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Non-Probabilistic Design Optimization with Insufficient Data using Possibility and Evidence Theories

By Zissimos P. Mourelatos and Jun Zhou


Abstract: Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets due to insufficient data or information for modeling the uncertainties. Design decisions are therefore, based on fuzzy information that is vague, imprecise qualitative, linguistic or incomplete. The uncertain information is usually available as intervals with lower and upper limits. In this paper, the possibility and evidence theories are used to account for uncertainty in design with incomplete information. The formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures. The first part of the paper highlights how the possibility theory can be used in design. A computationally efficient and accurate hybrid (global-local) optimization approach is used to calculate the confidence level of “fuzzy ” response combining the advantages of the commonly used vertex and discretization methods. A possibility-based design optimization method is proposed where all design constraints are expressed possibilistically. It is shown that the method gives a conservative solution compared with all conventional reliability-based designs obtained with different probability distributions. Also, a general possibility-based design optimization method is presented which handles a combination of random and possibilistic design variables. The secon

Year: 2013
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