An improved multidimensional parallelepiped non-probabilistic model for structural uncertainty analysis

Ni, Bingyu; Jiang, Chao; Han, Xu

doi:10.1016/j.apm.2015.11.047

Cited by 79 publications

(36 citation statements)

References 30 publications

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“…Through theoretic analysis, it is found that the ME model possesses better property, while the MP-I model is proved to be an invalid convex model. 23 To evaluate the applicability of convex models to a specific problem, two model assessment indexes, namely, the "fitness" and the "volume ratio", are also given. The index "fitness" is used to quantify the adaptability of a constructed convex model for a specific uncertain problem with given experimental samples, by which engineers can judge how well the model fits for the samples.…”

Section: Discussionmentioning

confidence: 99%

“…As two typical convex models for uncertainty quantification, the ellipsoid model and the interval model were compared for carrying out dynamic response analysis and buckling failure analysis of bars [19]. Recently, some variants of the traditional convex models were also developed, including the multi-ellipsoid model [20,21], the multidimensional parallelepiped model [22,23], the super-ellipsoidal model [24], the convex model process [25], etc. Also, the convex model approach presently has been applied in various areas in structural mechanics, such as finite element analysis [26,27], non-probabilistic reliability analysis [5,18,[28][29][30][31], uncertain optimization [32][33][34][35][36][37], hybrid reliability analysis [38][39][40][41], etc.…”

Section: Introductionmentioning

confidence: 99%

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Discussions on non-probabilistic convex modelling for uncertain problems

Jiang

Huang

2018

Applied Mathematical Modelling

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Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To overcome the complexity and diversity of the formulations of current convex models, in this paper, a unified framework for construction of the non-probabilistic convex models is proposed. By introducing the correlation analysis technique, the mathematical expression of a convex model can be conveniently formulated once the correlation matrix of the uncertain parameters is created. More importantly, from the theoretic analysis level, an evaluation criterion for convex modelling methods is proposed, which can be regarded as a test standard for validity verification of subsequent newly proposed convex modelling methods. And from the practical application level, two model assessment indexes are proposed, by which the adaptabilities of different convex models to a specific uncertain problem with given experimental samples can be estimated. Four numerical examples are investigated to demonstrate the effectiveness of the present study.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discussions on non-probabilistic convex modelling for uncertain problems

Jiang

Huang

2018

Applied Mathematical Modelling

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“…By substituting the mean value and deviation of and into (28) and using the method introduced in Section 3, the interval nonprobabilistic reliability index can be solved, and the interval nonprobabilistic reliability index was obtained. …”

Section: Interval Nonprobabilistic Reliabilitymentioning

confidence: 99%

“…( (28); the corresponding interval nonprobabilistic reliabilities are obtained according to (13) and (14). The change regulation is shown as solid blue star in Figure 6(a).…”

Section: Sensitive Analysismentioning

confidence: 99%

“…The interval nonprobabilistic reliability analysis methods for structures [27][28][29][30][31][32][33] based on interval theory provide a useful approach to evaluate these uncertainties. Interval values can better reflect the uncertainty of a parameter value when the number of samples is scarce, thus reducing the demand for data information.…”

Section: Introductionmentioning

confidence: 99%

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Theoretical and Case Studies of Interval Nonprobabilistic Reliability for Tailing Dam Stability

Dong

Sun

2017

Geofluids

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The stability of the operation of a tailing dam is affected by reservoir water level, phreatic line, and mechanical parameters of tailings. The values of these factors are not a definite value in different situations. Meanwhile, the existence of the phreatic line makes it a more complex issue to analyze the stability of the tailing dam. Additionally, it is very hard to give a definite limit to the state of tailing dam from security to failure. To consider the uncertainty when calculating the stability of the tailing dams, interval values are used to indicate the physical and mechanical parameters of tailings. An interval nonprobabilistic reliability model of the tailing dam, which can be used when the data is scarce, is developed to evaluate the stability of the tailing dam. The interval nonprobabilistic reliability analysis model of tailing dam is established in two cases, including with and without considering phreatic line conditions. The proposed model was applied to analyze the stability of two tailing dams in China and the calculation results of the interval nonprobabilistic reliability are found to be in agreement with actual situations. Thus, the interval nonprobabilistic reliability is a beneficial complement to the traditional analysis method of random reliability.

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Novel solution framework for inverse problem considering interval uncertainty

Tang

et al. 2021

Numerical Meth Engineering

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This article proposes a novel solution framework for the inverse problem considering interval uncertainty in structural or systemic responses, which provides an efficient tool for the uncertain inverse problems of nonlinear structures or systems. Interval is used to model and characterize the uncertainty, and the bounds of uncertain structural responses are only required. In each iterative step, the approximate deterministic inverse problem is constructed according to the interval analysis results, and then the identified intervals of inputs are updated by solving the approximate deterministic inverse problem. Therefore, the interval inverse problem is decoupled into a series of interval analyses and deterministic inverse problems that are alternately solved, which dramatically promotes the computational efficiency of the interval inverse problem. Besides, an iterative mechanism is proposed to ensure the convergence of the whole procedure. Finally, two numerical examples and an engineering application are investigated to demonstrate the accuracy and efficiency of the proposed method.

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An improved multidimensional parallelepiped non-probabilistic model for structural uncertainty analysis

Cited by 79 publications

References 30 publications

Discussions on non-probabilistic convex modelling for uncertain problems

Discussions on non-probabilistic convex modelling for uncertain problems

Theoretical and Case Studies of Interval Nonprobabilistic Reliability for Tailing Dam Stability

Novel solution framework for inverse problem considering interval uncertainty

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