Bernd Möller

Safety assessment of structures in view of fuzzy randomness

Structural safety can be realistically assessed only if the uncertainty in the structural parameters is appropriately taken into consideration and realistic computational models are applied. Uncertainty must be accounted for in its natural form. Stochastic models are not always capable of fulfilling this task without restrictions, as uncertainty may also be characterized by fuzzy randomness or fuzziness. On the basis of the theory of the fuzzy random variables the fuzzy probabilistic safety concept is introduced and formulated as the fuzzy first order reliability method (FFORM). This concept permits fuzziness, randomness and fuzzy randomness to be accounted for simultaneously. FFORM is illustrated by way of an example; hereby, the influence of the computational model is also demonstrated.

Artificial Neural Networks for Forecasting of Fuzzy Time Series

: In this article, an artificial neural network for modeling and forecasting of fuzzy time series is presented. Modeling fuzzy time series with fuzzy data as random realizations of an underlying fuzzy random process enables forecasting of future fuzzy data following the observed time series. Analysis and forecasting of time series with fuzzy data may be carried out with the aid of artificial neural networks. A significant advantage is the fact that neural networks do not require a predetermined process model to simulate and forecast time series possessing fuzzy random characteristics. Artificial neural networks have the ability to learn the characteristics of an existing fuzzy time series, to represent the underlying fuzzy random process, and to forecast future fuzzy data following the time series observed. The algorithms developed are demonstrated using a numerical example.

Possibility Theory Based Safety Assessment

An assessment of the safety of structures may be carried out on the basis of different known safety concepts (global safety factor, semiprobabilistic approach using partial safety factors, probabilistic approximation solution using first- and second-order reliability theory, probabilistic “exact” solution). The application of these concepts presupposes special knowledge concerning input values, e.g., permissible or prescribed values, quantile values, distribution functions. This especially applies to probabilistic methods. Inaccuracies and statistically nondescribable uncertainties in the input data are either ignored in these methods or only accounted for approximately using crisp bounds. Fuzzy set theory enables such uncertainties to be described mathematically and processed in the analysis of structures. The uncertain results of fuzzy structural analysis may be evaluated by various methods. In this article a safety assessment method is described based on possibility theory. In contrast to the above-mentioned concepts, the safety assessment of structures described here takes into account nonstochastic uncertainties and subjective estimates of objective values by experts based on possibility theory. It is possible by this means to obtain sufficiently reliable descriptions of the input data for further processing. The uncertainties introduced into the analysis are later reflected in the results. A realistic description of system behavior is obtained by applying high-quality algorithms in the structural analysis. The uncertain results serve as a starting point for the safety assessment. The method described here forms a supplement to safety concepts already in use.

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.

UNCERTAINTY IN DAMAGE ASSESSMENT OF STRUCTURES AND ITS NUMERICAL SIMULATION

Supporting structures are subject to damage processes during their service lifetime. Damage may occur in the form of material or structural damage during the loading process. The parameters for describing damage are modeled as fuzzy values in the computational model. Damage is modeled by means of a fuzzy damage indicator, which assesses changes in stiffness as a result of damage. The damage indicator is applied for assessing damage development in plane reinforced concrete framework structures. Damage assessment with the aid of the introduced fuzzy damage indicator is demonstrated by way of two examples.

Processing uncertainty in structural analysis, design and safety assessment

A fuzzy method for determining appropriate structural design is presented. Nonstochastic uncertainty is quantified using fuzzy values and fuzzy random variables. Fuzzy structural parameters are processed on the basis of a generally applicable numerical method for arbitrary nonlinear fuzzy structural analyses. Fuzzy randomness is introduced into a fuzzy probabilistic safety assessment. This leads to fuzzy results representing fuzzy structural responses and fuzzy safety levels. Referring to permissible structural responses and safety levels uncertain structural design parameters are derived. The nonlinear fuzzy structural analysis including uncertain structural design is demonstrated by way of an example

Discussion on “Structural reliability analysis through fuzzy number approach, with application to stability”

Abstract We comment on the fuzzy number approach presented by Marco Savoia [Comput. Struct. 80 (2002) 1087]. Savoia’s statement regarding computational procedures for fuzzy structural analysis is corrected. A general and powerful numerical algorithm for nonlinear fuzzy structural analysis is presented.

Numerical Modeling of Textile-Reinforced Concrete

Textile-reinforced concrete (TRC) imposes several special requirements on the applicable simulation methods. TRC is highly heterogeneous at several levels of material structures and, therefore, it exhibits a very complex failure process. Examples of interacting effects are the strain localization due to local failure mechanisms in the yarn, bond, and matrix. As a result, except for standard features, the developed models must be able to reproduce discontinuities of the displacement fields, reflect the irregularity of the material structure, special kinematics relations, and the size effect induced either statistically or energetically. This paper reviews the modeling strategies developed and applied in research and development of TRC in the collaborative research centers in Aachen and Dresden.