پیش بینی رفتار سازه وابسته به زمان با شبکه های عصبی مکرر برای داده های فازی

In the paper, an approach is described which permits the numerical, model-free prediction of uncertain time-dependent structural responses. Uncertain time-dependent structural actions and responses are modelled by means of fuzzy processes. The prediction approach is based on recurrent neural networks for fuzzy data trained by time-dependent results of measurements or numerical analyses. An efficient solution for network training and prediction is developed utilizing α-cuts and fuzzy arithmetic. The approach is verified using a fractional rheological model. The capability of the approach is demonstrated by predicting the long-term structural behaviour of reinforced concrete plates strengthened by textile reinforced concrete layers.

The long-term behaviour of engineering structures depends on a multiplicity of environmental influences such as applied loadings, temperature and weathering. This results in uncertain time-dependent deformations and stress rearrangements inside the structure. This behaviour can be incorporated into a time-dependent structural analysis with rheological models [1], which are based mathematically on integer or fractional time derivatives of stresses and strains. Thereby, the model has to be selected a priori. The extension of conventional rheological models to fractional rheological models facilitates an improved fitting of material parameters to experimental data. However, the entire stress history has to be considered for the determination of the current stress and strain states, which leads to a high computational effort for fractional rheological models. As an alternative, a novel method for the numerical prediction of time-dependent structural responses under consideration of uncertain action processes is proposed here, which combines neural computing (artificial neural networks) and mapping of fuzzy data (fuzzy analysis, see e.g. [2]). The artificial neural network concept is adapted from the structure and the functionality of the human brain. It is a powerful tool to capture and to learn functional dependencies in data. An overview of neural network applications in civil engineering is given e.g. in [3]. The widely-used type in engineering applications is the multilayer perceptron network with feed forward architecture [4]. Advanced network architectures have to be applied in order to consider time-dependent effects of the structural behaviour. In [5], the rate-dependency of materials is considered by means of additional input neurons in a feed forward network for the approximation of time-dependent constitutive material behaviour. Moreover, recurrent neural networks have been developed for temporal signal processing (see e.g. [6]). They are suitable for the mapping of structural processes, obtained by experiments or numerical monitoring (see Section 2), onto time-dependent structural responses. If a structural process is observed experimentally with the help of measurement devices, it is not possible to assign precise values. 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 values are more or less characterized by data uncertainty which originates in imprecision (see e.g. [7]). In this contribution, the imprecision is modelled by means of fuzzy sets. However, intervals and deterministic data are also taken into account, as they represent special cases of fuzzy sets in view of the numerical treatment. Time-dependent structural parameters are quantified as fuzzy processes as described in Section 2.1. The treatment of fuzzy data with artificial neural networks requires specific prediction and training algorithms. A survey of processing fuzzy data with feed forward networks is given in [8]. For the prediction of fuzzy processes, three types of mapping fuzzy input processes onto fuzzy output processes with recurrent neural networks are introduced in Section 3. A prediction and a training algorithm are presented. As an extension to [9], fuzzy network parameters are considered. Beside fuzzy data, also intervals and deterministic numbers may be processed. The developed recurrent neural network approach for fuzzy data is verified using a fractional rheological material model in Section 4. Uncertain stress–strain–time dependencies obtained by numerical monitoring are trained. The resulting networks for fuzzy data are utilized for the prediction of further stress–strain–time dependencies. The developed recurrent neural network approach is applied in Section 5 for the prediction of the long-term displacements of reinforced concrete plates which were strengthened with textile reinforced concrete (TRC) layers.

A numerical prediction approach is introduced in the paper, which is based on advanced artificial neural networks. The developed recurrent neural networks for fuzzy data enable the processing of uncertain temporal sequences. The developed algorithm can be applied for the numerical prediction of fuzzy processes, e.g. fuzzy structural responses. Beside fuzzy intervals and fuzzy numbers, also intervals and deterministic numbers obtained by discretization of the input and output processes can be considered within the recurrent neural network approach. Because of this feature and due to the material independence, the new model-free approach has a high degree of generality and flexibility. It provides an innovative computational strategy for the numerical analysis of large-scale engineering structures. Applications of computational intelligence (recurrent neural networks) are combined with uncertainty quantification (fuzzy data). The capability of the approach and the quality of the prediction has been proven with verification tests. Thereby, the results of numerical analyses based on a fuzzy fractional rheological model and the model-free predictions computed with the introduced recurrent neural network approach show excellent agreements. A possible application is presented by an example. The long-term deformation behaviour of TRC strengthened reinforced concrete plates is investigated. Thereby, the fuzzy displacement processes of the plates are predicted by applying the developed recurrent neural network approach for fuzzy data. In future works, the approach can be applied for the approximation of the long-term constitutive material behaviour, if conventional material models are not valid or numerically inefficient. In so far, the recurrent neural networks trained by experimentally or numerically obtained fuzzy data can by considered as uncertain time-dependent material models in finite element analyses of engineering structures.