Research Papers

Imprecise Probabilities in Fatigue Reliability Assessment of Hydraulic Turbines

[+] Author and Article Information
Mounia Berdai

École de Technologie Supérieure, 1100, Rue Notre-Dame Ouest, Montréal, Québec H3C 1K3, Canada e-mail: mounia.berdai.1@ens.etsmtl.ca

Antoine Tahan

École de Technologie Supérieure,
1100, rue Notre-Dame Ouest, Montréal, Québec H3C 1K3, Canada e-mail: antoine.tahan@etsmtl.ca

Martin Gagnon

1800 Boulevard Lionel-Boulet, Varennes, Québec J3X 1S1, Canada e-mail: gagnon.martin@ireq.ca

1Corresponding author.

Manuscript received May 16, 2016; final manuscript received September 4, 2016; published online November 21, 2016. Assoc. Editor: Konstantin Zuev.

ASME J. Risk Uncertainty Part B 3(1), 011006 (Nov 21, 2016) (8 pages) Paper No: RISK-16-1083; doi: 10.1115/1.4034690 History: Received May 16, 2016; Accepted September 04, 2016

Risk analyses are often performed for economic reasons and safety purposes. In some cases, these studies are biased by epistemic uncertainties due to the lack of information and knowledge, which justifies the need for expert opinion. In such cases, experts can follow different approaches for the elicitation of epistemic data, using probabilistic or imprecise theories. But how do these theories affect the reliability calculation? What are the influences of using a mixture of theories in a multivariable system with a nonexplicit limit model? To answer these questions, we propose an approach for the comparison of these theories, which was performed based on a reliability model using the first-order reliability method (FORM) approach and having the Kitagawa–Takahashi diagram as limit state. We also propose an approach, appropriate to this model, to extend the reliability calculation to variables derived from imprecise probabilities. For the chosen reliability model, obtained results show that there is a certain homogeneity among the considered theories. The study also concludes that priority should be given to expert opinions formulated according to unbounded distributions, in order to achieve better reliability calculation accuracy.

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Fig. 1

(a) Reliability model based on Kitagawa–Takahashi diagram and (b) reliability index in the iso-probabilistic space

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Fig. 2

Example of the reliability index distribution, resulting from loading stress following a possibility distribution and defect size formulated according to a triangular distribution

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Fig. 3

Theories used in the case matrix

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Fig. 4

Points from the probabilistic domain used in the matrix case (Table 1). In this figure, defect size and loading stress are expressed with Gumbel distribution

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Fig. 5

Example of determining the mode of distribution#2 (D2) from distribution#1 (D1)

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Fig. 6

(a) Example of a belief function expressed as an evidence distribution and (b) example of a continuous belief function for the example in (a)

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Fig. 7

Reliability indices calculated according to different theories combinations (Table 1) for defect size and loading stress for G0, G01, G02, G03, G04, and G05 (Fig. 8)

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Fig. 8

Distributions used in the case matrix




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