Steffen Freitag

Recurrent Neural Networks for Uncertain Time-Dependent Structural Behavior

: In this article, an approach is introduced which permits the numerical prediction of future structural responses in dependency of uncertain load processes and environmental influences. The approach is based on recurrent neural networks trained by time-dependent measurement results. Thereby, the uncertainty of the measurement results is modeled as fuzzy processes which are considered within the recurrent neural network approach. An efficient solution for network training and prediction is developed utilizing α-cuts and interval arithmetic. The capability of the approach is demonstrated by means of the prediction of the long-term structural behavior of a reinforced concrete plate strengthened by a textile reinforced concrete layer.

Recurrent neural networks for fuzzy data

In this paper, a model-free approach for data mining in engineering is presented. The numerical approach is based on artificial neural networks. Recurrent neural networks for fuzzy data are developed to identify and predict complex dependencies from uncertain data. Uncertain structural processes obtained from measurements or numerical analyses are used to identify the time-dependent behavior of engineering structures. Structural action and response processes are treated as fuzzy processes. The identification of uncertain dependencies between structural action and response processes is realized by recurrent neural networks for fuzzy data. Algorithms for signal processing and network training are presented. The new recurrent neural network approach is verified by a fuzzy fractional rheological material model. An application for the identification and prediction of time-dependent structural behavior under dynamic loading is presented.

Structural Analysis with Fuzzy Data and Neural Network Based Material Description

A new approach is presented utilizing artificial neural networks for uncertain time-dependent structural behavior. Recurrent neural networks (RNNs) for fuzzy data can be trained by uncertain experimental data to describe arbitrary stress-strain-time dependencies. The benefit is a generalized formulation, which can be applied to describe the behavior of several materials without definition of a specific material model. Model-free material descriptions can be used as numerical efficient material formulations within the finite element method. In order to perform fuzzy or fuzzy stochastic finite element analyses, a new approach is introduced in this article. An α-level optimization is utilized for signal computation and training of RNNs for fuzzy data. The applicability is demonstrated by means of examples in this article.

Prediction of uncertain structural behaviour and robust design

Robust design of structures presupposes the prediction of time-dependent structural behaviour and the quantitative assessment of robustness. Thereby, the uncertainty has to be considered by means of adequate data models selected in accordance with the available information. On the basis of the generalised uncertainty model fuzzy randomness, model-based, model-free and hybrid approaches for the prediction of uncertain structural behaviour are presented in this paper. The introduced robustness measure is capable to assess the robustness under consideration of fuzzy random structural responses.

Reliability of Structures under Consideration of Uncertain Time-Dependent Material Behaviour

In this paper a concept for time-dependent reliability assessment of civil engineering structures is presented. This concept bases on the uncertainty model fuzzy randomness. The time-dependent behaviour of materials with fading memory is modelled with the aid of rheological elements using uncertain fractional time derivatives of strain. The presented method is applied to the reliability assessment of a pavement construction.

Fractional derivatives and recurrent neural networks in rheological modelling – part I: theory

The aim of this paper was to develop a general approach based on fractional time derivatives and recurrent neural networks to model the rheological behaviour of asphalt materials. The paper focuses on elastic and viscoelastic material characteristics. It consists of two parts. In this first part, the theoretical aspects of modelling are discussed. A brief introduction into the theory of rheological elements based on fractional time derivatives is provided. The fractional differential equation of a general rheological element (base element) is developed from which a huge variety of other rheological elements can be derived, e.g. fractional Newton, Kelvin and standard solid elements. A new approach is presented for solving the fractional differential equations. Artificial neural networks are developed to compute the stress–strain–time behaviour of fractional rheological elements in a numerical efficient way. The approach is tested and verified. The second part of this work will appear later. It will be focused on applications of the new theoretical work to pavement engineering problems.

REAL-TIME FUZZY ANALYSIS OF MACHINE DRIVEN TUNNELING

Reliability assessment in mechanized tunneling requires to take into account limited information describing the local geology and the corresponding geotechnical parameters. The geotechnical data are often quite limited and generally not available in the form of precise models and parameter values. In this case, epistemic uncertainty should be considered within the reliability assessment. The concept of fuzzy numbers is applied to predict tunneling induced settlements in real-time. An advanced numerical simulation is utilized as forward model for the settlement prediction. However, to achieve real-time capabilities, surrogate models are required. Deterministic surrogate models can be used together with an ↵-cut optimization approach to compute fuzzy data. In this paper, a surrogate modeling strategy is introduced to directly process fuzzy input-output data. Within this approach, the time-consuming optimization procedure is replaced by a surrogate model to obtain the fuzzy settlement field prediction in realtime. The significant reduction in computation time maintaining similar prediction performance leads to potential applications in steering of mechanized tunneling processes. 329 Available online at www.eccomasproceedia.org Eccomas Proceedia UNCECOMP (2017) 329-338 ©2017 The Authors. Published by Eccomas Proceedia. Peer-review under responsibility of the organizing committee of UNCECOMP 2017. doi: 10.7712/120217.5373.17151 Ba Trung Cao, Steffen Freitag and Günther Meschke

Numerical Predictions of Surface Settlements in Mechanized Tunneling: Hybrid POD and ANN Surrogate Modeling for Reliability Analyses

Computational reliability analyses of engineering structures are often time-consuming, in particular, if time-dependent structural behavior is considered. If (almost) real time prognoses are required, surrogate models may be used to approximate the structural behavior described by advanced numerical models. In this paper, a hybrid surrogate modeling strategy based on a combination of Proper Orthogonal Decomposition (POD) and Artificial Neural Networks (ANN) is introduced. The hybrid approach is developed for the approximation of time variant surface settlements in mechanized tunneling due to uncertain geological and process parameters. The approximation capabilities are demonstrated by means of an example. The new hybrid surrogate model can be applied for numerical, efficient, real-time reliability analyses in mechanized tunneling.

Identification and Prediction of Time-Dependent Structural Behavior with Recurrent Neural Networks for Uncertain Data

The long-term behavior of Civil Engineering structures depends on a variety of environmental influences such as applied loadings, temperature and weathering. In general, all time-dependent influences of a structure are uncertain p rocesses which lead to uncertain time-varying structural responses. Uncertain proces ses can be captured with nontraditional uncertainty models, see M ¨ oller and Beer (2008). For robust design of structures, numerical methods are required which can be used to identify and predict time-dependent material behavior. In this paper, a novel method for the numerical prediction of time-dependent structural responses under consideration of uncertain action processes is proposed, which combines neural computing (artificial neural networks, see e.g. Haykin (1999)) and mapping of fuzzy data (fuzzy analysis, see e.g. M ¨ oller et al. (2000)). Different types of mapping fuzzy processes with recurrent neural networks are introduced. Prediction and training algorithms for the mapping of fuzzy input onto fuzzy output values are described. Thereby, fuzzy network parameters can be considered. Beside fuzzy values, also intervals and deterministic numbers may be processed. The developed recurrent neural network approach for fuzzy data is verified with a fractional rheological material model, see Oeser and Freitag (2009). The new approach is applied to the prediction of the long-term behavior of texti le reinforced concrete structures.