Global stability failure of a 3D composite structure accompanied by unavoidable polymorphic uncertainties

Drieschner, Martin; Wolf, Claus; Petryna, Yuri

doi:10.23967/wccm-eccomas.2020.160

Cited by 1 publication

(4 citation statements)

References 9 publications

(14 reference statements)

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“…Furthermore, interval and fuzzy variables can be simultaneously present in the same problem. These aspects can be found, for example, in [35] but are beyond the scope of the present paper.…”

Section: Fuzzy-stochastic Problem: Uncertain Density ρmentioning

confidence: 88%

“…This approach of different uncertainty models leads to a polymorphic uncertainty modeling [30,[32][33][34], for which different solution methods for the uncertainty propagation and evaluation methods for the assessment have to be applied. The framework PolyUQ [35] has been developed in MATLAB for those issues. The output, denominated as augmented state vector z k (c) in Section 2.1.2, is in general influenced by the uncertain parameters c; see Section 2.3 in detail.…”

Section: Aleatory and Epistemic Uncertaintiesmentioning

confidence: 99%

“…In the fuzzy space, eleven equidistantly distributed α-levels from 0.0 to 1.0 are used. The framework PolyUQ [35] is used for the numerical model evaluation, with different uncertainty models simultaneously present. The prediction of the system state vector x(t) = (u(t), u(t)) T is practically exact, except for deviations at the beginning resulting from incorrect and scattering initial conditions.…”

Section: Academic Examplementioning

confidence: 99%

“…The real value ρ real is assumed on the core of the fuzzy variable. If an interval is preferred on the core, a trapezoidal fuzzy interval [31,35] can be used instead. The extension to Figure 9 is given in Figure 10.…”

Section: Fuzzy-stochastic Problem: Uncertain Density ρmentioning

confidence: 99%

See 3 more Smart Citations

The Data Assimilation Approach in a Multilayered Uncertainty Space

Drieschner,

Herrmann,

Petryna

2023

Modelling

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The simultaneous consideration of a numerical model and of different observations can be achieved using data-assimilation methods. In this contribution, the ensemble Kalman filter (EnKF) is applied to obtain the system-state development and also an estimation of unknown model parameters. An extension of the Kalman filter used is presented for the case of uncertain model parameters, which should not or cannot be estimated due to a lack of necessary measurements. It is shown that incorrectly assumed probability density functions for present uncertainties adversely affect the model parameter to be estimated. Therefore, the problem is embedded in a multilayered uncertainty space consisting of the stochastic space, the interval space, and the fuzzy space. Then, we propose classifying all present uncertainties into aleatory and epistemic ones. Aleatorically uncertain parameters can be used directly within the EnKF without an increase in computational costs and without the necessity of additional methods for the output evaluation. Epistemically uncertain parameters cannot be integrated into the classical EnKF procedure, so a multilayered uncertainty space is defined, leading to inevitable higher computational costs. Various possibilities for uncertainty quantification based on probability and possibility theory are shown, and the influence on the results is analyzed in an academic example. Here, uncertainties in the initial conditions are of less importance compared to uncertainties in system parameters that continuously influence the system state and the model parameter estimation. Finally, the proposed extension using a multilayered uncertainty space is applied on a multi-degree-of-freedom (MDOF) laboratory structure: a beam made of stainless steel with synthetic data or real measured data of vertical accelerations. Young’s modulus as a model parameter can be estimated in a reasonable range, independently of the measurement data generation.

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Section: Fuzzy-stochastic Problem: Uncertain Density ρmentioning

confidence: 88%