Advances in reliability-based design optimization and probability analysis

Deterministic optimum designs are pushed to design constraint boundaries using multidisciplinary design optimization techniques, leaving little or no room for manufacturing and operating tolerances. Consequently, deterministic optimum designs obtained without considering uncertainties in manufacture and operating processes could lead to unreliable designs, which necessitates the Reliability-Based Design Optimization (RBDO) method. RBDO involves the evaluation of probabilistic constraints, which can be executed in two different ways: the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). However, it is noted that RIA shows a slow rate of convergence or even divergence for many applications. To alleviate these difficulties, the Hybrid Mean Value (HMV) method is proposed to evaluate probabilistic constraints more effectively, and PMA using the HMV method develops the advanced RBDO methodology by converting the RBDO problem like a deterministic optimization problem.; However, even with the proposed advanced RBDO methodology, it could not provide an effective methodology to affordably perform RBDO for large-scale multidisciplinary applications. To achieve this objective, a generalized RBDO methodology is developed by integrating the advanced RBDO methodology with the proposed Response Surface Method (RSM), which is composed of the Moving Least Squares (MLS) method and a new Design of Experiments (DOE) suitable for reliability analysis. In addition to response information, if the design sensitivity data is available, it can be incorporated in the MLS method to accurately approximate the reliability-based design sensitivity for RBDO. By taking advantage of PMA, an axial star-selective interaction DOE framework is proposed to properly reproduce the main effects and interactions of design parameters.; The desire to identify, control, and mitigate the effects of system uncertainty underscores the need for an effective probability analysis process. However, it was found that existing probability analysis tools do not perform well in terms of numerical efficiency, accuracy, and/or robustness. These difficulties are resolved by employing the HMV method and the MLS method for more accurate approximation of an MPP locus, which enhance numerical performances in the probability analysis. A proposed probability analysis is proposed, which asymptotically approximates MPP locus by adaptively adding probability levels.