Fuzzy structural analysis using α-level optimization

Möller, Bernd; Graf, Wolfgang; Beer, Michael

doi:10.1007/s004660000204

Cited by 269 publications

(115 citation statements)

References 18 publications

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“…In general, computations with fuzzy numbers can be performed similar to interval analyses, i.e. by means of fuzzy arithmetic [5] or optimization based approaches [6], see also [7] for an overview. A typical fuzzy number with D ↵-cuts, as shown in Fig.…”

Section: Intervals and Fuzzy Numbersmentioning

confidence: 99%

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Cao¹,

Freitag²,

Meschke³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. 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.

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Section: Intervals and Fuzzy Numbersmentioning

confidence: 99%

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Cao¹,

Freitag²,

Meschke³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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“…The formal description of fuzzy randomness chosen by these authors is however not suitable for formulating uncertainty encountered in engineering problems. A suitable form of representation with the scope of numerical engineering problems is given with the so-called «-discretization by [1] and [3].…”

Section: Fuzzy Stochastic Analysismentioning

confidence: 99%

“…On the basis of point and time discretization, fuzzy functional values of the function x(s, , , ³) are determined at points in space j , time i , and parameters ³. The numerical simulation is carried out with the aid of the «-level optimization [3]. For the fuzzy variableã 1 and the fuzzy function x(s, , the input subspace E « assigned to the level « is formed.…”

Section: M(t) :X(t) →Z(t)mentioning

confidence: 99%

Numerical simulation of structures using generalized models for data uncertainty

Graf¹,

Sickert²,

Steinigen³

2009

WIT Transactions on Modelling and Simulation

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The challenging task in computational engineering is to model and predict numerically the behaviour of engineering structures in a realistic manner. Beside sophisticated computational models and numerical procedures to map physical phenomena and processes onto structural responses, an adequate description of available data covering the content of provided information is of prime importance. Generally, the availability of information in engineering practice is limited due to available resources. Far beyond the capability to specify crisp values, data are imprecise, diffuse, fluctuating, incomplete, fragmentary and frequently expert specified. Beside objective characteristics like randomness, available data are influenced by subjectivity to a considerable extend. This impedes the specification of probabilistic models with crisp parameter values to describe the uncertainty. Applying imprecise probabilities objective components of the uncertainty as well as subjective components can be considered simultaneously. A sophisticated procedure to handle imprecise probabilities provide the uncertainty model fuzzy randomness. Since fuzziness, randomness, and fuzzy randomness can be processed simultaneously, it is denoted as generalized uncertainty model. The models are demonstrated by means of a numerical example to emphasize their features and to underline their applicability.

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“…In recent years, there is an increasing focus on the development of FFEM, first for static analysis and then extended in dynamics [1][2][3][4][5][6][7][8][9]. Fundamental strategies for FFEM can be categorized into two main groups: the interval arithmetic approach and the optimization strategy.…”

Section: Introductionmentioning

confidence: 99%

“…Because of this characteristic, the optimization strategy is gradually acknowledged as the standard procedure for FFEM. In optimization strategy, the search process is performed on the input domain to seek the exact bounds of the objective function by iteratively evaluating the objective function at designated points [7][8][9]. Often, the search process is very time consuming because finite element analysis has to be carried out for every evaluation.…”

Section: Introductionmentioning

confidence: 99%

A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure

Tuan¹,

Huynh

Pham

2015

Vietnam J. Mech.

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Abstract. This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. In the design of the surrogate model, complete quadratic polynomials are selected with all fuzzy variables are transformed to standardized fuzzy variables. This methodology allows accurate determination of the fuzzy dynamic outputs, which is the major issue in response surface based techniques. The effectiveness of the proposed fuzzy finite element algorithm is illustrated through a numerical analysis of a linear two-storey shear frame structure.

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Fuzzy structural analysis using α-level optimization

Cited by 269 publications

References 18 publications

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Numerical simulation of structures using generalized models for data uncertainty

A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure

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