Stochastic modelling of uncertainty in timber engineering

Jenkel, Christian; Leichsenring, Ferenc; Graf, Wolfgang; Kaliske, Michael

doi:10.1016/j.engstruct.2015.04.049

Cited by 25 publications

(11 citation statements)

References 19 publications

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“…[32] A pure aleatoric modeling based on experimental data may not be sophisticating. [10,34,35] A polymorphic uncertainty modeling can be achieved by including those lacks of knowledge. Therefore, a fuzzy probability based random model is suggested.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Therefore, a fuzzy probability based random model is suggested. [10,34,35] (A) (B) If fuzzy probability based random fields, according to Sections 2.1.4 and 2.2.2, are used, a distance measure has to be chosen. Due to the anisotropic nature of timber, an anisotropic distance measure is assumed in the following, applying the approach of weighted distance measures of Section 3.3.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Strength parameters for spruce wood -stochastic variables with deterministic parameters modeled to = 1 from literature[10,35] …”

mentioning

confidence: 99%

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Development of fuzzy probability based random fields for the numerical structural design

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In structural analysis with multivariate random fields, the underlying distribution functions, the autocorrelations, and the crosscorrelations require an extensive quantification. While those parameters are difficult to measure in experiments, a lack of knowledge is included. Therefore, polymorphic uncertainty models are attained by involving uncertainty models with epistemic characteristic for the quantification of the stochastic models in this contribution. Three extensions for random fields with polymorphic uncertainty modeling are introduced. Interval probability based random fields, fuzzy probability based random fields, and structural dependent autocorrelations for random fields are shown. Applications for engineering problems are shown for each extension, where uncertainty analysis of structures with different materials is performed. In this contribution, a damage simulation of a concrete beam with interval valued parametrization of stochastic models, an application for porous media in a multiphysical structural analysis with fuzzy valued parametrization and an uncertainty analysis with structural dependent autocorrelations for timber structures are presented.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

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Development of fuzzy probability based random fields for the numerical structural design

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“…Because of the high influence (see [12]), the material properties shear strengths f v,rafter , f v,tie and radial/tangential compression strengths f cq,rafter , f cq,tie are modeled as random fields for each beam, respectively. The correlation lengths l Θ,rafter , l Θ,tie for the autocorrelation of the fields are assumed to be interval variables.…”

Section: Examplementioning

confidence: 99%

Polymorphic Uncertainty Modeling for Optimization of Timber Structures

Schietzold

Graf

Kaliske

2018

Proc Appl Math and Mech

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The uncertainty characteristics of wood are mainly affected by natural variation. Out of this, the traditional approach of stochastic variables can be expanded to a polymorphic uncertainty model. Therefore, e.g. fuzzy probability based randomness is used by extending stochastic variables with fuzzy variables in parameterization concerning the distribution functions, see [1] and [2]. The coupling of both aleatoric and epistemic uncertainty is involved in the uncertainty analysis.The FEM is applied as basic solution of particular load situations on the focused timber structure. A local orthotropic formulation is used and the properties are evaluated on each integration point with respect to the tree trunk axis.In this contribution, an approach to polymorphic uncertainty modeling for timber structures is introduced. According to [3], models representing the spatial variation and interdependencies of material parameters are necessary for a realistic representation in numerical simulation. For this purpose, on the one hand interactions between fuzzy variables, on the other hand correlations among random variables are considered. Random fields are utilized to capture spatially varying material properties in context with the discretization of FE. Approaches to both spatially and structurally depending autocorrelations along with crosscorrelations based on [4] are presented.The preliminary steps aim at an optimization in design of timber structures, provided that polymorphic uncertain design as well as a priori parameters are considered. The developed tools for uncertainty analysis and the basic FEM solution are prepared as a basis for an automated optimization processing, whereas they are preferably parallelized, incorporating methods for reducing the numerical effort. Results of the uncertainty analysis of a timber structure are shown exemplary.

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“…In Fink and Köhler (2014) and Köhler et al (2007), methods to model material parameters as random variables based on a few reference material parameters are presented. The stochastic modelling of typical material parameters of wood and the effect on the uncertain structural results are discussed in Jenkel et al (2015). The results show the limitations of stochastic approaches regarding limited empirical databases and serve as motivation for the work presented subsequently.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of wooden structures with polymorphic uncertainty in material properties

Leichsenring

Jenkel

Graf

et al. 2018

IJRS

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Uncertainties are inherently present in structural parameters such as loadings, boundary conditions or resistance of structural materials. Especially material properties and parameters of wood are strongly varying in consequence of growth and environmental conditions. To include this variation in structural analysis, available data needs to be modelled appropriately, e.g. by means of probability and, furthermore, fuzzy probability based random variables or fuzzy sets. In order to comprehend uncertainties induced by estimating the distribution parameters, the stochastic approach has been extended by fuzzy distribution parameters to fuzzy probability based random variables according to studies by Möller et al. To cope with epistemic uncertainties for e.g. geometric parameters of knotholes, fuzzy sets are used. The consequence for wooden structures is determined by fuzzy stochastic analysis in combination with a Finite Element (FE) simulation using a model suitable for characteristics of a timber structure by Jenkel and Kaliske.

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Stochastic modelling of uncertainty in timber engineering

Cited by 25 publications

References 19 publications

Development of fuzzy probability based random fields for the numerical structural design

Development of fuzzy probability based random fields for the numerical structural design

Polymorphic Uncertainty Modeling for Optimization of Timber Structures

Numerical simulation of wooden structures with polymorphic uncertainty in material properties

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