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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
1 School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China
2 Failure Mechanics & Engineering Disaster Prevention and Mitigation, Key Laboratory of Sichuan Province, Sichuan University, Chengdu, 610065, China
3 Yangzhou Yangjie Electronic Technology Co., Ltd., Yangzhou, 225008, China
4 Sichuan Special Equipment Inspection and Research Institute, Chengdu, 610100, China
5 Food Safety Inspection Technology Center of Administration for Market Regulation of Sichuan Province, Chengdu, 610017, China
* Corresponding Author: Tao Lin. Email:
(This article belongs to this Special Issue: Computer-Aided Structural Integrity and Safety Assessment)

Computer Modeling in Engineering & Sciences 2022, 132(2), 553-568.

Received 10 December 2021; Accepted 13 January 2022; Issue published 15 June 2022


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 solve RBMDO problems. Furthermore, the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO) are proposed. Finally, an engineering example is given to show the application of the GMM-SOMVSA-CO method.


Uncertain factors; reliability-based multidisciplinary design optimization; saddlepoint approximate; gaussian mixture model; collaborative optimization

Cite This Article

Meng, D., Yang, S., Lin, T., Wang, J., Yang, H. et al. (2022). RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation. CMES-Computer Modeling in Engineering & Sciences, 132(2), 553–568.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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