• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.64-79
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• 2003

In the risk and reliability analysis of complex technological systems, the primary concern of formal uncertainty analysis is to understand why uncertainties arise, and to evaluate how they impact the results of the analysis. In recent times, many of the uncertainty analyses have focused on parameters of the risk and reliability analysis models, whose values are uncertain in an aleatory or an epistemic way. As the field of parametric uncertainty analysis matures, however, more attention is being paid to the explicit treatment of uncertainties that are addressed in the predictive model itself as well as the accuracy of the predictive model. The essential steps for evaluating impacts of these model uncertainties in the presence of parameter uncertainties are to determine rigorously various sources of uncertainties to be addressed in an underlying model itself and in turn model parameters, based on our state-of-knowledge and relevant evidence. Answering clearly the question of how to characterize and treat explicitly the forgoing different sources of uncertainty is particularly important for practical aspects such as risk and reliability optimization of systems as well as more transparent risk information and decision-making under various uncertainties. The main purpose of this paper is to provide practical guidance for quantitatively treating various model uncertainties that would often be encountered in the risk and reliability modeling process of complex technological systems.

• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.81-87
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• 2001

A framework for reliability analysis of structural components and systems under conditions of statistical and model uncertainty is presented. The Bayesian parameter estimation method is used to derive the posterior distribution of model parameters reflecting epistemic uncertainties. Point, predictive and bound estimates of reliability accounting for parameter uncertainties are derived. The bounds estimates explicitly reflect the effect of epistemic uncertainties on the reliability measure. These developments are enhance-ments of second-moment uncertainty analysis methods developed by A. H-S. Ang and others three decades ago.

• Journal of the Korean Society of Propulsion Engineers
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• v.22 no.2
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• pp.131-137
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• 2018

This paper analyzes the probability of failure for the equivalence ratio error. The control error of the equivalence ratio is affected by the aleatory and epistemic uncertainties. In general, reliability analysis techniques are easily incorporated to handle the aleatory uncertainty. However, the epistemic uncertainty requires a new approach, as it does not provide an uncertainty distribution. The Bayesian inference incorporates the reliability analysis results to handle both uncertainties. The result gives a distribution of failure probability, whose equivalence ratio does not meet the requirement. This technique can be useful in the analysis of most engineering systems, where the aleatory and epistemic uncertainties exist simultaneously.

• Nuclear Engineering and Technology
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• v.46 no.1
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• pp.11-26
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• 2014

The analyses carried out within the Seismic Probabilistic Risk Assessments (SPRAs) of Nuclear Power Plants (NPPs) are affected by significant aleatory and epistemic uncertainties. These uncertainties have to be represented and quantified coherently with the data, information and knowledge available, to provide reasonable assurance that related decisions can be taken robustly and with confidence. The amount of data, information and knowledge available for seismic risk assessment is typically limited, so that the analysis must strongly rely on expert judgments. In this paper, a Dempster-Shafer Theory (DST) framework for handling uncertainties in NPP SPRAs is proposed and applied to an example case study. The main contributions of this paper are two: (i) applying the complete DST framework to SPRA models, showing how to build the Dempster-Shafer structures of the uncertainty parameters based on industry generic data, and (ii) embedding Bayesian updating based on plant specific data into the framework. The results of the application to a case study show that the approach is feasible and effective in (i) describing and jointly propagating aleatory and epistemic uncertainties in SPRA models and (ii) providing 'conservative' bounds on the safety quantities of interest (i.e. Core Damage Frequency, CDF) that reflect the (limited) state of knowledge of the experts about the system of interest.

