Fatigue Lifetime with Load Uncertainty Represented by Convex Model

Ben‐Haim, Yakov

doi:10.1061/(asce)0733-9399(1994)120:3(445)

Cited by 21 publications

(7 citation statements)

References 38 publications

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“…As an interval linear equation, or an interval eigenvalue problem [6][7][8][9][10][11][12], Eq. (19) represents the interval dynamical response problem.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Ben-Haim [5] evaluated the least time to failure of a linear elastic system with uncertain time varying input represented by an ellipsoidal Fourier-bound convex model. Convex models were extended by Tzan and Pantelides [6] for finding the maximum response of a structure to an impulse of known energy-bound but unknown shape and extensive numerical simulations were carried out.…”

Section: Introductionmentioning

confidence: 99%

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Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Qiu

Wang

2006

Acta Mech Mech Sinica

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Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

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“…As an interval linear equation, or an interval eigenvalue problem [6][7][8][9][10][11][12], Eq. (19) represents the interval dynamical response problem.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Qiu

Wang

2006

Acta Mech Mech Sinica

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“…While there are many models of damage accumulation, we adopt the simplest for purposes of illustration. Extensions can be found in Ben-Haim (1994b, 1996. We suppose that the increment of damage in a single transient is proportional to the integral squared displacement:…”

Section: Robust Reliabilitymentioning

confidence: 99%

Reliability of Vibrating Structures with Uncertain Inputs

Ben‐Haim¹

1998

The Shock and Vibration Digest

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We evaluate the reliability of vibrating systems subject to severely deficient information about the dynamic loads. We stress non-probabilistic information-gap models of uncertainty, which are adapted to severe lack of information. When some probabilistic information is available, we show how it can be incorporated in a hybrid probabilistic/info-gap analysis. We outline the theory of robust reliability, which replaces probabilistic reliability in those situations where prior information is insufficient to verify the choice of a probability density. We also illustrate a hybrid probabilistic/info-gap reliability analysis. Finally, we use the "gambler's theorem" and the idea of aversion to risk to provide an overall quantitative assessment of the performance of a system in an uncertain environment. 0 papers svd rev rev.tex 7.1.98

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“…In practice, only the bounds on their amplitude are often known. Therefore, in recent years some nonprobabilistic approaches, such as convex models (Ben-Haim and Elishakoff, 1990;Ben-Haim, 1994;Ben-Haim et al, 1996;Qiu, 2003) and interval analysis methods (Qiu and Elishakoff, 1998;Qiu and Wang, 2003), are developed to deal with the bounded uncertainties.…”

Section: Introductionmentioning

confidence: 99%