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Reliability-Based Design Optimization (RBDO) is an effective method to handle an optimization problem constrained by reliability performance. In spite of its great benefits, one of the most challenging issues for implementing RBDO is associated with very intensive computational demands of Reliability Analysis (RA). Moreover, an accurate and efficient RA method is indispensible to apply RBDO to practical engineering design problems. Among various RA methods, an enhanced Dimension Reduction (eDR) method is the most popular one due to the high computational efficiency. It is very desirable to obtain an accurate and efficient RA result by using the minimum number of sampling points. But, it is difficult to determine it. That is because it depends on the nonlinearity of a constraint from approximating a model and the degree of uncertainty from integrating a design factor. In this research, eDR method with variable sampling points has been studied and proposed to resolve the early mentioned difficulties. The main idea of the suggested method is to employ a different number of axial sampling points for each random design factor. It is according to the nonlinearity of a constraint and the degree of uncertainty of each random design factor. For each random variable, it begins to use three points first and decides to stop or increase the axial sampling points based upon the proposed criteria in this study. In case of increasing sampling points, it is incremented by one sampling point and ended up five sampling points at most. As it shown in the result, the efficiency of eDR method with variable sampling points for each random variable is superior to the one with fixed sampling points without sacrificing any accuracy. Through the three representative RA problems, it is verified that the proposed RA method generates the result 26.5% more efficiently on average than the conventional eDR method with fixed sampling points. Furthermore, the Performance Measure Approach (PMA) was used to evaluate the performance of RBDO using the new RA method. For the comparison, three mathematical and one engineering RBDO problems were solved by both eDR method with variable sampling points and conventional one with fixed sampling points. Finally, the comparison results clearly demonstrate that RBDO using the suggested RA method is superior to the conventional one in terms of accuracy and efficiency.

This study provides how the Dimension Reduction (DR) method as an efficient technique for reliability analysis can acquire its increased efficiency when it is applied to highly nonlinear problems. In the highly nonlinear engineering systems, 4N+1 (N: number of random variables) sampling is generally recognized to be appropriate. However, there exists uncertainty concerning the standard for judgment of non-linearity of the system as well as possibility of diverse degrees of non-linearity according to each of the random variables. In this regard, this study judged the linearity individually on each random variable after 2N+1 sampling. If high non-linearity appeared, 2 additional sampling was administered on each random variable to apply the DR method. The applications of the proposed sampling to the examples produced the constant results with increased efficiency.

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