A survey of non-probabilistic uncertainty treatment in finite element analysis

Moens, David; Vandepitte, Dirk

doi:10.1016/j.cma.2004.03.019

Cited by 298 publications

(114 citation statements)

References 61 publications

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“…In section 5, the bounds of the interval expected fatigue damage rate are obtained by the proposed method derived from the improved interval analysis and T-B method. Finally, in section 6, a numerical example concerning a truss structural system under random excitation is used to illustrate the accuracy and efficiency of the proposed method by comparing with the vertex method [15]. The results also demonstrate usefulness of the proposed method in view of decision-making in engineering practice.…”

Section: Presented the Improved Interval Analysis Via Extra Unitary Imentioning

confidence: 95%

Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

Zhu

Tian

2017

Period. Polytech. Civil Eng.

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This study presents a spectral method for fatigue damage evaluation of linear structures with uncertain-but-bounded parameters subjected to the stationary multi-correlated Gaussian IntroductionFatigue damage is one of the major factors in the failures of engineering structure and mechanical equipment. The traditional method on fatigue damage assessment usually can be divided into two groups, namely, time domain approach and spectral approach. For the former, the traditional method on fatigue damage assessment is the so-called nominal-stress approach [1], which uses numerical methods for cycle counting and damage accumulation stepwise. To compute the time histories of the stress or strain of critical points, time domain method is computationally very time-consuming, especially for large structures. For the spectral approach [2], the external loads are modeled as stationary Gaussian processes, and fatigue damage evaluation is derived from the power spectral density (PSD) function of the stress or strain process of critical points in frequency domain.The above two approaches always consider structural parameters like geometry, material properties, constitutive laws and boundary conditions as fixed values. However, it has been recently recognized that the model parameters are poorly known too, giving arise to structures with uncertain parameters. In these cases, the uncertain parameters are described by the following two methods, known as probabilistic and non-probabilistic approaches. For the first group, structural uncertain parameters are modeled as random variables or stochastic field, and structural generic response under external load is given by stochastic finite element method or Monte Carlo simulation method, and then the fatigue damage of the structure will be obtained based on the cumulative damage theory. However, the reliable probabilistic model requires a large amount of accurate sample data, which are sometimes difficult to get particularly in the preliminary design stage. Meanwhile, the characteristics of the structural uncertainty are not random. Therefore, nonprobabilistic model is more suitable than probabilistic model to define the structure with uncertain parameters.In the past decade, the non-probabilistic theory, which has made a considerable progress as a new method to describe the uncertainty, generally comprises convex set theory, fuzzy set theory and interval theory. Ben-Haim [3] first introduced

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Section: Presented the Improved Interval Analysis Via Extra Unitary Imentioning

confidence: 95%

Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

Zhu

Tian

2017

Period. Polytech. Civil Eng.

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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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“…Terminology Non-determinism has various causes. This paper applies the terminology proposed by Oberkampf (W. Oberkampf, 1999) and its refinements proposed by Moens (D. Moens, 2005).…”

Section: Non-deterministic Fields In the Femmentioning

confidence: 99%

“…This resulted in a variety of methods, ranging from the stochastic, to the nonprobabilistic fuzzy and interval finite element method (see e.g. (D. Moens, 2005)). Two general difficulties arise in both families of methods (probabilistic and non-probabilistic): the problem of dependency and the problem of high calculation costs.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Finite Element Analysis Technique for Structural Static Analysis Based on Interval Fields

Verhaeghe

Munck²,

Desmet³

et al. 2010

Proceedings of the 4th International Workshop on Reliable Engineering Computing Robust Design – Coping With Hazards, Risk and U

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Abstract. One of the main shortcomings of current fuzzy and interval finite element procedures is that mutual dependency between multiple uncertain model parameters cannot be included in the analysis. This limit is posed by the classical interval concept, where multi-dimensional interval quantities are generally treated as hypercubes, thus ignoring all possible dependency between vector components. For this reason, most literature on this subject focuses on one-dimensional output quantities.In order to cope with this problem, this work discusses the application of the concept of interval fields for static analysis of uncertain mechanical structures in the context of fuzzy finite element analysis. The theoretic background of the concept is explained, and it is shown how it can be applied to represent dependency between parametric uncertainties.Further, the paper concentrates on the calculation of interval fields resulting from static structural analysis. A procedure that enables the calculation of a joint representation of multiple output quantities of a single interval finite element problem while preserving the mutual dependency between the components of the output vector is introduced. This procedure is based on a projection of the original problem on the space composed by the classical static deformation patterns. This paper in particular introduces a novel projection in which the space of the classical deformation patterns is augmented with deviatoric parts. This novel projection leads to a better approximation of the results without a significant increase in computation time.Finally, a numerical case study illustrates the procedure and validates the improved accuracy of the results obtained with the novel projection technique.

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A survey of non-probabilistic uncertainty treatment in finite element analysis

Cited by 298 publications

References 61 publications

Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

Real-Time Fuzzy Analysis of Machine Driven Tunneling

A Fuzzy Finite Element Analysis Technique for Structural Static Analysis Based on Interval Fields

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