An approximation approach for uncertainty quantification using evidence theory

Bae, Ha-Rok; Grandhi, Ramana V.; Canfield, Robert A.

doi:10.1016/j.ress.2004.01.011

Cited by 183 publications

(65 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is usually used to quantify epistemic uncertainty if there is no conflicting evidence among experts, unlike classical probability theory, which is best suited to aleatory uncertainty (Bae et al, 2004a). In the area of reliability engineering, reliability estimation and design are investigated by (Mourelatos and Zhou, 2004), Kozine and Filimonov (2000); Moller et al (1999;Huang (1995;; Huang et al (2006a;; Huang (2012); Li et al (2012); Pang et al (2012); Wang et al (2011;2012) and Xiao et al (2012).…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

“…As a more general tool for uncertainty analysis, evidence theory has also been applied to many areas, including artificial intelligence (particularly in the development of expert systems) (Bae et al, 2004b;Nikolaidis and Haftka, 2001), object detection and approximate reasoning (Lowrance et al, 1986;Perrin et al, 2004;Xu and Smets, 1996;Borotschnig et al, 1999), design optimization (Mourelatos and Zhou, 2005), multidisciplinary design optimization (Agarwal et al, 2004), uncertainty quantification (Bae et al, 2004a;, risk and reliability evaluation (Yang et al, 2011b), remote sensing classification (Lee et al, 1987), pattern recognition and image analysis, decision making (Buckley, 1988;Limbourg, 2005), data fusion (Delmotte and Borne, 1998;Hall and Llinas, 1997;Sun et al, 2008;Yang et al, 2011a) and fault diagnosis (Fan and Zuo, 2006a;Wu et al, 1990). The popularity of evidence theory has risen, however, because evidence theory requires epistemological assumptions that are at odds with those underlying classical and Bayesian probability theories (Fioretti, 2004).…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

“…To date, most existing works are in theoretic construction and modification (Cai et al, 1991a;1991b;1993;Cappelle and Kerre, 1993;Moller et al, 2004;Nikolaidis et al, 2004;Huang et al, 2010), or practical connections in engineering (Cappelle and Kerre, 1995a;Bae et al, 2004a;Bai and Asgarpoor, 2004;Moller et al, 1999;Li et al, 2012). Cai et al (1991a;1991b) has considered Posbist reliability theory for typical systems, such as series, parallel and k-out-of-n systems as well as for cold and warm redundant systems (Cai et al, 1995a;.…”

Section: Ajeasmentioning

confidence: 99%

“…It is only recently that evidence-based methods are used to propagate epistemic uncertainty (Bae et al, 2002;Bae et al, 2004a), e.g., in large-scale engineering structure systems. One of the major difficulties of applications for evidence theory, investigated by Bae et al (2004a; may be its high computational cost.…”

Section: Ebdomentioning

confidence: 99%

See 3 more Smart Citations

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

show abstract

Section: General Topics Of Applicationsmentioning

confidence: 99%

Section: General Topics Of Applicationsmentioning

confidence: 99%

Section: Ajeasmentioning

confidence: 99%

Section: Ebdomentioning

confidence: 99%

See 2 more Smart Citations

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

show abstract

“…More recently, the info-gap decision theory Article published by EDP Sciences was developed in order to solve decision problems under severe uncertainty [15]. Other non-probabilistic techniques, less developed in structural mechanics, are used to model uncertainties, such as the generalized information theory [16] and the evidence theory, also called DempsterShafer theory [17].…”

Section: Introductionmentioning

confidence: 99%

Uncertainties in structural dynamics: overview and comparative analysis of methods

Daouk

Louf

Dorival

et al. 2015

Mechanics & Industry

View full text Add to dashboard Cite

-When studying mechanical systems, engineers usually consider that mathematical models and structural parameters are deterministic. However, experimental results show that these elements are uncertain in most cases, due to natural variability or lack of knowledge. Therefore, engineers are becoming more and more interested in uncertainty quantification. In order to improve the predictability and robustness of numerical models, a variety of methods and techniques have been developed. In this work we propose to review the main probabilistic approaches used to model and propagate uncertainties in structural mechanics. Then we present the Lack-Of-Knowledge theory that was recently developed to take into account all sources of uncertainties. Finally, a comparative analysis of different parametric probabilistic methods and the Lack-Of-Knowledge theory in terms of accuracy and computation time provides useful information on modeling and propagating uncertainties in structural dynamics.

show abstract

Random and Stochastic Structural–Acoustic Analysis

Sepahvand

Marburg

2016

Engineering Vibroacoustic Analysis

View full text Add to dashboard Cite

An approximation approach for uncertainty quantification using evidence theory

Cited by 183 publications

References 14 publications

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Uncertainties in structural dynamics: overview and comparative analysis of methods

Random and Stochastic Structural–Acoustic Analysis

Contact Info

Product

Resources

About