Reliability Estimation and Design with Insufficient Data Based on Possibility Theory
Reliability Estimation and Design with Insufficient Data Based on Possibility Theory
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DOI：
10.2514/1.12044
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发表时间：
2004-08
期刊：
影响因子：
2.5
通讯作者：
Z. Mourelatos;Jun Zhou-
中科院分区：
文献类型：
--
作者：
Z. Mourelatos;Jun Zhou-
在工程设计周期的早期，由于没有足够的数据或信息对不确定性进行建模，因此难以量化产品的可靠性或对性能目标的符合性。因此，设计决策是基于模糊的，不精确的，定性的，语言的，或不完整的模糊信息。不确定性信息通常以具有下限和上限的区间形式提供。在这项工作中，可能性理论用于评估设计可靠性与不完全信息。可能性理论可以看作是模糊集合论的一个变种。使用模糊测度的理论基础，首先介绍了处理不确定性的正式理论。随后描述了一种计算效率高且精确的混合（全局-局部）优化方法，用于计算模糊响应的置信度。该方法结合了常用的顶点和离散化方法的优点。随后，将可能性理论应用于设计中。提出了一种基于可能性的设计优化方法，其中所有的设计约束都以可能性的方式表示。结果表明，该方法给出了一个保守的解决方案相比，所有传统的基于可靠性的设计得到不同的概率分布。最后，一个通用的基于可能性的设计优化方法，它处理的随机和可能性的设计变量的组合，提出。几个数值例子说明了可能性理论在设计中的应用。
Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets because of 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 work, the possibility theory is used to assess design reliability with incomplete information. The possibility theory can be viewed as a variant of fuzzy set theory. The formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures. A computationally efficient and accurate hybrid (global-local) optimization approach is subsequently described for calculating the confidence level of fuzzy response. The method combines the advantages of the commonly used vertex and discretization methods. Subsequently, the possibility theory is used in design. A possibility-based design optimization method is proposed where all design constraints are expressed in a possibilistic way. It is shown that the method gives a conservative solution compared with all conventional reliability-based designs obtained with different probability distributions. Finally, a general possibility-based design optimization method, which handles a combination of random and possibilistic design variables, is presented. Several numerical examples demonstrate the application of possibility theory in design.