Abstract
A moment method known as the fourth moment method can perform reliability analysis without optimization using the first four statistical moments. Numerical integration is used to calculate the statistical moments, where a moment-based quadrature rule can be used for integration nodes and weights. However, the moment-based quadrature rule has to solve a system of linear equations that can be numerically unstable. Considering this point, an improved moment-based quadrature rule is proposed and is applied to reliability-based design optimization. Finally, the moment-based RBDO is applied to numerical examples with a variety of random variables and target reliability indexes. From the numerical results, the performance of the improved moment-based quadrature rule can be confirmed and several guidelines are given for the moment-based RBDO.
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Ju, B.H., Lee, B.C. Improved moment-based quadrature rule and its application to reliability-based design optimization. J Mech Sci Technol 21, 1162–1171 (2007). https://doi.org/10.1007/BF03179031
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DOI: https://doi.org/10.1007/BF03179031