Jan-Uwe Sickert

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.

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.

Robust Design with Uncertain Data and Response Surface Approximation

The aim of the presented approach is to combine two views on robustness within a comprehensive design approach. These two main views are on the one hand the resistance to extraordinary (unforeseen) events, and on the other hand the consideration of uncertainty in structural parameters in order to monitor and reduce the variation of structural responses. To capture this, an enhanced robustness measure is defined and applied as design objective within the design approach which is based on the solution of an optimization problem. In addition to sophisticated numerical procedures to map physical phenomena and processes, the adequate description of available data covering the content of provided information is of prime importance. Thus, the generalized uncertainty model fuzzy randomness is applied. Furthermore, the robustness measure as well as the optimization approach are enhanced to fuzzy random based solutions.

Numerical simulation based on fuzzy stochastic analysis

In this paper mathematical methods for fuzzy stochastic analysis in engineering applications are presented. Fuzzy stochastic analysis maps uncertain input data in the form of fuzzy random variables onto fuzzy random result variables. The operator of the mapping can be any desired deterministic algorithm, e.g. the dynamic analysis of structures. Two different approaches for processing the fuzzy random input data are discussed. For these purposes two types of fuzzy probability distribution functions for describing fuzzy random variables are introduced. On the basis of these two types of fuzzy probability distribution functions two appropriate algorithms for fuzzy stochastic analysis are developed. Both algorithms are demonstrated and compared by way of an example.

An inverse solution of the lifetime-oriented design problem

This paper presents a new solution of the lifetime-oriented design problem. This solution is based on a point-to-point allocation between the space of the design parameters and the space of structural responses. Each point in the space of the design parameters defines a feasible or non-feasible design, and all feasible designs guarantee compliance with a predetermined lifetime. From the set of feasible designs, one or more designs may be selected with the aid of technical or economic criteria. The presented solution permits the consideration of non-statistical data uncertainty, thereby leading to an uncertain lifetime. Because of the unavoidable information deficit, for example incomplete data in practical problems, the application of non-statistical data uncertainty is more realistic than the application of stochastic data models. The selection of feasible design variants is based on methods of explorative data analysis.

Fuzzy random processes and their application to dynamic analysis of structures

In many engineering problems the dynamical reactions of structures depend on uncertain data. For considering this uncertainty, fuzzy random processes are applied. An enhanced dynamic analysis method called fuzzy stochastic finite element method (FSFEM) has been developed in order to consider the fuzzy random processes within the dynamic analysis of structures. A suitable discretization strategy enables the repeated processing of FE algorithms as deterministic fundamental solution. In this paper the FE multi-reference-plane model is extended to fuzzy randomness and dynamic loads. The numerical solution is based on the fuzzy stochastic sampling (FSS). FSS and FSFEM are applied for the numerical simulation of the load-bearing capacity of a strengthened RC plate under static and dynamic loads.

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.

Modeling and Processing of Uncertainty in Civil Engineering by Means of Fuzzy Randomness

The paper focuses on the adequate quantification of uncertainty which usually influences all numerical simulations of structures in the field of civil engineering. Fuzzy randomness provides adequate modeling of specific uncertainty phenomena, not only in the field of civil engineering. In this paper, approaches for modeling of data and model uncertainty by means of convex fuzzy random variables, including fuzzy variables and random variables as special cases, are presented. Numerical processing of those uncertain variables succeeds with the help of fuzzy stochastic structural analysis. By means of fuzzy stochastic analysis, it is possible to map fuzzy random input variables onto fuzzy random result variables. Thus, safety assessment of structures under precise distinction of the different kinds of uncertainty is feasible. The principal approaches are illustrated by means of two model problems in the field of civil engineering in order to show the significance and the applicability of the methods.

Numerical design approaches of textile reinforced concrete strengthening under consideration of imprecise probability

The paper focuses on numerical approaches valuable in the design of strengthening layers made of textile reinforced concrete (TRC) applied on surfaces of RC structures. The presented methods aim at the design of structures that are components of significant buildings, e.g. power stations, historic valuable buildings and life lines. The generally existing uncertainty of material and geometry parameters of the RC structures and the TRC layers is modelled by imprecise probability. Reliability, lifetime and robustness are assessed by means of generalised uncertainty measures and considered as design objectives or constraints. Three computational methods are developed for the computation of preferential designs under consideration of imprecise probability. The methods are applied for the design of a porch roof strengthening comparing the robustness of different variants and for the reliability-based design of a T-beam strengthening.

Fuzzy and Fuzzy Stochastic Methods for the Numerical Analysis of Reinforced Concrete Structures Under Dynamical Loading

This paper is mainly devoted to enhanced computational algorithms to simulate the load-bearing behavior of reinforced concrete structures under dynamical loading. In order to take into account uncertain data of reinforced concrete, fuzzy and fuzzy stochastic analyses are presented. The capability of the fuzzy dynamical analysis is demonstrated by an example in which a steel bracing system and viscous damping connectors are designed to enhance the structural resistance of a reinforced concrete structure under seismic loading.