• Structural Engineering and Mechanics
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• v.62 no.4
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• pp.507-517
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• 2017

Due to the discontinuous nature of uncertainty quantification in conventional evidence theory(ET), the computational cost of reliability analysis based on ET model is very high. A novel ET model based on fuzzy distribution and the corresponding combination rule to synthesize the judgments of experts are put forward in this paper. The intersection and union of membership functions are defined as belief and plausible membership function respectively, and the Murfhy's average combination rule is adopted to combine the basic probability assignment for focal elements. Then the combined membership functions are transformed to the equivalent probability density function by a normalizing factor. Finally, a reliability analysis procedure for structures with the mixture of epistemic and aleatory uncertainties is presented, in which the equivalent normalization method is adopted to solve the upper and lower bound of reliability. The effectiveness of the procedure is demonstrated by a numerical example and an engineering example. The results also show that the reliability interval calculated by the suggested method is almost identical to that solved by conventional method. Moreover, the results indicate that the computational cost of the suggested procedure is much less than that of conventional method. The suggested ET model provides a new way to flexibly represent epistemic uncertainty, and provides an efficiency method to estimate the reliability of structures with the mixture of epistemic and aleatory uncertainties.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.6
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• pp.605-613
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• 2014

Epistemic uncertainty, the lack of knowledge, is often more important than aleatory uncertainty, variability, in estimating reliability of a system. While the probability theory is widely used for modeling aleatory uncertainty, there is no dominant approach to model epistemic uncertainty. Different approaches have been developed to handle epistemic uncertainties using various theories, such as probability theory, fuzzy sets, evidence theory and possibility theory. However, since these methods are developed from different statistics theories, it is difficult to interpret the result from one method to the other. The goal of this paper is to compare different methods in handling epistemic uncertainty in the view point of calculating the probability of failure. In particular, four different methods are compared; the probability method, the combined distribution method, interval analysis method, and the evidence theory. Characteristics of individual methods are compared in the view point of reliability analysis.

• Journal of the Korean Society of Safety
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• v.23 no.5
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• pp.125-130
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• 2008

To optimize the selected reinforcing method for application to PSC Beam bridges, the reliability analysis was performed with consideration for the increase and decrease of the member section based on the standard design section, and the minimum life-cycle cost(LCC) was calculated from this analysis with consideration for the aleatory uncertainty. Moreover, the mean, 50%, 75%, and 90% distributions of the analysis results were re-evaluated quantitatively by considering the effect of the epistemic uncertainty. The reliability results gained from the application of the reinforcing method, as well as the optimal design method based on the minimum LCC, will provide more reasonable design criteria for the PSC Beam bridges.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.413-431
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• 2016

A sensitivity analysis estimates the effect of the change in the uncertain variable parameter on the probability of the structural failure. A novel fuzzy random reliability sensitivity measure of the failure probability is proposed to consider the effect of the epistemic and aleatory uncertainties. The uncertainties of the engineering variables are modeled as fuzzy random variables. Fuzzy quantities are treated using the ${\lambda}$-cut approach. In fact, the fuzzy variables are transformed into the interval variables using the ${\lambda}$-cut approach. Genetic approach considers different possible combinations within the search domain (${\lambda}$-cut) and calculates the parameter sensitivities for each of the combinations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.10
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• pp.1163-1170
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• 2009

Reliability analysis is of great importance in the advanced product design, which is to evaluate reliability due to the associated uncertainties. There are three types of uncertainties: the first is the aleatory uncertainty which is related with inherent physical randomness that is completely described by a suitable probability model. The second is the epistemic uncertainty, which results from the lack of knowledge due to the insufficient data. These two uncertainties are encountered in the input variables such as dimensional tolerances, material properties and loading conditions. The third is the metamodel uncertainty which arises from the approximation of the response function. In this study, an integrated method for the reliability analysis is proposed that can address all these uncertainties in a single Bayesian framework. Markov Chain Monte Carlo (MCMC) method is employed to facilitate the simulation of the posterior distribution. Mathematical and engineering examples are used to demonstrate the proposed method.

• Earthquakes and Structures
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• v.6 no.1
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• pp.19-43
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• 2014

A risk assessment framework for evaluating building structures is implemented in this study. This framework allows considering sources of uncertainty both on structural capacity and seismic demand. In particular randomness on seismic load, incident angle, material properties, floor mass and structural damping are considered; in addition the choice of fibre modelling versus plastic hinge model is also considered as a source of uncertainty. The main objective of this work is to study the contribution of these sources of uncertainty on the fragilities of steel and steel-reinforced concrete composite 3D building structures. The fragility curves are expressed in the form of a two-parameter lognormal distribution where vertical statistics in conjunction with metaheuristic optimization are implemented for calculating the two parameters.