A credibilistic failure indicator for modeling structural reliability design optimization

Structural reliability design optimization under epistemic uncertainty has attracted the attention of many researchers, which plays a pivotal role both in theory and engineering application. However, many traditional fuzzy reliability indicators are formulated by fuzzy measure without self-duality. For this reason, we reconsider structural system with fuzzy parameters, and a new credibilistic failure indicator (CFI) is presented based on self-dual credibility measure, which provides the exact expression of structural failure degree under fuzzy environment. Then, for the structure with fuzzy trapezoidal parameters, the explicit expressions of the CFI formulations are presented under fuzzy linear limit-state function and nonlinear limit-state function. Furthermore, CFI-based design optimization is formulated to obtain the optimal structural design under the given reliability level. Meanwhile, one theorem on the reliability constraint is provided to facilitate us to obtain the equivalent deterministic constraint of the reliability constraint. Finally, two illustrative examples are performed to demonstrate the efficiency of the proposed CFI formulation and the corresponding computational methods.