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  • Open Access

    REVIEW

    Saddlepoint Approximation Method in Reliability Analysis: A Review

    Debiao Meng1,2,*, Yipeng Guo1,2, Yihe Xu3, Shiyuan Yang1,2,*, Yongqiang Guo4, Lidong Pan4, Xinkai Guo2

    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2329-2359, 2024, DOI:10.32604/cmes.2024.047507

    Abstract The escalating need for reliability analysis (RA) and reliability-based design optimization (RBDO) within engineering challenges has prompted the advancement of saddlepoint approximation methods (SAM) tailored for such problems. This article offers a detailed overview of the general SAM and summarizes the method characteristics first. Subsequently, recent enhancements in the SAM theoretical framework are assessed. Notably, the mean value first-order saddlepoint approximation (MVFOSA) bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation (MVSOSA); the latter serves as an auxiliary approach to the former. Their distinction is rooted in the varying expansion orders of the performance function as… More >

  • Open Access

    ARTICLE

    An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

    Yongqiang Guo1,2,*, Zhiyuan Lv3

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 1855-1870, 2023, DOI:10.32604/cmes.2022.022211

    Abstract In uncertainty analysis and reliability-based multidisciplinary design and optimization (RBMDO) of engineering structures, the saddlepoint approximation (SA) method can be utilized to enhance the accuracy and efficiency of reliability evaluation. However, the random variables involved in SA should be easy to handle. Additionally, the corresponding saddlepoint equation should not be complicated. Both of them limit the application of SA for engineering problems. The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments. However, the traditional moment matching method is not very accurate generally. In order to take advantage of… More >

  • Open Access

    ARTICLE

    RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

    Debiao Meng1,2,3, Shiyuan Yang1, Tao Lin4,5,*, Jiapeng Wang1, Hengfei Yang1, Zhiyuan Lv1

    CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.2, pp. 553-568, 2022, DOI:10.32604/cmes.2022.020756

    Abstract Actual engineering systems will be inevitably affected by uncertain factors. Thus, the Reliability-Based Multidisciplinary Design Optimization (RBMDO) has become a hotspot for recent research and application in complex engineering system design. The Second-Order/First-Order Mean-Value Saddlepoint Approximate (SOMVSA/FOMVSA) are two popular reliability analysis strategies that are widely used in RBMDO. However, the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution, which significantly limits its application. In this study, the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation (GMM-SOMVSA) is introduced to tackle above problem. It is integrated with the Collaborative Optimization (CO) method to… More >

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