A dimension-wise method and its improvement for multidisciplinary interval uncertainty analysis

Wang, Lei; Xiong, Congcong; Xu, Menghui; Li, Yunlong

doi:10.1016/j.apm.2018.02.022

Cited by 103 publications

(27 citation statements)

References 35 publications

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“…Then, the bounds of structural compliance under any source of unknown-but-bounded uncertainties can be solved by Equation (19)- (22).…”

Section: Structural Compliance Rules With Unknown-but-bounded Uncertamentioning

confidence: 99%

“…Under the circumstance, nonprobabilistic models, which avoid probability distribution function uncertain parameters, are proposed. There are mainly three nonprobabilistic models: the interval set model, [20][21][22][23] the ellipsoid convex model, [24][25][26][27][28] and the fuzzy set model. [29][30][31] The fuzzy set describes uncertainties with some membership functions, which to some extent are a subjective choice.…”

Section: Introductionmentioning

confidence: 99%

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Truss layout design under nonprobabilistic reliability‐based topology optimization framework with interval uncertainties

Wang

Liu

Yang

2019

Numerical Meth Engineering

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Summary A nonprobabilistic reliability‐based topology optimization (NRBTO) method for truss structures with interval uncertainties (or unknown‐but‐bounded uncertainties) is proposed in this paper. The cross‐sectional areas of levers are defined as design variables, while the material properties and external loads are regard as interval parameters. A modified perturbation method is applied to calculate structural response bounds, which are the prerequisite to obtain structural reliability. A deviation distance between the current limit state plane and the objective limit state plane, of which the expression is explicit, is defined as the nonprobabilistic reliability index, which serves as a constraint function in the optimization model. Compared with the deterministic topology optimization problem, the proposed NRBTO formulation is still a single‐loop optimization problem, as the reliability index is explicit. The sensitivity results are obtained from an analytical approach as well as a direct difference method. Eventually, the NRBTO problem is solved by a sequential quadratic programming method. Two numerical examples are used to testify the validity and effectiveness of the proposed method. The results show significant effects of uncertainties to the topology configuration of truss structures.

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“…Then, the bounds of structural compliance under any source of unknown-but-bounded uncertainties can be solved by Equation (19)- (22).…”

Section: Structural Compliance Rules With Unknown-but-bounded Uncertamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Truss layout design under nonprobabilistic reliability‐based topology optimization framework with interval uncertainties

Wang

Liu

Yang

2019

Numerical Meth Engineering

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“…However, the explicit function of the response a is usually hard to get, which brings huge difficulty for researching changes of the studied damaged structure. Fortunately, many function approximation methods have been developed to describe or estimate responses of structures …”

Section: Nonprobabilistic Structural Damage Identificationmentioning

confidence: 99%

A nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics

Wang

Qiu

et al. 2019

Struct Control Health Monit

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In this study, a nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics is proposed for uncertainty-oriented damage identification with insufficient parametric information. A deterministic damage identification method is firstly reviewed. By means of a nonnegative least squares algorithm that combines truncated singular value decomposition and the L-curve method, the illposed damage equation is then solved, and the damage index is simultaneously obtained. In terms of the uncertainty quantification issue, the material elastic modulus and density in structural models herein are described as unknownbut-bounded interval numbers. On the basis of orthogonal polynomial expansion and interval mathematics, the set collocation methodology is presented to determine the upper and lower bounds of the damage index. The interval bounds can provide supports for structural health diagnosis under uncertain conditions. A nonprobabilistic identification using the first-order Taylor series expansion is also proposed for comparison's purpose. Two numerical applications and one test are finally given under single damage and multidamage scenarios with different uncertainty degree. Results suggest that the presented nonprobabilistic structural damage identification approach can identify the damage location and degree with consideration of uncertainties. KEYWORDSinterval mathematics, interval-based set collocation methodology, nonprobabilistic structural damage identification, the first-order Taylor expansion | INTRODUCTIONVarious mechanical equipments and engineering structures like aircrafts and civil structures suffer from deterioration due to environmental erosion, overloading, accidental bumping, and other factors in service. 1 The deteriorations in structures accumulate as time goes on and are gradually reflected by performance degradation and structural damage. In order to avoid safety accidents, how to detect, locate, and characterize damage in structural and mechanical systems and estimate their residual life become critical problems. 2 Structural health monitoring and damage identification emerge in such demand and have attracted many researchers' attentions.

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“…Of course, this approach is multiplicative in its expense, rendering all but the simplest problems intractable. Other approaches to limited test data include appealing to an interval approach; we do not consider these techniques in this work.…”

Section: Introductionmentioning

confidence: 99%

Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Rosario

Fenrich

Iaccarino

2019

Numerical Meth Engineering

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Summary Parametric uncertainties complicate engineering design—confounding regulated design approaches and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double‐loop simulation, a nested Monte Carlo method that, for practical problems, is intractable. In this work, we introduce a flexible, general approximation technique that obviates the double loop. This approximation is constructed in the context of a novel theory of reliability design under parametric uncertainty: we introduce metrics for measuring the efficacy of reliability‐based design optimization strategies (epistemic design gap and effective reliability), minimal conditions for controlling uncertain reliability (precision margin), and stricter conditions that guarantee the desired reliability at a designed confidence level. We provide a number of examples with open‐source code to demonstrate our approaches in a reproducible fashion.

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A dimension-wise method and its improvement for multidisciplinary interval uncertainty analysis

Cited by 103 publications

References 35 publications

Truss layout design under nonprobabilistic reliability‐based topology optimization framework with interval uncertainties

Truss layout design under nonprobabilistic reliability‐based topology optimization framework with interval uncertainties

A nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics

Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

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