical prediction of time-dependent structural responses under consideration of uncertain action processes is proposed, which combines neural computing and mapping of fuzzy data (fuzzy analysis [1]).

If a structural process is observed experimentally with the help of measurement devices, it is not possible to assign precise values to the observed events. That means, data uncertainty occurs which may result from scale-dependent effects, varying boundary conditions which are not considered, inaccuracies in the measurements, and incomplete sets of observations. Therefore, measured results are more or less characterized by data uncertainty which originates in imprecision. In this contribution, the imprecision is modelled by means of the uncertainty data model fuzziness. Time-dependent structural parameters are quantified as fuzzy processes.

A model-free concept based on neural networks is employed to extract and to evaluate information obtained from experiments. Artificial neural networks are utilized for the approximation of time-dependent effects of the structural behaviour. Structural processes obtained by experiments or numerical analyses are mapped onto time-dependent structural responses. Therefore, the neural network requires a temporal signal processing. Suitable network types for this purpose are recurrent neural networks. They are trained with uncertain values obtained by discretization of fuzzy processes. That is, the input and output training data sets contain fuzzy values. However, also intervals and deterministic numbers may be processed as special cases beside fuzzy intervals and fuzzy numbers. Three types of mapping with recurrent neural networks for fuzzy data are introduced. A prediction and a training algorithm are presented. Beside fuzzy input and output values, also fuzzy network parameters are considered in the new approach. An efficient solution of the mapping with recurrent artificial neural networks for fuzzy data is obtained utilizing alpha-cuts [1] and interval arithmetic.

The developed numerical prediction method is verified with a fractional rheological material model [2]. Uncertain time-dependent stress-strain-dependencies obtained by numerical monitoring are trained. The resulting networks for fuzzy data are utilized for the prediction of further stress-strain-dependencies. The capabilities of the presented approach are demonstrated by means of an example. The long-term displacement of a textile strengthened reinforced concrete plate is predicted based on uncertain experimentally obtained data.

1

B. Möller, W. Graf, M. Beer, "Fuzzy structural analysis using alpha-level optimization", Computational Mechanics, 26, 547-565, 2000. doi:10.1007/s004660000204

2

M. Oeser, S. Freitag, "Modeling of materials with fading memory using neural networks", International Journal for Numerical Methods in Engineering, 2009. doi:10.1002/nme.2518

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