A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model

Jiang, Chao; Zhang, Q. F.; Han, Xu; Qian, Youhua

doi:10.1007/s00707-013-0975-2

Cited by 77 publications

(31 citation statements)

References 26 publications

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“…Secondly, it can also be recognized that the ME model is more adaptable to the geometric parameters in this problem, since that the ellipsoid-shaped domain is smaller in volume than the parallelepiped. With the ME or the MP-II convex uncertainty domain obtained, subsequent uncertainty analyses such as non-probabilistic reliability analysis [16,18,28,29] can be then carried out. Herein we employ the non-probabilistic reliability index to evaluate the reliability degree of a structure under uncertainty, which represents a minimal distance from the original point to the limit-state surface in a standardized space [16,29].…”

Section: A Cantilever Beam Problemmentioning

confidence: 99%

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: A Cantilever Beam Problemmentioning

confidence: 99%

Discussions on non-probabilistic convex modelling for uncertain problems

Jiang

Huang

2018

Applied Mathematical Modelling

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“…Already known are the minimal distance = 1.5 Hz, the gust frequency ∈ [8,14] Hz, and the range of natural frequencies shown in Table 2. Transform the frequencies into standard ones.…”

Section: The Garteur Planementioning

confidence: 99%

“…A new method was developed for reliability analysis of the uncertain structures with both random and interval variables by Jiang et al [7]. And then a new nonprobabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model was developed by Jiang et al in the literature [8]. The model was constructed using marginal intervals for the variables and correlation information between any two variables.…”

Section: Introductionmentioning

confidence: 99%

A Vibration Reliability Analysis Method for the Uncertain Space Beam Structure

Guo

Tang

2016

Shock and Vibration

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Considering that uncertainty is inherent and unavoidable in engineering practice and the available information about the uncertain parameters is always not sufficient, the paper tries to carry out the nonprobabilistic vibration reliability analysis so as to avoid resonance on uncertain structure with bounded parameters. The input uncertain-but-bounded parameters are treated as interval variables, and an interval model is adopted to describe bounded uncertainties. Then a theory of nonprobabilistic reliability is introduced, in which the dimensionless nonprobabilistic reliability index and system reliability index are defined. In order to investigate the resonance failure with reliability method, the resonance failure domains are stated according to the relationships between the natural frequencies and the excitation frequencies. Then the uncertain structure is modeled as a series system and a system reliability index is proposed to evaluate the safety of the structure. The paper also takes a frequency analysis on the uncertain space beam structure to get the resonance failure modes. A frequency analysis method based on the monotonicity discriminant of the frequency sensitivity is presented. Then an optimization algorithm is introduced to verify the validity of the former frequency analysis method. Two examples are provided to illustrate the effectiveness and feasibility of the presented method.

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“…It is noteworthy that traditional convex models such as interval model and ellipsoidal model are found not capable of dealing with complex "multisource uncertainty" problems. Therefore, a more general convex model, namely, "multidimensional parallelepiped (MP) model", was proposed in recent work [49][50][51]. This kind of convex model can take into account the independent and dependent uncertain parameters in a unified framework.…”

Section: Introductionmentioning

confidence: 99%

A New Formulation on Seismic Risk Assessment for Reinforced Concrete Structures with Both Random and Bounded Uncertainties

Liu

Wang

2018

Discrete Dynamics in Nature and Society

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A new formulation on seismic risk assessment for structures with both random and uncertain-but-bounded variables is investigated in this paper. Limit thresholds are regarded as random variables. The median of random variables is described through an improved multidimensional parallelepiped (IMP) convex model, in which the uncertain domain of the dependent bounded variables can be explicitly expressed. The corresponding Engineering Demand Parameters are taken to be dependent and follow a multidimensional lognormal distribution. Through matrix transformation, a given performance function is transformed into the regularized one. An effective method based on active learning Kriging model (ALK) is introduced to approximate the performance function in the region of interest rather than in the overall uncertain space. Based on ALK model, the failure probabilities for different limit states are calculated by using Monte Carlo Simulation (MCS). Further, the failure probabilities for different limit states in 50 years can be obtained through coupling the seismic failure probability with the ground motion hazard curve. A six-story reinforced concrete building subjected to ground motions is investigated to the efficiency and accuracy of the proposed method. The interstory drift and the acceleration as two responses of the case study are, respectively, obtained by utilizing Incremental Dynamic Analysis and nonlinear history analysis.

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A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex model

Cited by 77 publications

References 26 publications

Discussions on non-probabilistic convex modelling for uncertain problems

Discussions on non-probabilistic convex modelling for uncertain problems

A Vibration Reliability Analysis Method for the Uncertain Space Beam Structure

A New Formulation on Seismic Risk Assessment for Reinforced Concrete Structures with Both Random and Bounded Uncertainties

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