Integration of Reliability- and Possibility-Based Design Optimizations Using Performance Measure Approach

Since deterministic optimum designs obtained without considering uncertainty lead to unreliable designs, it is vital to develop design methods that take account of the input uncertainty. When the input data contain sufficient information to characterize statistical distribution, the design optimization that incorporates the probability method is called a reliability-based design optimization (RBDO). It involves evaluation of probabilistic output performance measures. The enriched performance measure approach (PMA+) has been developed for efficient and robust design optimization process. This is integrated with the enhanced hybrid mean value (HMV+) method for effective evaluation of non-monotone and/or highly nonlinear probabilistic constraints. When sufficient information of input data cannot be obtained due to restrictions of budgets, facilities, human, time, etc., the input statistical distribution is not believable. In this case, the probability method cannot be used for reliability analysis and design optimization. To deal with the situation that input uncertainties have insufficient information, a possibility (or fuzzy set) method should be used for structural analysis. A possibility-based design optimization (PBDO) method is proposed along with a new numerical method, called maximal possibility search (MPS), for fuzzy (or possibility) analysis and employing the performance measure approach (PMA) that improves numerical efficiency and stability in PBDO. The proposed RBDO and PBDO methods are applied to two examples to show their computational features. Also, RBDO and PBDO results are compared for implications of these methods in design optimization.