A non-probabilistic measure of reliability of linear systems based on expansion of convex models

Ben‐Haim, Yakov

doi:10.1016/0167-4730(95)00004-n

Cited by 144 publications

(50 citation statements)

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“…In this spirit, for the n-dimensional case we will use the formula (11) to evaluate the reliability of interval variables, then using the formula (12) and the joint probability density function, we can obtain the reliability of all regions and whole structure system.…”

Section: Probabilistic and Interval Hybrid Reliability Modelmentioning

confidence: 99%

“…The bounds on the uncertain information can be obtained more easily than the probability densities. Thus, Ben-Haim [9][10][11] advanced a non-probabilistic (convex model) reliability model, which was called by him as the robust reliability. This reliability model regarded the allowable maximum amount of uncertainty before structure failure as the structural reliability through.…”

Section: Introductionmentioning

confidence: 99%

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The reliability analysis of probabilistic and interval hybrid structural system

Wang

Qiu

2010

Applied Mathematical Modelling

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Interval reliability model Probabilistic and interval hybrid reliability model Main failure modes a b s t r a c tThe aim of this paper is to evaluate the reliability of probabilistic and interval hybrid structural system. The hybrid structural system includes two kinds of uncertain parametersprobabilistic parameters and interval parameters. Based on the interval reliability model and probabilistic operation, a new probabilistic and interval hybrid reliability model is proposed. Firstly, we use the interval reliability model to analyze the performance function, and then sum up reliability of all regions divided by the failure plane. Based on the presented optimal criterion enumerating the main failure modes of hybrid structural system and the relationship of failure modes, the reliability of structure system can be obtained. By means of the numerical examples, the hybrid reliability model and the traditional probabilistic reliability model are critically contrasted. The results indicate the presented reliability model is more suitable for analysis and design of these structural systems and it can ensure the security of system well, and it only needs less uncertain information.Ó

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Section: Probabilistic and Interval Hybrid Reliability Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The reliability analysis of probabilistic and interval hybrid structural system

Wang

Qiu

2010

Applied Mathematical Modelling

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“…More discussions on non-probabilistic reliability can be found in [76][77][78][79][80][81]. According to the discussion in Figure 1, another mathematical definition of NPRI η can be provided by [72][73][74][75]: …”

Section: Npri For Problems With Interval Parametersmentioning

confidence: 99%

“…The maximum allowable variability can be defined by the shortest distance between LSC y = g(q) = 0 and the coordinate origin in the normalized space in the form of infinite norm [72][73][74][75], which can be employed to measure the reliable extent of the system, i.e., non-probabilistic reliability index. More discussions on non-probabilistic reliability can be found in [76][77][78][79][80][81].…”

Section: Npri For Problems With Interval Parametersmentioning

confidence: 99%

A Non-Probabilistic Solution for Uncertainty and Sensitivity Analysis on Techno-Economic Assessments of Biodiesel Production with Interval Uncertainties

et al. 2018

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Abstract:Techno-economic assessments (TEA) of biodiesel production may comply with various economic and technical uncertainties during the lifespan of the project, resulting in the variation of many parameters associated with biodiesel production, including price of biodiesel, feedstock price, and rate of interest. Engineers may only collect very limited information on these uncertain parameters such as their variation intervals with lower and upper bound. This paper proposes a novel non-probabilistic strategy for uncertainty analysis (UA) in the TEA of biodiesel production with interval parameters, and non-probabilistic reliability index (NPRI) is employed to measure the economically feasible extent of biodiesel production. A sensitivity analysis (SA) indicator is proposed to assess the sensitivity of NPRI with regard to an individual uncertain interval parameter. The optimization method is utilized to solve NPRI and SA. Results show that NPRI in the focused biodiesel production of interest is 0.1211, and price of biodiesel, price of feedstock, and cost of operating can considerably affect TEA of biodiesel production.

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“…To overcome the limitations of probabilistic methods in the process of reliability-based design optimization, scholars have gradually turned to nonprobabilistic methods for handling uncertainties since non-probabilistic models have advantages such as low requirements for sample data and simplicity of calculation (Ben-Haim, 1994;1995;Elishakoff et al, 1994;Qiu et al, 1995;2004;Elishakoff and Elettro, 2014). Ben-Haim (1994) first proposed the concept of non-probabilistic reliability based on convex set theory, where non-probabilistic convex models of uncertainty were utilized to formulate reliability in terms of acceptable system performance given an uncertain operating environment or uncertain geometrical imperfections.…”

Section: Introductionmentioning

confidence: 99%

Direct reliability-based design optimization of uncertain structures with interval parameters

Cheng

Tang

Liu

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:In order to enhance the reliability of an uncertain structure with interval parameters and reduce its chance of function failure under potentially critical conditions, an interval reliability-based design optimization model is constructed. With the introduction of a unified formula for efficiently computing interval reliability, a new concept of the degree of interval reliability violation (DIRV) and the DIRV-based preferential guidelines are put forward for the direct ranking of various design vectors. A direct interval optimization algorithm integrating a nested genetic algorithm (GA) and the Kriging technique is proposed for solving the interval reliability-based design model, which avoids the complicated model transformation process in indirect ones and yields an interval solution that provides more insights into the optimization problem. The effectiveness of the proposed algorithm is demonstrated by a numeric example. Finally, the proposed direct reliability-based design optimization method is applied to the optimization of a press upper beam with interval uncertain parameters, the results of which demonstrate its feasibility and effectiveness in engineering.

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A non-probabilistic measure of reliability of linear systems based on expansion of convex models

Cited by 144 publications

References 1 publication

The reliability analysis of probabilistic and interval hybrid structural system

The reliability analysis of probabilistic and interval hybrid structural system

A Non-Probabilistic Solution for Uncertainty and Sensitivity Analysis on Techno-Economic Assessments of Biodiesel Production with Interval Uncertainties

Direct reliability-based design optimization of uncertain structures with interval parameters

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