Novel data-driven method for non-probabilistic uncertainty analysis of engineering structures based on ellipsoid model

Wang, Chong; Qiang, Xin; Fan, Haoran; Wu, Tao; Chen, Yuli

doi:10.1016/j.cma.2022.114889

Cited by 11 publications

(7 citation statements)

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“…The non-probabilistic reliability analysis method is a structural stability assessment method that uses a convex model [16] to describe parameter uncertainty, which requires only the value bounds of uncertain variables without their specific distribution characteristics. Currently, the commonly used convex models are the interval model and the ellipsoidal model [18][19][20]. Compared with the interval model, the ellipsoidal model provides a more compact uncertainty region, has the ability to consider the correlation between parameters when reflecting the unknown and bounded nature of uncertain parameters, and provides better results in line with the actual geotechnical engineering situation.…”

Section: Non-probabilistic Reliability Analysis Methods Based On the ...mentioning

confidence: 99%

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Shu,

Qian,

Gong

et al. 2023

Applied Sciences

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Aimed at the problem of fuzzy uncertainty of geotechnical parameters in slope stability analysis, a non-probabilistic reliability analysis method for slopes based on fuzzy set theory is proposed. Geotechnical parameters are described as fuzzy numbers, which are transformed into interval numbers at different cut set levels by taking fuzzy sets. The corresponding non-probabilistic reliability indexes and failure degrees of the slope are calculated by the non-probabilistic reliability analysis method based on the ellipsoidal model, and then the overall failure degree of the slope is obtained by weighted average to judge the stability state of the slope. The feasibility of the method was verified by a case analysis. The results show that the type and shape parameters of the fuzzy affiliation function of geotechnical parameters have a great influence on the non-probabilistic reliability of the slope. The slope failure degrees obtained from trapezoidal fuzzy numbers were larger, the slope failure degrees obtained from triangular fuzzy numbers and normal fuzzy numbers were medium, and the slope failure degrees obtained from lognormal fuzzy numbers were smaller. When considering soil parameters as triangular fuzzy numbers, normal fuzzy numbers, or lognormal fuzzy numbers, with the reduction of the shape parameters, the non-probabilistic reliability indexes of the slope increased while the failure degrees decreased. Additionally, adopting the overall failure degree to evaluate the stability of the slope can effectively solve the problem where the calculation results are too conservative (if the non-probabilistic reliability index is greater than 1) to judge the stability state of the slope in the traditional non-probabilistic reliability method.

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Section: Non-probabilistic Reliability Analysis Methods Based On the ...mentioning

confidence: 99%

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Shu,

Qian,

Gong

et al. 2023

Applied Sciences

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“…Probabilistic approaches have offered a stable framework for uncertainty analysis, with the premise that sufficient experimental samples are available to construct the precise probability distribution of uncertain parameters. However, the experimental conditions or costs of many practical engineering problems often restrict the acquisition of adequate data, which further leads to the inapplicability of the probabilistic method [40,41]. To procure more credible results for engineering problems with insufficient data, many nonprobabilistic methods have flourished in recent decades, providing an attractive framework for uncertainty analysis.…”

Section: Non-probabilistic Modelsmentioning

confidence: 99%

“…Ellipsoid model. To remedy the deficiency that the interval model can only handle independent variables, the ellipsoid model has been applied to tackle various engineering problems with dependent variables [41,53,54]. The explicit mathematical formula to represent the ellipsoid model Ω e is given as follows…”

Section: Non-probabilistic Modelsmentioning

confidence: 99%

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Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Wang

Qiang

et al. 2022

Symmetry

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Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested.

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“…For example, the interval analysis method is one of the conventional uncertainty analysis methods, in which the uncertain parameters are defined as interval variables with lower and upper bounds. Various interval analysis methods have been proposed (Moens and Vandepitte, 2004;Chen et al, 2009;Moens and Hanss, 2011;Faes and Moens, 2020;Wang et al, 2022). In interval analysis, there is no need to use the probability quantities required for variation based on probability theory since it yields definite upper and lower bounds on the range of the variation of the parameters.…”

Section: Introductionmentioning

confidence: 99%

Robust optimal damper placement based on robustness index simultaneously considering variation of elastoplastic design criteria and input level

Hosoda,

Fujita

2024

Front. Built Environ.

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Dampers should be installed at appropriate quantities and locations to control building vibrations against excitations such as earthquakes and wind loads. One of the objectives of the structural optimization problem for damper placement is to minimize the initial cost of damper installation to satisfy various structural constraints under a set of input levels and target performance values. However, it is arbitrary what input levels should be used in the design, and it is also necessary to account for various uncertainties in the inputs and structural properties. This study presents a new method for assessing the robustness of building structures with design variables while simultaneously considering various phases of structural performance criteria and input amplitudes. The proposed robustness index is a multidimensional function that can take into account the influence of different input levels on the structural performance. In this paper, the proposed new robustness index is applied to the robust optimal design of the damper placement, where the damping coefficient of the linear oil damper added to the building is uncertain. The worst resonant seismic motion for the building is investigated based on the critical double impulse method and its equivalent one-cycle sine wave, which is used as the input seismic motion. By applying the equivalent one-cycle sine wave to the structural response analysis with variations in the input velocity amplitude, the proposed robustness index is effective in comprehensively assessing the relationships between the input velocity amplitude of the seismic motion and the upper response limit of the structure under the variation of the damping coefficient of the oil damper. The comprehensive and efficient evaluation of these relationships enables a more detailed assessment of the influence of uncertainties in design variables on structural performance. In the numerical examples, the optimal damper placement for a 12-story building model is discussed based on the robustness and structural performance of both acceleration and story ductility distribution.

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Novel data-driven method for non-probabilistic uncertainty analysis of engineering structures based on ellipsoid model

Cited by 11 publications

References 50 publications

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Robust optimal damper placement based on robustness index simultaneously considering variation of elastoplastic design criteria and input level

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