Inverse Possibility Analysis Method for Possibility-Based Design Optimization

Structural analysis and design optimization have recently been extended to the stochastic approach to consider various uncertainties. However, in areas where it is not possible to produce accurate statistical information for input data, the probabilistic method is not appropriate for stochastic structural analysis and design optimization, because improper modeling of uncertainty could cause a greater degree of statistical uncertainty than those of physical uncertainty. For systems with insufficient information for input data, possibility-based (or fuzzy set) methods have recently been introduced in structural analysis and design optimization. Using possibility methods, the extended fuzzy operations are much simpler than of random variables. Possibility-based design optimization will provide more conservative designs than those from probability methods, and will provide a system level of failure possibility automatically. This paper proposes a new formulation of possibility-based design optimization using the performance measure approach. For the inverse possibility analysis, the maximal possibility search method is proposed to improve numerical efficiency and accuracy comparing with the vertex method and the multilevel-cut method. Two mathematical examples, including a nonmonotonic response and a physical example of vehicle side impact, are used to demonstrate the proposed maximal possibility search method and possibility-based design optimization.