A non-probabilistic concept of reliability

Ben‐Haim, Yakov

doi:10.1016/0167-4730(94)90013-2

Cited by 337 publications

(100 citation statements)

References 19 publications

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“…As for the probabilistic structural reliability, different methods are available, although the related literature is by far more limited than the previous case. One of the most common approach consists of treating epistemic uncertainty using set of descriptor values, such as in the case of intervals [10], convex models [2], random sets [20] and fuzzy sets [22].…”

Section: Structural Reliability Methodsmentioning

confidence: 99%

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Tolo¹,

Patelli²,

Beer³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. A computational framework for the reduction and computation of Bayesian Networks enhanced with structural reliability methods is presented. During the last decades, the inner flexibility of the Bayesian Network method, its intuitive graphical structure and the strong mathematical background have attracted increasing interest in a large variety of applications involving joint probability of complex events and dependencies. Furthermore, the fast growing availability of computational power on the one side and the implementation of robust inference algorithms on the other, have additionally promoted the success of this method. Inference in Bayesian Networks is limited to only discrete variables (with the only exception of Gaussian distributions) in case of exact algorithms, whereas approximate approach allows to handle continuous distributions but can either result computationally inefficient or have unknown rates of convergence.This work provides a valid alternative to the traditional approach without renouncing to the reliability and robustness of exact inference computation. The methodology adopted is based on the combination of Bayesian Networks with structural reliability methods and allows to integrate random and interval variables within the Bayesian Network framework in the so called Enhanced Bayesian Networks. In the following, the computational algorithms developed are described and a simple structural application is proposed in order to fully show the capability of the tool developed.

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Section: Structural Reliability Methodsmentioning

confidence: 99%

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

Tolo¹,

Patelli²,

Beer³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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show abstract

“…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%

“…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. Elishakoff (1995a) later put forward a possible definition in the discussion of this concept, which indicated that nonprobabilistic reliability index should be an interval rather than a specific value.…”

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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“…The reason of hinder development is that there are many uncertainties stemming from practical engineering, such as geometric dimensions, material properties and external loads, all these inherent uncertain factors may lead to large variations of the structural optimization models. Thus the probability RBDO approach (PRBDO), fuzzy reliability and NRBDO method are proposed to solve this problem [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

The Exploration of Superiority about the Non-probability Reliability-Based Design Optimization Compared to the Safety Factor Method

Fan¹,

Wang²,

Wang³

et al. 2017

dtetr

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Abstract. Non-probability reliability-based design optimization (NRBDO) theory has been widely acknowledged as an advanced and advantageous methodology for complex structural system design, especially in practical engineering of aerospace. Conversely, the traditional safety factor (SF) design method faded out of the horizon of the designer since it considers only the mean value of design variable without the effect of dispersion properties, which has been verified to be not reasonable. In previous studies, only the physical interpretation that NRBDO method is superior compared to the SF method was given. In this paper, we make attempts to seek a mathematical explanation through design domain in which NRBDO method and SF method search for the optimal design solution, which presents strong evidences why NRBDO theory is more advanced and reasonable method from the aspects of mathematical proof. Eventually, the advancement of the NRBDO and the weakness of the SF method are illustrated with three numerical cases.

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A non-probabilistic concept of reliability

Cited by 337 publications

References 19 publications

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

A Computational Tool for Bayesian Networks Enhanced With Reliability Methods

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

The Exploration of Superiority about the Non-probability Reliability-Based Design Optimization Compared to the Safety Factor Method

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