American Journal of Engineering and Applied Sciences

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Hong-Zhong Huang, Liping He, Yu Liu, Ning-Cong Xiao, Yan-Feng Li and Zhonglai Wang

DOI : 10.3844/ajeassp.2013.95.136

American Journal of Engineering and Applied Sciences

Volume 6, Issue 1

Pages 95-136


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.


© 2013 Hong-Zhong Huang, Liping He, Yu Liu, Ning-Cong Xiao, Yan-Feng Li and Zhonglai Wang. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.