Reliability Estimation and Design with Insufficient Data Based on Possibility Theory

Mourelatos, Zissimos P.; Zhou, Jun

doi:10.2514/1.12044

Cited by 129 publications

(27 citation statements)

References 23 publications

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“…We may induce a compatibility capacity of evidence theory, with possibility theory and probability theory. Briefly we can say that the classical probability theory and the possibility theory are subsets of the evidence theory (Mourelatos and Zhou, 2004). In other words, both of them are complementary or alternative theories, neither of which is a generalization of the other (Klir and Folger, 1988) …”

Section: Compatibility Of Evidence Theory With Possibility Theory Andmentioning

confidence: 99%

“…Thus possibility theory deals with special bodies of evidence, where F is a nested family of subsets of U in each body of evidence. In addition to the well-known fuzzy-set interpretation, possibility can also be interpreted in the framework of evidence theory, as a subset of evidence theory (Mourelatos and Zhou, 2004).…”

Section: Ajeasmentioning

confidence: 99%

“…• Lack of information in input data, small sample size, insufficient information or scarce data (Chen et al, 1999;Mourelatos and Zhou, 2004;Nikolaidis and Haftka, 2001;Huang et al, 2004; • Imprecise data or lack of knowledge Youn and Choi, 2004a;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005b;2006d;Limbourg, 2005;Mourelatos and Zhou, 2005) • Large-scale, complex or costly systems (Zhuang et al, 2000) …”

Section: Ajeasmentioning

confidence: 99%

“…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). Modeling of reliability using a new data fusion rule is proposed by Delmotte and Borne (1998); Sun et al (2008) and Yang et al (2011a); Possibility-based design optimization is studied and developed by (Mourelatos and Zhou, 2004;Youn, 2005;Youn and Choi, 2004a;Youn et al, 2004;Choi et al, 2004;2012b;Zhang et al, 2010b).…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

“…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). Modeling of reliability using a new data fusion rule is proposed by Delmotte and Borne (1998); Sun et al (2008) and Yang et al (2011a); Possibility-based design optimization is studied and developed by (Mourelatos and Zhou, 2004;Youn, 2005;Youn and Choi, 2004a;Youn et al, 2004;Choi et al, 2004;2012b;Zhang et al, 2010b). Fuzzy reliability theory in the context of possibility theory is proposed and developed by (Cai et al, 1991a;1991b;1993;Utkin and Gurov, 1996;Onisawa, 1988;Huang et al, 2004;.…”

Section: General Topics Of Applicationsmentioning

confidence: 99%

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Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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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.

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Section: Compatibility Of Evidence Theory With Possibility Theory Andmentioning

confidence: 99%

Section: Ajeasmentioning

confidence: 99%

Section: Ajeasmentioning

confidence: 99%

Section: General Topics Of Applicationsmentioning

confidence: 99%

Section: General Topics Of Applicationsmentioning

confidence: 99%

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Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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References

2014

System Design and Control Integration for Advanced Manufacturing

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A State‐of‐Art Review on Prediction Model for Fatigue Performance of Welded Joints via Data‐Driven Method

Feng

Zhao

et al. 2023

Adv Eng Mater

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Fatigue fracture of welded joints is an important cause for engineering accidents. Due to the coexistence of so many influencing factors, the current prediction model of fatigue behavior cannot be used for all service conditions. The progress of each module (database establishment, data processing, data augmentation, dimension reduction, and comprehensive consideration of influencing factors) during the process of constructing a prediction model is summarized herein. Specifically, the state‐of‐art prediction models of fatigue strength, fatigue crack growth rate, fatigue life, and fatigue reliability are introduced. Moreover, suggestions for future work are given at the end of each section. Finally, according to the influential prediction methods, the establishment of fatigue performance prediction methods of welded joints via data‐driven method is summarized.

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Reliability Estimation and Design with Insufficient Data Based on Possibility Theory

Cited by 129 publications

References 23 publications

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Possibility and Evidence-Based Reliability Analysis and Design Optimization

References

A State‐of‐Art Review on Prediction Model for Fatigue Performance of Welded Joints via Data‐Driven Method

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