Unified reliability-based design optimization with probabilistic, uncertain-but-bounded and fuzzy variables

Abstract

Reliability-based design optimization (RBDO) is critical in improving the design objective and guaranteeing the safety level of mechanical and engineering structures. However, a large number of multi-source uncertainties exist in the real-world, and their applications pose significant challenges owing to the lack of unity and generality of the RBDO theory and high performance computational methods. This study proposes a unified reliability-based design optimization (URBDO) method to deal with multi-source uncertainties, in which probabilistic, uncertain-but-bounded, and fuzzy parameters are simultaneously considered. First, a novel URBDO model is proposed by combining the probabilistic, non-probabilistic, and fuzzy theories, and it consists of nested quadruple optimization loops. Second, the single-loop URBDO method is further developed based on the Lagrangian function to ease the unaffordable computational burden, where the probabilistic analysis, non-probabilistic analysis, fuzzy analysis, and deterministic optimization are simultaneously implemented. Third, the directional properties of non-probabilistic and fuzzy computations are disclosed, and the directional chaos single-loop method (DCSLM) and conjugate gradient single-loop method (CGSLM) are constructed based on the chaos control theory and conjugate gradient method. Finally, three numerical examples and three practical engineering examples are tested to validate the effectiveness of the proposed URBDO model and the high performances of the DCSLM and CGSLM.